Citation
SUPPLY CHAIN MANAGEMENT OF APPLICATION SERVICE PROVIDERS: COORDINATION STRATEGIES AND QUEUING EFFECTS

Material Information

Title:
SUPPLY CHAIN MANAGEMENT OF APPLICATION SERVICE PROVIDERS: COORDINATION STRATEGIES AND QUEUING EFFECTS
Copyright Date:
2008

Subjects

Subjects / Keywords:
Application service providers ( jstor )
Capacity costs ( jstor )
Channel coordination ( jstor )
Coordinate systems ( jstor )
Cost functions ( jstor )
Diseconomies of scale ( jstor )
Market prices ( jstor )
Prices ( jstor )
Supply chain management ( jstor )
Unit costs ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright the author. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
8/8/2004
Resource Identifier:
51573081 ( OCLC )

Downloads

This item is only available as the following downloads:


Full Text

PAGE 1

SUPPLYCHAINMANAGEMENTOFAPPLICATIONSERVICEPROVIDERS: COORDINATIONSTRATEGIESANDQUEUINGEFFECTS By HALUKDEMIRKAN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2002

PAGE 2

Copyright2002 by HalukDemirkan

PAGE 3

Thisthesisisdedicatedtomyfatherandmymotherwhodidanoutstandingjobofraising me.Theyhavesupportedandhelpedmeforallmygoals.

PAGE 4

iv ACKNOWLEDGMENTS Iwouldliketoexpressmygratitudetothemembersofmycommittee,Drs.Hsing KennethCheng,S.SelcukErenguc,AsooJ.Vakharia,HaldunAytug,andJosephP. Geunes,fortheiradviceanddirections.Foremost,Iamdeeplyindebtedtomyadvisors, Dr.ChengandDr.Erengucfortheirguidance,direction,encouragementandcontinuous supportthroughoutmyresearchandeducation.Withoutthissupportandtrustinme,I wouldneverhavebeenabletoreachthispointinmyeducation.Iamalsogratefultomy teachersandprofessors. Iamtrulygratefultomyfamilyandfriendsfortheirsupportandhelp.

PAGE 5

v TABLE OF CONTENTS page ACKNOWLEDGMENTS..............................................................................................iv LIST OF TABLES ........................................................................................................vii LIST OF FIGURES........................................................................................................ix ABSTRACT.................................................................................................................xiv CHAPTER 1 INTRODUCTION ......................................................................................................1 1.1 Application Service Providers.............................................................................1 1.1.1 Overview of the Information Technology Challenges................................1 1.1.2 Brief History of Outsourcing and Application Service Providers ...............2 1.1.3 Application Service Providers Market Landscape......................................4 1.1.4 Analyzing the ASP Business Model ..........................................................4 1.1.5 Bus iness Issues..........................................................................................5 1.2 Organization of this Thesis .................................................................................7 2 RISK AND INFORMATION SHARING OF THE APPLICATION SERVICES SUPPLY CHAIN .......................................................................................................9 2.1 Introduction of the Application Services Supply Chain .......................................9 2.2 Application Service Providers Supply Chain Model..........................................14 2.3 Supply Chain Coordina tion Strate gies ...............................................................18 2.3.1 Scenario 1: Overall Supply Chain Coordination Strategy........................18 2.3.2 Scenario 2: AIP Coordinates the Supply Chain.......................................20 2.3.3 Scenario 3: ASP Coordinates the Supply Chain ......................................22 2.3.4 Scenario 4: Competitive Aligned Coordination Strategy.........................23 2.4 Numerical Explorations for the 1st Model...........................................................25 3 COORDINATION STRATEGIES OF APPLICATION SERVICES SUPPLY CHAIN: THE QUE UING EFFE CT S.......................................................................39 3.1 Introduction of the ASP Model with Queuing Effects .......................................39 3.2 Application Service Providers Supply Chain Model With Queuing Effects.......44 3.2.1 Information Sharing ................................................................................44 3.2.2 Transaction or Job Arrival.......................................................................45

PAGE 6

vi 3.2.3 Application Infrastructure Provider’s Profit Function ..............................46 3.2.4 Application Service Provider’s Profit Function........................................47 3.3 Analysis of Coordination Strategies ..................................................................48 3.3.1 Coordination Strategies When AIP’s Expected Profit Function Is Linear.49 3.3.1.1 Scenario 1i: Supply Chain Coordina tion Stra tegy .......................49 3.3.1.2 Scenario 2i: AIP Coordinates t he Supply C hain..........................51 3.3.2 Coordination Strategies When the AIP’s Expected Profit Function Includes Diseconomies of Scale.............................................................................54 3.3.2.1 Scenario 1j: Supply Chain Coordina tion Stra tegy .......................54 3.3.2.2 Scenario 2j: AIP Coordinates t he Supply C hain..........................56 3.3.2.3 Scenario 3j: ASP Coordinates the Supply Chain.........................58 3.3.2.4 Scenario 4 j: Competitive Aligned Coordination Strategy...........60 3.4 Numerical Explorations ....................................................................................62 3.4.1 Numerical Exploratio ns – Condition 1: AIP’s Expected Profit Function is Linear....................................................................................67 3.4.2 Numerical Exploratio ns – Condition 2: AIP’s Expected Profit Function Includes Diseconomies of Scale................................................75 4 DUOPOLISTIC PRICE AND CAPACITY COMPETITION OF APPLICATION SE RVICE PROVIDE RS WITH THE QUE UING EFFE CT S....................................94 4.1 Introduction of Duopolistic Price and Capacity Competitions ...........................94 4.2 Model of Duopolistic Competition with Influence of Delay Costs.....................98 4.2.1 Price Competition of ASPs...................................................................100 4.2.1.1 Application Service Provider1’s short-run problem...................101 4.2.1.2 Application Service Provider2’s short-run problem...................102 4.2.2 Capacity Competition of ASPs ..............................................................110 4.2. 2.1 Application Service Provider1’s long-run problem....................110 4.2. 2.2 Application Service Provider2’s long-run problem....................111 4.3 Numerical Explorations for Capacity Competition of ASPs ............................113 5 CONCLUSIONS AND DIRECTIONS FOR FUT URE RESEARCH .....................138 APPENDIX A ANALYTICAL PROOF OF CONCAVITITY OF SUPPLY CHAIN PROFIT FUNCTION IN THE RISK AND IN FO RMATION SHARING OF APPLICATION SE RVICES SUPPLY CHAIN ...............................................................................144 B PROOF OF THE PROPOSITIONS FOR THE DUOPOLISTIC PRICE AND CAPACITY COMPETITION OF APPLICATION SERVICE PROVIDERS WITH THE QUE UING EFFE CT S....................................................................................146 LIST OF RE FE RE NCES.............................................................................................150 BIOGRAPHICAL SKETCH.......................................................................................154

PAGE 7

vii LISTOFTABLES Table page 2-1 Baseline parameters for numerical explorations for Model 1...............................28 2-2 Impact of price elasticity, ................................................................................29 2-3 Impact of capacity cost, c ...................................................................................30 2-4 Impact of dis economy of scale, e........................................................................31 2-5 Impact of distribution range, b ............................................................................32 3-6 Summary of notation for Model 2.......................................................................66 3-7 Baseline parameters for numerical explorations for Model 2...............................66 3-8 Impact of delay cost, v (per unit of time per job) when the AIP has a linear cost function .............................................................................................................68 3-9 Impact of capacity c ost, c (per unit of capacity) when the AIP has a linear cost function .............................................................................................................69 3-10 Impact of delay cost, v (per unit of time per job) when the AIP’s cost function includes dis economies of s cale (for Scenario 2.1 and Scenario 2.2)....................76 3-11 Impact of delay cost, v (per unit of time per job) when the AIP’s cost function includes dis economies of s cale (for Scenario 2.3 and Scenario 2.4)....................77 3-12 Impact of capacity cost, c (per unit of capacity) when the AIP’s cost function includes dis economies of s cale (for Scenario 2.1 and Scenario 2.2)....................78 3-13 Impact of capacity cost, c (per unit of capacity) when the AIP’s cost function includes dis economies of s cale (for Scenario 2.3 and Scenario 2.4)....................79 3-14 Impact of diseconomy of scale, e (per unit of capacity) when the AIP’s cost function includes diseconomies of s cale (for Scenario 2.1 and Scenario 2.2)......80 3-15 Impact of diseconomy of scale, e (per unit of capacity) when the AIP’s cost function includes diseconomies of s cale (for Scenario 2.3 and Scenario 2.4)......81 4-16 Proof by contradiction for Lemma 1 .................................................................106

PAGE 8

viii 4-17 Summary of notation for Model 3.....................................................................118 4-18 Baseline parameters for numerical explorations for Model 3.............................118 4-19 Impact of delay cost, v , and capacity when mu1 = 6 < lambda = 7, mu2 =< lambda = 7 (Scenario 1: mu2 is decreasing, v is increas ing) .........................................119 4-20 Impact of delay cost, v, and capacity when mu1 = 10 > lambda = 7, mu2 > lambda = 7 (Scenario 2: mu2 is increas ing, v is increas ing)..........................................120 4-21 Impact of delay cost, v , and capacity when mu1 = 6 < lambda = 7, mu2 >= lambda = 7 (Scenario 3: mu2 is increas ing, v is increas ing).........................................121 4-22. Impact of delay cost, v w hen mu1 = < lambda, mu2 = lambda (Scenario 4: mu1 = 6 < lambda = 7, mu2 = lambda = 7, v is increasing) .........................................122 4-23 Impact of delay cost, v when mu1 > lambda, mu2 > lambda (Scenario 5: mu1 = 10 > lambda = 7, mu2 > lambda = 7, v is increas ing) ............................................122 4-24 Impact of delay cost, v when mu1 < lambda, mu2 > lambda (Scenario 6: mu1 = 6 < lambda = 7, mu2 => lambda = 7, v is increas ing) ...........................................122 4-25 Impact of delay cost, v when mu1 = mu2 < lambda (Scenario 7: mu1 = mu2 < lambda = 7, v is increas ing) .............................................................................123 4-26 Impact of delay cost, v when mu1 = mu2 > lambda (Scenario 8: mu1 = mu2 = 10 > lambda = 7, v is increasing) ..........................................................................123 4-27 Impact of unit capacity cost, b when b1 NE b2, b2 decreasing (Sc enario 1: b1 NE b2, b2 is decreas ing) ........................................................................................132 4-28 Impact of delay cost, v when b1 NE b2, v is increasing (Scenario 2: b1 NE b2, v is increasing) .......................................................................................................132 4-29 Impact of delay cost, v when b1 = b2, v is increasing (Scenario 3: b1 = b2 = 1, v is increasing) .......................................................................................................132

PAGE 9

ix LISTOFFIGURES Figure page 2-1 Components of the Application Service Providers Bus iness Model....................10 2-2 Application Services Supply Chain....................................................................14 2-3 Price-sensitive random demand .........................................................................15 2-4 Impact of price elasticity on overall supply chain...............................................33 2-5 Impact of price elasticity on ASP’s expected profit............................................33 2-6 Impact of price elasticity on AIP’s expected profit.............................................34 2-7 Impact of capacity cost on overall supply chain .................................................34 2-8 Impact of capacity cost on ASP’s expected profit ..............................................35 2-9 Impact of Capacity Cost on AIP’s expected profit .............................................35 2-10 Impact of diseconomy of scale on overall supply chain......................................36 2-11 Impact of diseconomy of scale on ASP’s expected profit...................................36 2-12 Impact of diseconomy of scale on AIP’s expected profit....................................37 2-13 Impact of distribution ra nge on overall supply chain..........................................37 2-14 Impact of distribution range on ASP’s expected profit .......................................38 2-15 Impact of distribution range on AIP’s expected profit........................................38 3-16 Overview of the ASP infrastructure with queuing delays ...................................44 3-17 Impact of delay cost on overall supply chain when the AIP has a linear cost function ............................................................................................................70 3-18 Impact of delay cost on utilization ratio when the AIP has a linear cost function 70 3-19 Impact of delay cost on capacity when the AIP has a linear cost function ..........71

PAGE 10

x 3-20 Impact of delay cost on market price when the AIP has a linear cost function....71 3-21 Impact of delay cost on arrival rate when the AIP has a linear cost function.......72 3-22 Impact of delay cost on expected profit share w hen the AIP has a linear cost function ............................................................................................................72 3-23 Impact of capacity c ost on ove rall supply chain when the AIP has a linear cost function ............................................................................................................73 3-24 Impact of capacity c ost on utilization ratio when the AIP has a linear cost function ............................................................................................................73 3-25 Impact of capacity c ost on e xpected profit share when the AIP has a linear cost function ............................................................................................................74 3-26 Impact of delay cost on overall supply chain when the AIP’s cost function includes diseconomies of scale..........................................................................82 3-27 Impact of delay cost on AIP’s expected profit when the AIP’s cost function includes diseconomies of scale..........................................................................82 3-28 Impact of delay cost on ASP’s expected profit when the AIP’s cost function includes diseconomies of scale..........................................................................83 3-29 Impact of delay cost on utilization ratio when the AIP’s cost function includes diseconomies of scale ........................................................................................83 3-30 Impact of delay cost on capacity when the AIP’s cost function includes diseconomies of scale ........................................................................................84 3-31 Impact of delay cost on market price when the AIP’s cost function includes diseconomies of scale ........................................................................................84 3-32 Impact of delay cost on arrival rate w hen the AIP’s cost function includes diseconomies of scale ........................................................................................85 3-33 Impact of delay cost on AIP’s expected profit share w hen the AIP’s cost function includes dis economies of s cale...........................................................................85 3-34 Impact of delay cost on ASP’s expected profit share when the AIP’s cost function includes dis economies of s cale...........................................................................86 3-35 Impact of capacity cost on overall supply chain when the AIP’s cost function includes dis economies of s cale...........................................................................86 3-36 Impact of capacity c ost on AIP’s expected profit when the AIP’s cost func tion includes dis economies of s cale...........................................................................87

PAGE 11

xi 3-37 Impact of capacity c ost on ASP’s expected profit when the AIP’s cost func tion includes dis economies of s cale...........................................................................87 3-38 Impact of capacity c ost on utilization ratio when the AIP’s cost func tion includes diseconomies of scale ........................................................................................88 3-39 Impact of capacity c ost on AIP’s expected profit share when the AIP’s c ost function includes diseconomies of s cale.............................................................88 3-40 Impact of capacity cost on ASP’s expected profit share when the AIP’s cost function includes diseconomies of s cale.............................................................89 3-41 Impact of diseconomies of scale on overall supply chain when the AIP’s cost function includes diseconomies of s cale.............................................................89 3-42 Impact of diseconomies of scale on AIP’s expected profit w hen the AIP’s cost function includes diseconomies of s cale.............................................................90 3-43 Impact of diseconomies of scale on ASP’s expected profit w hen the AIP’s cost function includes diseconomies of s cale.............................................................90 3-44 Impact of diseconomies of scale on utilization ratio when the AIP’s cost func tion includes dis economies of s cale...........................................................................91 3-45 Impact of diseconomies of scale on capacity when the AIP’s c ost function includes dis economies of s cale...........................................................................91 3-46 Impact of diseconomies of scale on market price when the AIP’s cost function includes dis economies of s cale...........................................................................92 3-47 Impact of diseconomies of scale on AIP’s expected profit share when the AIP’s cost function includes diseconomies of s cale......................................................92 3-48 Impact of diseconomies of scale on ASP’s expected profit share when the AIP’s cost function includes diseconomies of s cale......................................................93 4-49 Overview of the duopolistic competitions of ASPs ............................................98 4-50 Impact of capacity on arrival rate (Scenario 1).................................................124 4-51 Impact of capacity on utilization ratio (Scenario 1)..........................................124 4-52 Impact of capacity on price (Scenario 1)..........................................................125 4-53 Impact of capacity on profit (Scenario 1).........................................................125 4-54 Impact of capacity on arrival rate (Scenario 2).................................................126 4-55 Impact of capacity on utilization ratio (Scenario 2)..........................................126

PAGE 12

xii 4-56 Impact of capacity on price (Scenario 2)..........................................................127 4-57 Impact of capacity on profit (Scenario 2).........................................................127 4-58 Impact of capacity on arrival rate (Scenario 3) ................................................128 4-59 Impact of capacity on utilization ratio (Scenario 3)..........................................128 4-60 Impact of capacity on price (Scenario 3)..........................................................129 4-61 Impact of capacity on profit (Scenario 3).........................................................129 4-62 Impact of unit delay cost on arrival rate (Scenario 4) .......................................130 4-63 Impact of unit delay cost on utilization ratio (Scenario 4) ................................130 4-64 Impact of unit delay cost on price (Scenario 4) ................................................131 4-65 Impact of unit delay cost on profit (Scenario 4) ...............................................131 4-66 Impact of unit capacity cost on arrival rate (Scenario 1)...................................133 4-67 Impact of unit capacity cost on utilization ratio (Scenario 1)............................133 4-68 Impact of unit capacity cost on price (Scenario 1)............................................134 4-69 Impact of unit capacity cost on profit (Scenario 1)...........................................134 4-70 Impact of unit delay cost on capacity (Scenario 1)...........................................135 4-71 Impact of unit delay cost on arrival rate (Scenario 2) .......................................135 4-72 Impact of unit delay cost on utilization ratio (Scenario 2) ................................136 4-73 Impact of unit delay cost on price (Scenario 2) ................................................136 4-74 Impact of unit delay cost on profit (Scenario 2) ...............................................137 4-75 Impact of unit delay cost on capacity (Scenario 2)...........................................137 B-1 Plot of the equilibrium function for given parameters, () 1 f for12 7 ,0 . 1 , 6 , 1 0 v====and1 77 t o= ................................................148 B-2 Plot of the equilibrium function w hen the arrival rate is zero, ()1 00 f =
PAGE 13

xiii B-3 Plot of the first order condition of the equilibrium function in terms of ASP1’s arrival rate,() 1 1 0 df d > for 12 <<1 7, 2, 2, v === 156. o 9 t 9 9 9 = and27.1111 to 10 0 = . .........................................................................................149

PAGE 14

xiv AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy SUPPLYCHAINMANAGEMENTOFAPPLICATIONSERVICEPROVIDERS: COORDINATIONSTRATEGIESANDQUEUINGEFFECTS By HalukDemirkan August2002 Chair:Dr.HsingKennethCheng Cochair:Dr.S.SelcukErenguc Department:DecisionandInformationSciences Inthisresearch,weanalyzeoneoftheInformationTechnologyoutsourcing models;theApplicationServiceProviders(ASP),andreviewanapplicationservices supplychainconsistingofoneApplicationServiceProviderandoneApplication InfrastructureProvider(AIP)thatareoperatingtomeetprice-sensitiverandomdemand. TheAIPsuppliesthecomputercapacitytotheASPthatinturnsellsthevalue-added applicationservicestothemarketbyusingarental-pricingmodel.Thefirstmodel examinesthesupplychainÂ’sperformanceunderdifferentcoordinationstrategies involvingriskandinformationsharingbetweentheASPandtheAIP.Wefindan effectivedecentralizedmechanismtoachievethesamegoalofmaximizingtheoverall supplychainperformance.Absentthiseffectivemechanism,wefindthatitisbetterto lettheplayerclosertothemarketcoordinatethesupplychain.

PAGE 15

xv Then,weextendtheproblemtoanalyzerelationshipsbetweentheASPandthe AIPundertheinfluenceofqueuingdelaysandrelatedcostsinordertomaximizeeach partyÂ’sexpectedprofitinadditiontothoseofthewholesupplychain.Also,potential customersconsideringjoiningtheASPÂ’sservicewilltakeintoaccountthecostcausedby thequeuingdelay,inadditiontothepricechargedbytheASP.Wefindthatthesupply chainprofitismaximizedcomparedtoindividuallydefinedcoordinationstrategieswith theexistenceofqueuingdelays.Underallcoordinationscenarios,thesupplychainÂ’s expectedprofit,utilizationratio,capacityandarrivalratedecreaseasthedelaycost increasesasthemarketpriceincreases. Third,westudytheduopolisticpriceandcapacitycompetitionoftwoASPsunder theinfluenceofqueuingdelaysandrelatedcosts.Assumingallotherfactsbeingequal, thefirmwithhighercapacityprovidesfasterservicewithhigherpriceandreceivesthe largermarketshare.Inthemeantime,thelowcapacityfirmhastheadvantageofbeing abletochargelowerprice.Inthepricecompetitionproblem,surprisingly,thereisno impactofdelaycostonthearrivalrate.Alsowhenthecapacitydecreases,congestion causeshigherserviceprice.Finally,wediscusstheconclusionsofourstudyandprovide directionsforfutureresearch.

PAGE 16

1 CHAPTER1 INTRODUCTION 1.1ApplicationServiceProviders ThischapterpresentsanoverviewoftodayÂ’sinformationtechnologychallenges anddescribestheapplicationserviceprovidersÂ’businessmodelbyintroducingthe variousrolesusedinthefollowingchapters. 1.1.1OverviewoftheInformationTechnologyChallenges IntodayÂ’sincreasinglycompetitivebusinessmarketplace,businessorganizations faceanumberofchallenges.Consumersmostfrequentlyrequestfasterservice,better products,andlowerprices.Someofthemanychallengesforanyorganizationbutmostly fortheInformationTechnologyorganizationarethefollowing:achievingacompetitive advantagethroughapplicationsandnetworks,increasingcostpredictability,rapidly changinginfrastructurerequiringconstanttechnologyupdatesandmaintenance,and maintainingstableInformationTechnology(IT)professionals.Traditionally, organizationsbuymorehardwareandsoftware,hiremorestaffandtrainadditional peopletosolvethesebusinessissuesknowingthatthesearecostlysolutionswithlongterminvestmentsinmaintenance,expensesandstaffing.Manyorganizations increasinglyuseoutsourcingasanalternativemethodtoreducethecostofinternalIT investments.Therearethreetypesofoutsourcinginthecomputerindustry:providing applicationservices,hostingandfull-serviceoutsourcing(PaulakandTerdiman,2000). TheApplicationServiceProvider(ASP)isatypeofoutsourcingthatprovidesaccessto applicationsandrelatedservicestomultiplecustomersacrossanetworkusingarental-

PAGE 17

2 pricingmodel.TherearesomefundamentaldifferencesbetweentheASPsandtheother outsourcingmodels.Full-serviceoutsourcingincludeshousingandmaintenanceofall majorITfunctions(includingthedatacenter,desktop,applicationmanagement, resources,etc.)byanexternalserviceprovider.Applicationhostinginvolvesproviding operationsandhostingservicesonsharedordedicatedserversforamonthlyfeefor customers.TheASPsontheotherhandofferaccesstostandardpackagedapplications ratherthanhostingusers’custom-developedormodifiedsoftware(PaulakandTerdiman, 2000). 1.1.2BriefHistoryofOutsourcingandApplicationServiceProviders Intheearlyyearsofbusinesscomputing,outsourcingwasknownas“time sharing.”Largecorporationshousedexpensiveandverycomplexmainframecomputers, andmanybusinessessharedtheprocessortimefromthesesystems.Whenpersonal computerswereintroduced,demandfortime-sharingdroppedbecauseoffinancial economics,reliabilityandsecurity(McKie,1999).Today’scompetitivebusiness environmentrequiresthecapacityofoff-sitecomputersystemsforadvancedusage. Internet’sandnetworkcomputing’srecentevolutionofspeed,security,highperformance andavailabilityprovideanewfoundation,“rent-an-application,”forapplicationstobe deliveredinalesscostlyandshorterimplementationtimeline.Typically,theASP remotelyhostsandmaintainsanapplicationforitscustomers.Customersrenttheuseof ASPapplicationratherthanlicensing.EmelieRutherford(2000)fromtheCIO OutsourcingResearchCenterdescribestheASPas“companiesthatrentsoftware functionalityovertheInternetoraprivatenetwork”(p.1). ThevaluepropositionofferedbytheASPmodeltoorganizationsisvery attractive.Someoftheadvantagesarelistedhere:

PAGE 18

3 € TheASPgivessmallandmid-levelcompaniesaccesstotheenterprise applicationswithpayonausageinmuchshortertimeframe,ratherthanspending largeamountsofmoneyforup-frontsetupcost(ChengandKoehler,2002). € Itenablesorganizationstofocusonachievingstrategicbusinessobjectives,rather thankeepingtheITinfrastructureup-to-date. € Thisbusinessmodelfreesuptheorganization’sinternalITresourcestospend theirtimefocusingonthecompetitiveadvantageneedsofthecompany,andalso itcompensatesforlackofinternalITresources(PatnayakuniandSeth,2001). € ASPsenableorganizationstokeepupthemostcurrentapplicationsbyproviding fasterupgrades. € Itenablesseamlessaccesstoapplicationsfromremoteofficesandlocations (O’Reilly,2001). € Withaset-upandmonthlyfeemodel,itisamorecompellingvalueproposition thanthe“rentalversusbuy”argument. € Assumingverypowerfulbackupsystems,itiseasytoseethate-BusinessarchitectapplicationsaremuchmorescalableandreliableinASPsthan traditionalmodels. However,therearesomedrawbackstoASPbusinessmodels.Switchingfroman internallymanagedlocal-orwide-areanetworkstopubliclymanagedandaccessible Internet,opensthedoorforslowdownsfromheavyInternettrafficandsecurityconcerns fromnon-permittedaccess(E llinger, 2000).Also,noteveryapplicationisavailablefor Internet-basedaccess.Complexityofintegratingsomeoftheenterpriseapplicationssuch asERPsystemswiththeorganizations’internalplatformscanbeachallenge.Inaddition thelossoforganizationalknowledgeandreducinganorganization’sabilitytoimplement changescanbeasignificantcompromisefromtheorganization(CroftsandSwatman, 2001).Alsoorganizationsworryaboutlosingsystemcontrolandarenotconvincedof systemavailability.

PAGE 19

4 1.1.3ApplicationServiceProvidersMarketLandscape Inrecentyears,therehasbeenagrowinginterestinthefieldofInternetand applicationserviceproviders.Thismarketplaceincludesbusinessfrompersonal applicationsthroughanalyticaldatawarehouseswithvariouslevelsofserviceofferings, includingcoreservice,managementandsupport.Currentlyusershaveaccessto applications,communicationsandinfrastructurecapabilities,enterpriseapplications includingEnterpriseResourcePlanning,CustomerRelationshipManagement,Supply ChainManagement,humanresources,finance,personalapplicationslikeMicrosoft,and e-commerceplatformslikewebsitehosting(Braunstein,1999). 1.1.4AnalyzingtheASPBusinessModel InordertodeliverthebestbreedofASPbusinessapplicationstothemarketover anIPnetwork,theentirevaluechainmustbeseamlesslydesigned.Theindividual componentsofthischainincludethenetworkproviderswhosupportthelogicaland physicalconnectivityservicesincludingISPsandtelcos,theApplicationInfrastructure Provider(i.e.,platformproviderswhoservethehardwareforserverandstorage,in additiontosoftwarefortoolsandinfrastructure);theapplicationservicesproviderwho deliverstherequiredbusinessfunctionality;theoperationsmanagerswhofacilitate management,platformoperationanddeployment;theendservicessuchasconsulting, systemintegrationandcustomizationandmanagementskills;andthedistributors(Maoz, 2000). WhenASPsgrowveryquickly,manydifferentbusinessmodelsemergeunderthe umbrellatermASP.Typicalmodelsarethefollowing(ASPNews,2001;Corio,2000; MacLennan,2000;Maozz,2000;MasonandGrieser,2000;Muse2001):

PAGE 20

5 € EnterpriseASP(EASP)providesenterpriseclasssoftwareapplicationssuchas ERP,CRM,e-procurementandB2Bapplications(e.g.,Oracle,PeopleSoft, Agilera,BlueStartSolutions,Corio,QwestCyber.Solutions,Surebridge.com, Usinternetworking,andSAP). € CollaborativeASP(CASP)providescollaborationapplicationssuchasNotesor MicrosoftExchange. € Full-serviceProvider(FSP)providesfull-servicesystemsintegrationandIT managementservicesinadditiontoASPservice(e.g.,Telecomputing). € PersonalASP(PASP)targetstheconsumerandsmalloffice/homeofficemarket segmentswithfreeapplications.Theymakemoneyfromadvertisements,andthe like. € VerticalASP(VASP)targetsaverticalindustrysuchasfinancialservicesor healthcare(e.g.,PorteraSystems,TriZettoGroup). € BusinessServiceProvider(BSP)providescompletebusinessservices,including softwareapplicationsandbusinesspersonnel(e.g.,DigitalRiver,Salesforce.com, andWebEx). € ASPPortalprovidesasinglepointofaccesstomultipleASPssuchas consolidatedbillingandcustomerservice(e.g.,Salesforce.com). € NetworkServiceProvider(NSP)providesnetworkaccess(e.g.,Qwest). € ApplicationInfrastructureProvider(AIP)providesanyinfrastructurebackend needsforASPssuchashardware,software,network,hosting(e.g.,Digex, Hewlett-Packard,IBM,SunMicrosystems,andiPlanet). € IndependentSoftwareVendorASP(ISVASP)publishestheirsoftware(e.g., Abridean,CitrixSystems,ComputerAssociates,ProgressSoftware,Xevo). € ManagementServiceProvider(MSP)providesperformancemonitoring, reporting,performanceloadtesting,desktopmanagement,andservicelevel tracking(e.g.,AndersonConsulting). 1.1.5BusinessIssues GiventhebenefitsoftheASPbusinessmodel,anumberofchallengesexist.That maynotberesolvedbytraditionaloperationalmanagementtechniques(suchasdecision trees,activity-basedcostingetc.).ThefirstchallengeishowtocoordinatetheASP playersincludinghardware,software,network,application,service,andoperation

PAGE 21

6 vendorsanddistributorstoprovideawholesolution(InternationalDataCorporation, 1999).ThesearethebuildingblocksoftheASPSupplyChain.Supplychain managementisoneofthetechniquesthatisusedinthefieldofproductionmanagement formanyyears.Asupplychainisanetworkoforganizationsandactivitiesthatwork togethertoprovideaservicewithvaluetotheconsumer(Kumaretal.,2000). Second,asknownfrompaststudiesandindustryimplementationsincluding operationandinformationmanagement,thevaluepropositiongrowsincrementallywhen anumberofapplicationsarebundledtogether.Integrationofsuchasolutiontoinclude thefrontandbackoffice(encompassingproducts,services,integrationandsupport)is anotherbigchallenge.Third,theownershipofthecustomerisanotherimportanttopic fortheenterprisesoftwarevendorandtheASPinsuchacrossdependentenvironment. AdoptionoftheASPbytheorganizationsisanotherconcern.Patnayakunietal. (2001)reviewedthefactorsthataffectadoptionofanASPbusinessmodelby organizations.Theyshowedthatcostsavings,accessibility,reliabilityandspeedof deliveryeffecttheadoptionofASPapplicationssignificantly.Traditionally,most organizationsdonotliketochangethewaytheydobusiness.Movingfromanin-house ITenvironmenttoarent-an-applicationstructureisaculturechangeformanypeople. AnotherchallengeoftheASPmodelistofindthepricingstructuresbetween manycross-dependentparties.SomeofthesepartiesincludeASPpureplayslikeUSI, Corio,softwarevendorslikeSAP,PeopleSoft,andhardwarevendorslikeHP. OutsourcinglikeEDSchargesforthevariouscomponentsdifferently(Davison,2000). EvenmostoftheASPschargefortheserviceperuser,perapplicationandpertime usage,whichmayincludethecostofsoftwarelicense,hardwarepurchase,integration

PAGE 22

7 andservicefeeoverthecontractlife.SomeASPsachargeset-upfeebasedonthe applicationtype(Wendland,1999).Thereismuchconfusion,inconsistencyandworryin themarketregardinghowtopriceanASPservicebecauseofcomplexproduct positioningandcoststructures,andimmaturemarket. Intheirdecisionprocess,consumersmostlyreviewthereliability,availability, scalabilityandaffordabilitystructureofASPs.Lastly,definingtheinitialcapacityofthe system,whichrequiresalargeamountofup-frontinvestmentisanotherimportant questionfortheASPs.Especiallybecauseofsignificantlylowsearchcostcreatedbythe Internet,thewaitingtimeisoneofthemostimportantaspectsofconsumersÂ’usage patterns. Pricingandservicequalitythatincludesspeed,reliabilityandsecurityisthemost criticalfactorindeterminingmarketsuccessorfailureforanyASP.Therefore,thegoal ofthisstudyistodefinetheframeworkofanASPbusinessmodeltoanalyzethepricing andrelationshipstructureoftwomajorplayersofASPbusiness,consistingofone ApplicationServiceProvider(ASP)andoneApplicationInfrastructureProvider(AIP). Basicallyinthisstudy,weanalyzethepartoftheASPsupplychain.ASPNews.com describesAIPsasatypeofbackendinfrastructuresupport(Bernard,2000). 1.2OrganizationofthisThesis Theremainderofthisthesisisstructuredasfollows.Chapter2discussesan applicationservicessupplychainconsistingofoneApplicationServiceProvider(ASP) andoneApplicationInfrastructureProvider(AIP).TheAIPsuppliesthecomputer capacitytotheASP,thatinturnsellsthevalue-addedapplicationservicestothemarket. Themarketischaracterizedbyaprice-sensitiverandomdemand.TheASPÂ’sobjectiveis todeterminetheoptimalpriceofitsservicetothemarketandtheoptimalcapacityto

PAGE 23

8 purchasefromtheAIP.TheAIPÂ’sgoal,ontheotherhand,istomaximizeitsprofitfrom sellingthecapacitytotheASP.Chapter3examinessupplychainperformanceunder differentcoordinationstrategiesandqueuingeffects,involvinginformationsharing betweentheASPandtheAIP.Chapter4studiestheduopolisticpriceandcapacity competitionofASPsundertheinfluenceofqueuingdelaysandrelatedcosts.Consider EnterpriseResourcePlanning(ERP)market,whichconsistsoftwoserviceproviderswho renttheircomputercapacitiestothecustomers.Bothserviceprovidersneedtodecide howmuchcapacitytheyneedandwhatpricetochargeinordertohavealargermarket shareandmakeahigherprofit.Finally,thelastsectionsummarizesthesestudiesand givesdirectionsforfutureresearch.

PAGE 24

9 CHAPTER2 RISKANDINFORMATIONSHARINGOFTHEAPPLICATIONSERVICES SUPPLYCHAIN 2.1IntroductionoftheApplicationServicesSupplyChain Untilrecently,theonlywaytoreapthebenefitsofanenterpriseresourceplanning (ERP)systemistomakesubstantialfinancialinvestmentsinERPsoftware,servers, networks,andothercomputingresources,renderingitbeyondthereachofsmalland medium-sizedcompanies.Theneedsofthemiddle-marketbusinessestablishmentsfor cost-effectiveaccesstotheERPsoftwareandtheinexpensiveandubiquitousInternetbasedcommunicationnetworksheraldedthearrivalofApplicationServiceProviders (ASP)inearly1999. Figure 2 -1 shows various segments of the ASP bu siness model. The emerg ence ofApplicationServiceProvidersalsosignifiesanewshiftofinformationtechnology evolution.AccordingtoarecentreportbyWainewright(1999), Thepackagingofapplicationservicesfordeliverythroughonlinerental computingmarksashiftinevolutionofInformationTechnology,more significantthantheadventofthePC.Itwillradicallychangethestatus quoandbecometheengineofanew,networkedeconomy.(p.1) InareportbyDeloitteResearch,itisestimatedthatthetotalU.S.ASPmarket willbe$48.5billionby2003(Roddy,1999).ApplicationServiceProvidersIndustry Consortium(1999)describestheASPthisway: ApplicationServiceProviders(ASPs)deliverandmanageapplications andcomputerservicesfromremotedatacenterstomultipleusersviathe Internetoraprivatenetwork.Obtainingtheseapplicationsfromanoutside supplierisacost-effectivesolutiontothedemandsofsystemsownership:

PAGE 25

10 up-frontcapitalexpenses,implementationchallenges,andacontinuing needformaintenance,upgradesandcustomization.(p.1) IntheupstreamoftheASPvaluechainistheApplicationInfrastructureProviders (AIP).ASPNews.comdescribestheAIPsas“thecompaniesthatprovideany infrastructurebackendneedsforASPssuchashardware,software,network,hosting, etc.”(Bernard,2000,p.1). Figure2-1ComponentsoftheApplicationServiceProvidersBusinessModel Inthisthesis,weanalyzethesupplychainconsistingofoneApplicationService Provider(ASP)andoneApplicationInfrastructureProvider(AIP).TheASPpurchases computercapacityfromtheAIPandsellsthecapacitywithvalue-addedservicessuchas ERPsoftwareaccesstothemarket.Themarketischaracterizedbyaprice-sensitive randomdemand.TheASP’sobjectiveistooptimizeitsexpectedprofitbydecidinghow muchcapacitytoorderfromtheAIPandhowmuchtochargeitsservicestothemarket. Meanwhile,theAIPseekstomaximizeitsexpectedprofitbysettinganoptimalpriceof Customers ApplicationService Providers MarketingandSales DataCenterHostingServices Applications Integration Support NetworkServicesASPSolution Distributors,Resellers HardwareVendors Server Network Storage OtherSoftwareVendors Tools Infrastructure NetworkProviders ISPs Telcos Hosting ServiceFirms SystemIntegrators Consultants Outsourcers ApplicationVendorsApplicationInfrastructure

PAGE 26

11 thecomputercapacityitsellstotheASP.Weexaminefourdifferentsupplychain coordinationscenariosinvolvingvariousmechanismsofriskandinformationsharing betweentheASPandtheAIP.Severalimportantmanagerialinsightsarederivedand reportedhere. SupplyChainManagement(SCM),definedasthe“managementofmaterialand informationflowsbothinandbetweenfacilities,suchasvendors,manufacturingand assemblyplantsanddistributioncenters…”(ThomasandGriffin,1996,p.1),hasbeena veryactiveresearcharea.Erengucetal.(1999)reviewedtheeffectivemanagementof operationsusingSCM.Theysuggestedthatafirm’scompetitivepositionandthenature oftherelationshipamongSCMparticipantsplayasignificantrole.Theyalsoexplain whythedeterminationofcontractualagreementsbetweenthechannelmembersandthe incentivestructuresforinformationsharingshouldbefurtherresearched. Recentliteratureonsupplychainmanagementisdevotedtostudyingcoordination strategiesthathelpimproveboththerelationshipbetweenthemanufacturerandthe distributorandtheoverallsupplychain’sperformance.“Traditionalmechanismsto optimizetheoverallsupplychannelperformanceincludeverticalorhorizontal integration,supplychainpartnershipssuchasvendormanagedreplenishments,contracts specifyingdecisionrulesforallchannelmembers,andprofit-sharingschemes”(Chenet al.,2001,p.693).Thepreferredcoordinationmechanismistheonetoachievesystem wideperformanceobjectivethroughdecentralizedsupplychaincostandreward structure.Adecentralizedcoordinationmechanismisconsidered“perfect,”ifitresultsin thesamesupplychainprofitsasthoseunderacentralizedsystem.

PAGE 27

12 Cachon(1998)showedthatnocompetitivestrategybetweenindependentsupply chainagentsachievestheoptimaloverallsupplychainprofit.Whenallagentscooperate tomaximizetheoverallsupplychainprofitaswellaseachparty’sprofit,anumberof coordinationstrategiescanbeimplemented.Forexample,buy-backandquantity discountstomanagethetransferofpaymentsbetweenpartiesaretwoalternatives. Absentbuy-backandquantitydiscountsinthispaper,wefinda“perfect”competitive alignedcoordinationmechanismthatmaximizestheoverallsupplychainprofit.Inthis coordinationstrategy,theASPandtheAIPindividuallyoptimizetheirownprofit functionsandthennegotiateamutuallyagreeablepolicy.Thispolicyresultsinthesame expectedsupplychainprofitasifthewholesupplychainiscoordinatedbyacentral planner. Themarketingliteratureonsupplychaincoordinationfocusesonpricing decisionswithoutinventoryreplenishmentconsiderations,e.g.JeulandandShugan (1983)whereasimplequantitydiscountinduces“perfect”coordination.Moorthy(1987) foundthatthesameperfectcoordinationcanbeachievedbyatwo-parttariff.Ingeneand Parry(1995)extendedtheresultstoamulti-retailersetting.Ontheotherhand,the operationsliterature“hasuntilrecentlybeenconfinedtoreplenishmentdecisions assumingthatalldemandprocessesareexogenouslygiven”(Cheneta.,2001,p.695). Weng(1995)andWeng(1999)representedonesofthefirstattemptstocombinethe aforementionedmarketingandoperationsstreamsofresearch.Chenetal.’s(1995) modeltoallowforanarbitrarynumberofnonidenticalretailers. OurmodelissimilarinveintotheonestudiedinWeng(1999).However, Weng’s(1999)modeldoesnotexplicitlyconsidertheunder-capacitycost.Instead,

PAGE 28

13 Weng(1999)firstspecifiedasupplychainservicelevelrequirement.Thisservicelevel requirementandtheorder/productionquantitywillinturndeterminethedistributor’sunit saleprice.WedepartfromtheWeng(1999)modelbyexplicitlytakingintoaccountthe under-capacitycostandbyallowingthepricetobecomeakeydecisionvariableforthe ASP.Themajorcontributionsofthispaperincludethesimultaneousdeterminationof priceandquantityfortheASP(thedistributor)withauniqueapproachtomodelingprice sensitiverandomdemand.Whentheunderlyingdistributionofthepricesensitive randomdemandisuniform,weareabletoderivesomeinterestinganalyticalresults.For example,theASPalwaysordersthecapacityuptothemaximumlimitofthemarket demand,iftheASPdoesnotbeartheriskofover-andunder-capacitycosts.Thehigher theAIPchargestheASPperunitcapacity,thehigherthepricetheASPwillchargethe market.TheASPsimplypassesthecapacitycosttothemarket.Furthermanagerial insightsarealsoderivedfromextensivenumericalexplorationwheretheresultsindicate thatthedecentralized“competitivealigned”mechanismachievesthesamesupplychain performanceasacentralizedsystem.Wealsoshowtheuniqueexistenceofthis decentralizedmechanismanalytically.Severalinsightsnotreportedinpriorliteratureare discussedintheNumericalExplorationsection. Therestofthischapterisstructuredasfollows.WepresenttheASPsupplychain modelinSection2.2.Fourmajorsupplychaincoordinationstrategiesaredescribedin Section2.3.Section2.4reportstheinsightsderivedfromnumericalexplorations,suchas theimpactofvariousparametersontheperformanceofthesupplychain.Theresults showseveralimportantandusefulmanagerialimplicationsfromourmodel.Chapter5of thisresearchprovidesconcludingremarksanddescribesfutureresearch.

PAGE 29

14 2.2ApplicationServiceProvidersSupplyChainModel Toprovideapplicationservicesforitsclients,theApplicationServiceProvider (ASP)acquiresacomputercapacity Q fromtheApplicationInfrastructureProvider(AIP) whocharges w perunitofcapacity.TheASPsellsitsvalue-addedservicetothemarket atprice p perunitofcapacity.TheASPfacesaprice-sensitiverandommarketdemand, x ,foritsservicecharacterizedbytheprobabilitydistribution () Xfxp .Althoughthe actualdemand x isarandomvariable,theexpectedmarketdemandfortheASP’sservice isaffectedbytheprice, p ,thatitchargesandisdescribedby () xpdp =,(2.1) where ,0,and/ 0. ddp>Figure 2-2 shows the application services supplychainmodel. Figure2-2ApplicationServicesSupplyChain InourASPsupplychainmodel,theprice-sensitiverandomdemandfollowsa uniformdistributionovertherange [(),()] xpbxpb +acrosstimeperiodsforaprofit, maximizing the players selling nonstorable product as shown in by Figure 2-3 (Skiera andSpann,1999).Adifferentpricingwillentailadifferentexpecteddemand () x pas describedinEq.(2.1),resultinginadistributionshiftingtotheleftortotheright.One mightconsiderusingaNormaldistributiontodescribetheprice-sensitiverandom Serviceat price p Market ASP Capacity Q Random demand x w perunitof capacity AIP

PAGE 30

15 demand.TheNormaldistributionisnotsuitableinthiscontext,asitslefttailwillextend intotheunrealisticnegativedemandregion. Figure2-3Price-sensitiverandomdemand Facingaprice-sensitiverandomdemanddescribedbytheprobabilitydistribution () Xfxp ,theApplicationServiceProvider’s(ASP)expectedprofit,excludingtheoverandunder-capacitycosts,equals () () (,)[()](/)[()](/) Qxpb XX xpbQ A PpQpwxfxpdxpwQfxpd x + Š=Š+Š.(2.2) ThefirstterminEq.(2.2)representstheexpectedprofitwhentheactualdemand isbelowthecapacity Q orderedfromtheAIP,whilethesecondtermdescribesthe expectedprofitiftheactualdemandexceeds Q .Theover-andunder-capacitycosts representtheriskduetouncertaintyofthemarketdemandandwillbedefinedshortly. Thisriskplaysanimportantroleinvarioussupplychaincoordinationmechanisms discussedinthenextsection.TheuniformdistributiondescribedinFigure2-3isusedfor allsubsequentexpositions.Aftersomealgebra,theASP’sexpectedprofitinEq.(2.2) undertheuniformdistributionbecomes 22 ()()(())()(()) (,) 424 p wQpwxpbQpwxpb APpQ b bb ŠŠ+ŠŠ =Š+Š .(2.3)

PAGE 31

16 TherevenueforApplicationInfrastructureProvider(AIP)equalsthecomputer capacityorderedfromtheASP, Q ,multipliedbytheunitcapacityprice, w .Thecost structureofAIPhastwocomponentsconsistingofperunitcostofprovidingthecapacity describedbytheparameter c ,andadiseconomyofscalecostparameter, e, relatedtothe managementofinfrastructure.Theparameter c reflectstheconstanteconomyofscalein computingpower(Mendelson,1987).Thediseconomyofscaleininfrastructure managementresultsfromincreasingcostsofcapacityanduseraccessmanagement (Cotton,1975;Selwyn,1970)andrisingcomplexityofthebusinessmodel(Rubens, 2001).Hence,theAIP’sprofitfunctionequals 2 () H PQwQcQeQ =ŠŠ .(2.4) TheASP’sobjectiveistomaximizeitsexpectedprofitbydecidinghowmuch capacity( Q )tobuyfromtheAIPandwhatprice( p )tochargetothemarket.TheAIPis concernedwithsettinganappropriateperunitcapacityprice( w )totheASPinorderto maximizeitsprofit. Becauseoftherandomnatureofmarketdemand,costsassociatedwithordering toomuchcapacity(over-capacitycost)andorderingtoolittle(under-capacitycost)will arise.Wedefinetheover-capacitycost, (,) OpQ ,andunder-capacitycost, (,) UpQ ,as follows[] () ( ,)()()(/)Q X xpb O pQwrQxfxpd x Š=ŠŠ,(2.5) and () (,)()(/) xpb X Q U pQkxQfxpd x +=Š,(2.6)

PAGE 32

17 wheretheparameter r representsthesalvagevalueofunusedcapacity,andtheparameter k isthe“opportunitycost”oflostsalesduetoinsufficientcapacity.Fortheuniform distributionunderconsiderationshowninFigure2-3,Eq.(2.5)and(2.6)become 22 2 (()) (,)(()) 222 w rQxpb OpQQQxpb bŠŠ =ŠŠŠ+ ,(2.7) and 22 (()) (,)(()) 222 k Qxpb UpQQxpb b+ =Š++ .(2.8) Amajorpurposeofthisthesisistoexaminevariouscoordinationstrategiesinthis supplychainintermsofriskandinformationsharingbetweentheASPandtheAIP. Whenoneparty“coordinates”thesupplychain,itbearstheover-andunder-capacity costswhiletakingintoaccountthepricingandcapacitydecisionruledisclosedbythe otherpartner. TheASPhasbetterinformationregardingthebehaviorofthemarketastheASP isclosertothemarketinthesupplychain.TheASPmaychoosetodisclosetotheAIP theinformationregardingboththemarketandhowitwouldsettheprice p .Inthiscase, theAIPisinchargeofcoordinatingthewholesupplychainandbearstheriskofoverandunder-capacitycostsdescribedinEqs.(2.7)and(2.8).Alternatively,theASPmay approachtheAIPforaquoteofprice-quantityschedule(i.e., w asafunctionof Q )and coordinatesthesupplychainbybearingtheover-andunder-capacityrisk.Thefollowing sectiondiscussesfourprominentmechanismsofcoordinatingthesupplychain. SeveralobservationsaboutourASPsupplychainmodelareinorder.First,the ASP’scapacityacquisitionproblemisframedasasingle-perioddecisionsince customers’contractswithASParelong-terminnature,typicallylastingfiveyears.

PAGE 33

18 Second,ourmodelfocusesonthoseASPsspecializinginasingleapplication.For example,eOnlineoffersservicesaroundSAP’sR/3ERPproducts,andNetAbacus providesonlyonlinepurchasingsolutions.Third,thecomputercapacityboughtandsold bytheASPinourmodelisanaggregatemeasureoftheprocessingpowerdesiredbythe customers.AcommonmeasureofsuchcomputercapacityisMIPS(millioninstructions persecond).ThisaggregatemeasureofcomputercapacityinMIPSisalsothebasisof contractsbetweentheASPanditscustomers.TheASPisrequiredbyitscustomersto provideaspecificcapacity(say,10MIPS)withcompleteprotectionofvarioussystem resourcestorunacertainapplication.TheASPmeetsthisrequirementbyprovidinga “virtualmachine”havingthedesiredcapacitythroughpartitionsbyoperatingsystems, seeSilberschatzet.al(1991).2.3SupplyChainCoordinationStrategiesInthissection,weconsiderfourcoordinationstrategiesincluding(1)overall supplychaincoordinationstrategy,(2)AIPcoordinatesthesupplychain,(3)ASP coordinatesthesupplychain,and(4)thecompetitivealignedstrategyasfollows.2.3.1Scenario1:OverallSupplyChainCoordinationStrategyInthisscenario,asinglefirm(oracentralplanner)playstheroleofboththeAIP andtheASP.Or,theAIPandtheASPformajointventureandachievethegoalof optimizingthesupplychainasawhole.Thewholesupplychain’sexpectedprofitisthe sumoftheexpectedprofitfunctionsoftheAIPandtheASPminustheexpectedoverandunder-capacitycostsasfollows.Thisscenarioisatypicalprofitmaximization newsboyproblem(SilverandPeterson,1975).1 (,)(,)()(,)(,) S PpQAPpQHPQOpQUpQ =+ŠŠ ,(2.9)

PAGE 34

19 where (,) APpQ , (,) HPpQ , (,) OpQ and, (,) UpQ aredefinedinEqs.(2.3),(2.4),(2.7) and(2.8).Usingtheuniformdistributionofprice-sensitiverandomdemandandafter somealgebra,onehas () 2 1 22 ( )()2() 4 (,) 42 ()()() . 44 Q pkdpbbcrdpb pberk SPpQQ bb rpdpbkdpb bb +Š+ŠŠŠŠ ŠŠ+Š=+ ŠŠŠŠ+ +Š(2.10) WhenthepriceofASPserviceisgreaterthatthesalvagevalueofunusedcapacity (p>r) ,itcanbeeasilyshownthattheobjectivefunctionoftheSupplyChainisstrictly concave,therebyensuringtheexistenceofauniqueoptimalsolution.Pleaseseethe AppendixAfordetails. Theprice w perunitofcapacitychargedtotheASPbytheAIPdropsoutinEq. (2.10).Inthiscase,theprice w servestheroleofinternaltransferpriceandhasnoeffect ontheoverallsupplychain’sprofit.Apparently,thewholesupplychainwillachieveits maximumexpectedprofitunderthisscenarioandthisvaluewillbeusedasthe benchmarktocomparewithothercoordinationstrategies. Tofindtheoptimalsupplychainprofit,firstorderconditions require 1(,) 0 dSPpQ dQ = and 1(,) 0 dSPpQ dp = .Aftersomealgebra,firstorderconditions leadto 222()()() 20 4 44222 pQrQkQpdpbrdpbkdpb eQc b bbbbbŠŠ+ŠŠŠ+ Š+Š+ŠŠ+=, and 2 2()()()() (())0. 42224 QQprdpbkdpbdpb dpbpkr bbbbb ŠŠŠŠŠ+ŠŠ +Š+Š+Š++Š=

PAGE 35

20 Close-formsolutionsofoptimal * p and * Q aredifficult,ifnotimpossible,toderive. Thedifficultyofderivingaclosed-formsolutionof p* and Q* isillustratedasfollows. FromthefirstequationofF.O.C., Q canbeexpressedasanexpressioninvolving quadratictermsof p inthenumeratorandlineartermsofpinthedenominator.When thisexpressionof p issubstitutedintothesecondequationofF.O.C.,thequadraticterm of Q andcrossmultiplicationof p and Q ofthesecondequationfurthercomplicatesthe possibilityofaclosed-formsolution.Mathematicalpackage,e.g.,Maple6,generates overlymessyandnon-meaningfulsolutionsof * p and * Q .Inthenextsection,numerical solutionsofoptimal * p and * Q areobtainedforfurtherinsights.2.3.2Scenario2:AIPCoordinatestheSupplyChainInthiscoordinationstrategy,theprice-sensitiverandomdemandinformationand theASP’spricingandorderquantitydecisionsaredisclosedtothecomputercapacity provider,AIP.TheAIPcoordinatesthesupplychainandbearstheriskofover-and under-capacitycosts.Underthisscenario,theASPtakesthepurchasecostofperunit computercapacity w asgivenandoptimizesitsexpectedprofitdescribedbyEq.(2.3).Proposition2.1.WhenAIPcoordinatesthesupplychainbytakingtheriskof over-andunder-capacitycosts,theASPwillorderthemaximumlimitofthemarket demand, () xpb +,fromtheAIP,andchargestheprice 22 dw +tothemarket.Proof.Let2 (,) A PpQ betheexpectedprofitfortheASPwherethesubscript2 denotesScenario2.Then, 22 2 ()()(())()(()) (,) 424 p wQpwxpbQpwxpb APpQ bbb ŠŠ+ŠŠ =Š+Š .(2.11) Aftersomealgebra,firstorderconditionsleadto

PAGE 36

21 * 2 22 dw p=+and * 2 ( ) 2 dw Q dbdpbxp b + =Š+=Š+=+.Q.E.D. WhentheASPdoesnotbeartheriskofover-andunder-capacitycosts,italways ordersthecapacityuptothemaximumlimitofthemarketdemand.ThehighertheAIP chargestheASPperunitcapacity( w ),thehigherthepricetheASPwillchargethe market.TheASPsimplypassesthecapacitycosttothemarket. UnderScenario2wheretheAIPcoordinatesthesupplychain,thecapacitythe ASPwillorderfromtheAIP( * 2 Q )andthepricetheASPwillchargetothemarket( * 2 p ) willbecommunicatedtotheAIP.Usingthisinformation,theAIPdeterminesthe optimalperunitcapacityprice * 2 w thatmaximizesitsprofitbyconsideringboththeoverandunder-capacitycostsasfollows. ***** 222222 max()()(,)(,) w H PwHPQOpQUpQ =ŠŠ (2.12) Noticethat * 2 p and * 2 Q derivedfromProposition2.1arefunctionsof w .When theyaresubstitutedintoEqs.(2.4),(2.7)and(2.8), * **** 2 2222 ()(,)(,) H PQOpQUpQ ŠŠ becomes2 () H Pw ,afunctionof w .ItshouldbeapparentthattheAIPonlyneedstobe concernedwiththeover-capacitycostwhentheASPordersthemaximumpossible capacitythemarketwouldconsume. TheobjectivefunctionoftheAIP,2 () H Pw ,hasincorporatedtheinformation disclosedfromtheASP.Theoptimalperunitcapacityprice, * 2 w ,theAIPshouldcharge theASPwhentheAIPiscoordinatingthesupplychainisspecifiedbyProposition2.2.Proposition2.2.WhentheAIPiscoordinatingthesupplychain,theoptimalper unitcapacitypricetheAIPshouldchargetheASPequals * 2 22 2 dcedbe w e +++ = +.

PAGE 37

22Proof.Theoptimalperunitcapacityprice * 2 w isderivedbysubstituting * 2 p and * 2 Q fromProposition2.1intoEq.(2.12),theAIP’sobjectivefunction,andinvokingthe firstordercondition.WealsonoticethatAIP’sunitpriceincreasesasthezero-price demand, d ,rangeparameterofuniformdistribution, b, andperunitcapacitycost, c , increases. ThetotalsupplychainprofitunderScenario2wheretheAIPcoordinatesthe supplychainisthusgivenby * *** 2 22222 ()(,) S PHPwAPpQ =+ .(2.13)2.3.3Scenario3:ASPCoordinatestheSupplyChainInthiscoordinationstrategy,theASPdoesnotcommunicateanymarketdemand informationanditspricingdecisionswiththecomputercapacityprovider,theAIP. Instead,theASPapproachestheAIPforaquoteofprice-quantityscheduleand coordinatesthesupplychaindecisions.TheASPbearstheriskofover-andundercapacitycostsofthesupplychain. WhenapproachedbytheASP,theAIPderivestheprice-quantityscheduleby findingtheoptimalquantitythatmaximizesitsprofitfunctiondescribedbyEq.(2.4). FirstorderconditionofEq.(2.4)leadsto () 2 wc Q e Š =.Hence,theAIPwillannouncethe followingprice-quantityscheduletotheASP. 2 wceQ =+(2.14) SincetheASPnowcoordinatesthesupplychain,itincludestheover-andundercapacitycostsinitsobjectivefunctionasfollows.3 (,)(,)(,)(,) A PpQAPpQOpQUpQ =ŠŠ ,(2.15)

PAGE 38

23 wherethethreetermsontheright-handsidearefromEqs.(2.3),(2.7)and(2.8).The ASPthensubstitutestheprice-quantityscheduleofEq.(2.14)intotheobjectivefunction todeterminetheoptimalpriceandquantity.Aftersomealgebra,firstorderconditions requirethat 3(,)222 4() 4442 ()()0 22 dAPpQpQrQQkp e Qdpb c dQbbbb rk dpbdpb b b =ŠŠ+Š+Š+Š ŠŠŠ+Š+= (2.16) and 2 3 2(,) (())()() 422 () ()0 24 dAPpQ Q Qdpbpkrdpbpr dpbbb kdpb dpb bb Š+Š+ŠŠŠŠ =Š++ ŠŠ +Š+Š= .(2.17) Let * 3 p and * 3 Q aretheoptimalpriceandquantityfortheASPderivedfromEqs. (2.16)and(2.17).Define * * 3 33 (,) APpQ and * 3 3 () HPQ astheoptimalprofitsfortheASP andtheAIPrespectivelyunderScenario3.SubstitutingEq.(2.14)intoEq.(2.4),onehas 2 * * 3 33() H PQeQ =.(2.18) Hence,thetotalsupplychainprofitinthisscenarioequals * **** 3 3333333 (,)(,)() SPpQAPpQHPQ =+. Consequently,theexpectedsharesoftheASP’sandtheAIP’sprofitswithrespect tothewholesupplychainare * * 3 33 * * 3 33 (,) (,) A PpQ S PpQ and * 33 * * 3 33 () (,) HPQ SPpQ .2.3.4Scenario4:CompetitiveAlignedCoordinationStrategy–ASPBearstheRiskInthisscenario,boththeASPandtheAIPdeterminetheirownoptimalpolicies individually.Then,theycoordinatetheirdecisionstoreachamutuallyagreeablepolicy.

PAGE 39

24 Specifically,foragivenperunitcapacityprice w ,thecomputercapacityproviderAIP maximizesitsprofitfunctionofEq.(2.4),andfindsthefollowingoptimalquantityit wantstoselltotheASP. 4, () () 2 AIP w c Qw e Š =(2.19) Giventhesameperunitcapacityprice w ,theASPinthisCompetitiveAligned ScenariowillfindtheoptimalquantityitwantstobuyfromtheAIP.SincetheASP bearstheriskofthesupplychaininthisscenario,theover-andunder-capacitycostsare includedintheASP’sobjectivefunction,havingthesameformasEq.(2.15).Firstorder conditionsrequirethat 4(,)()2()() 2 424 ()2()0 242 dAPpQpwQpwdpbwr Q dQbbb wrkk dpbQdpb b bb ŠŠŠ+Š =Š+Š Š +ŠŠŠ+Š+= (2.20) and () 2 4 2(,)(()) () 422 () ()0 24 pr dAPpQQdpbpkrQ d pb dpbbb kdpb dpb bb Š Š+Š+Š =Š++ŠŠ ŠŠ +Š+Š=.(2.21) Foragivenperunitcapacitycostof w ,let4, () ASP Qw betheoptimalquantityfor theASPsatisfyingthefirstorderconditionsof(2.20)and(2.21).Then4, () ASP Qw representsthequantitytheASPwantstobuyfromtheAIP.Themutuallyagreeable policyimpliesthat4,4, ()() ASPAIP QwQw =.(2.22)

PAGE 40

25 Thatis,thequantitytheASPwantstobuywillbethesameasthequantitythe AIPdesirestosell.Mathematicallyspeaking,Eq.(2.22)shouldyieldafeasiblesolution of w forboththeASPandtheAIPtoreachanagreement.Inthisscenario,bydefinition 4,() 1 0when0 2 AIPdQw e d we =>> ,4, () AIP Q wisastrictlyincreasingfunctionof w and 4,() 2 0 when 0 ()ASPdQw b b dwprk =<> + ,4, () ASP Q wisastrictlydecreasingfunctionofw. ThusthereisauniquesolutioninScenario4.2.4NumericalExplorationsforthe1stModelTogainfurtherinsightsoftheapplicationservicessupplychain,weconduct numericalanalysesofthefoursupplychaincoordinationscenariosdescribedinSection 2.3.Further,weexploretheimpactoffourkeyparametersonthesupplychain performanceunderthosefourdifferentscenarios,including(1)thepriceelasticityofthe expecteddemand,,(2)theperunitcapacitycostoftheAIP, c ,(3)thediseconomyof scaleparameterofprovidingthecapacity, e ,and(4)therangeparameteroftheuniform distribution, b .Wefirstselectasetofbaselineparametersforthesupplychainmodel, Table 2-1. Then for each scenario, we vary one parame ter at a time over a wide range of valuesandcalculatefivestatistics—theASP’sprofit,theAIP’sprofit,thewholesupply chain’sprofit,thepercentofASP’sprofitagainstthatofthesupplychain,andthe percentage of the AIP’s profit. The results are shown in Table 2-2 to Table 2-5. Threefiguresarecreatedforeachofthefourparametersunderexplorations, resulting in Figure 2-4 to Figure 2-15. The first group of figures for example, Figure 2-4 to Figure 2-6, examines the impact of price elasticity of expected demand, ,onvarious supplychaincoordinationstrategies.Thefirstfigureineachgroupshowsthewhole

PAGE 41

26 supplychain’sexpectedprofitunderdifferentsupplychaincoordinationscenarios.The secondfigureinthegroupplotsASP’sexpectedprofit,whilethethirdfiguredepicts AIP’sexpectedprofitunderdifferentscenarios. Severalimportantfindingsarederivedfromthenumericalanalyses.First,forall possible combination of parameters in Figure 2-4 to Figure 2-15, the competitive aligned coordinationstrategygeneratesthesameperformance(expectedprofit)forthewhole supplychainasforthecasewherethesupplychainiscoordinatedbyacentralplanner. Thatis,wediscoveradecentralizedcoordinationmechanismtoachievethesamegoalof maximizingthewholesupplychain’sperformance.Inthecompetitivealigned coordinationmechanism,boththeASPandtheAIPoptimizetheirownprofitfunctions andthencomebacktonegotiateamutuallyagreeablepolicy.Thecomputercapacitythe ASPagreestobuyandtheAIPagreestosellbecomesthecapacitythatmaximizesthe wholesupplychain’sperformance.Oneprobableinterpretationofthisresultisthe following.Thecapacityasafunctionofperunitprice w theAIPiswillingtosell,4, () AIP Qw ,representsthesupplyfunctionofthecapacity. ThecapacitytheASPwantstobuy,4, () ASP Qw ,isequivalenttothedemandcurve ofthecapacity.Then,themutuallyagreedcapacityunderthecompetitivealigned scenariocorrespondstothemarketequilibriumofsupplyanddemand,whichhasthe sameeffectasifthewholesupplychainiscoordinatedbyacentralplanner. From the whole supply chain’s perspective as shown in Figure 2-4, Figure 2-7, Figure 2-10, and Figure 2 -13, the competitive aligned mechanism is better than letting the ASPcoordinatethesupplychain,whichinturnsisbetterthanthescenariowheretheAIP coordinatesthesupplychain.Thisfindingseemstosuggestthatabsentacompetitive

PAGE 42

27 alignedmechanism,itisbettertolettheplayerclosertothemarketcoordinatethesupply chain.AsdescribedinProposition2.1inSection2.3,whentheAIPiscoordinatingthe supplychainbybearingtheriskofunder-andover-capacitycost,theASPwillalways orderthemaximumpossiblemarketdemandfromtheAIP.TheASPsimplydoesnot havetheincentiveinthiscasetobetterpredictthemarketdemand,resultinginan inefficiencyofthesupplychain. Secondly, we observe from Figure 2-5, Figure 2-6, Figure 2-8, Figure 2-9, Figure 2-11, Figure 2 -12, Figure 2-14 and Figure 2 -15 that whoever coordinates the supply chain standstorealizegreaterprofitthanthecasewheretheotherpartnercoordinatesthechain, withtheexpectedprofitofthecompetitivealignedscenariobeinginbetween.Moreover, whoevercoordinatesthesupplychainattainsgreaterprofitthantheotherpartner,afact not shown in th ose figures but readily available from Table 2-2 to Table 2-5. The managerialimplicationisthatwhoevercoordinatesthesupplychainexploitsthe informationsharedfromtheotherpartnerbyincludingtheinformationintheobjective function. Thirdly, from Figure 2-4 to Figure 2-6, we find that the expected profits for all scenariosdecreaseasthepriceelasticityofexpecteddemandincreases.Inotherwords, theexpectedprofitsaregreaterwhentheexpecteddemandofthemarketislessprice sensitive.SimilarbehaviorisexhibitedforAIP’sperunitcapacitycostparameter, c ,as shown in Figure 2-7 to Figure 2-9. However, this parameter seems to have much less impactthanthepriceelasticityofexpecteddemand. Finally, from Figure 2-10 and Figure 2-11, the expected profits of the whole supplychainandtheASPunderallcoordinationscenarioswilldecreaseasthe

PAGE 43

28 diseconomyofscaleparameter, e ,increases.Surprisingly,whenthediseconomyofscale parameterincreases,theAIP’sexpectedprofitactuallyincreasesunderthecompetitive aligned and the ASP coordination scenarios as shown in Figure 2-12. Equation (2.18) in theprevioussectionprovidessomeinsightstothisseeminglycounterintuitiveresultas theAIP’sexpectedprofitisanincreasingfunctionofthediseconomyfactor, e .The impact of the distribution range, b , exhibits the same pattern shown in Figure 2-13 to Figure 2-15. Table2-1BaselineparametersfornumericalexplorationsforModel1 ParametersBaselineValues Zero-pricedemand, d () m pd p =100.0 Priceelasticityofexpecteddemand,2.0 Rangeparameterofuniformdistribution, b 20.0 Perunitcapacitycost, c 0.5 Diseconomyscaleparameter, e 0.1 Salvagevalueofperunitovercapacity, r 5.0 Opportunitycostoflostsaleduetounder capacity, k 8.0

PAGE 44

29 Table2-2Impactofpriceelasticity, PriceElasticityofExpectedDemand,1.501.601.701.801.902.002.102.202.302.402.50 Scenario1: SupplyChain * 1 S P1333.861234.051146.361068.74999.6937.66881.87831.39785.52743.67705.36 ** 222 ( , ) A PpQ313.52288.41266.35246.82229.44213.87199.85187.18175.67165.18155.59 * 22 () H Pw734.07672.96627.97588.07552.47520.51491.68465.54441.75420.01400.07 * 2 S P1037.60961.37894.32834.90782.91734.38691.53652.72617.42585.19555.66 ** 222 () H PwSP0.700.700.700.700.710.710.710.710.720.720.72 Scenario2:AIP Coordinatesthe SupplyChain * 2 ** 222 )(,Q APpSP 0.300.300.300.300.290.290.290.290.280.280.28 ** 333 ( , ) A PpQ1085.50993.54913.23842.58780.02724.29674.39629.50588.94552.15518.65 * 33 () H PQ202.62194.66187.25180.34173.87167.81162.12156.77151.72146.95142.44 * 3 S P1288.121188.211100.491022.92953.89892.10836.52786.27740.66699.10661.10 ** 333 ()/ H PQSP0.160.160.170.180.180.190.190.200.200.210.22 Scenario3:ASP Coordinatesthe SupplyChain *** 3333 (,)/ A PpQSP0.840.840.830.820.820.810.810.800.800.790.78 444, ( , ) ASPAPpQ1027.89935.35854.58783.57720.75664.84614.83569.89529.34492.60459.20 44, () AIPHPQ305.97298.70291.78285.17278.86272.82267.04261.50256.18251.07246.16 4 S P1333.861234.051146.361068.74999.60937.66881.87831.39785.52743.67705.36 44, 4 ()/AIP H PQSP0.230.240.250.270.280.290.300.310.330.340.35 Scenario4: CompetitiveAligned444, 4 ( ,)/ASP APpQSP 0.770.760.750.730.720.710.700.690.670.660.65

PAGE 45

30 Table2-3Impactofcapacitycost,cCapacityCostParameter, c 0.100.200.300.400.500.600.700.800.901.00 Scenario1: SupplyChain * 1 S P958.67953.39948.13942.89937.66932.44927.24922.05916.88911.72 ** 222 ( , ) A PpQ217.65216.70215.75214.81213.87212.93211.99211.06210.13209.19 * 22 () H Pw536.82532.74528.66524.58520.51516.45512.38508.33504.28500.23 * 2 S P754.47749.43744.41739.39734.38729.38724.38719.39714.40709.42 ** 222 () H PwSP0.710.710.710.710.710.710.710.710.710.71 Scenario2:AIP Coordinatesthe SupplyChain * 2 ** 222 )(,Q APpSP 0.290.290.290.290.290.290.290.290.290.29 ** 333 ( , ) A PpQ740.76736.63732.50728.39724.29720.20716.12712.05707.99703.94 * 33 () H PQ171.26170.40169.53168.67167.81166.96166.10165.25164.40163.56 * 3 S P912.03907.03902.04897.07892.10887.16882.22877.30872.39867.50 ** 333 ()/ H PQSP0.190.190.190.190.190.190.190.190.190.19 Scenario3:ASP Coordinatesthe SupplyChain *** 3333 (,)/ A PpQSP0.810.810.810.810.810.810.810.810.810.81 444, ( , ) ASPAPpQ679.82676.06672.31668.57664.84661.11657.4653.69650646.31 44, () AIPHPQ278.85277.33275.82274.32272.82271.33269.84268.36266.88265.41 4 S P958.67953.39948.13942.89937.66932.44927.24922.05916.88911.72 44, 4 ()/AIP H PQSP0.290.290.290.290.290.290.290.290.290.29 Scenario4: CompetitiveAligned444, 4 ( ,)/ASP APpQSP 0.710.710.710.710.710.710.710.710.710.71

PAGE 46

31 Table2-4Impactofdiseconomyofscale,eCapacityCostDiseconomiesofScale, e 0.050.060.070.080.090.100.110.120.130.140.15 Scenario1: SupplyChain * 1 S P1097.461061.181027.30995.57965.75937.66911.13886.03862.23839.62818.10 ** 222 ( , ) A PpQ255.81246.80238.11229.73221.66213.87206.36199.11192.11185.37178.85 * 22 () H Pw607.20589.21571.55554.22537.21520.51504.11488.00472.18456.63441.36 * 2 S P863.01836.01809.66783.96758.87734.38710.47687.11664.29642.00620.21 ** 222 () H PwSP0.700.700.710.710.710.710.710.710.710.710.71 Scenario2:AIP Coordinatesthe SupplyChain * 2 ** 222 )(,Q APpSP 0.300.300.290.290.290.290.290.290.290.290.29 ** 333 ( , ) A PpQ937.66886.03839.62797.59759.32724.29692.07662.33634.76609.13585.24 * 33 () H PQ136.41146.60154.34160.20164.59167.81170.12171.68172.64173.11173.18 * 3 S P1074.071032.63993.96957.80923.91892.10862.19834.00807.40782.24758.42 ** 333 ()/ H PQSP0.130.140.160.170.180.190.200.210.210.220.23 Scenario3:ASP Coordinatesthe SupplyChain *** 3333 (,)/ A PpQSP0.870.860.840.830.820.810.800.790.790.780.77 444, ( , ) ASPAPpQ909.50850.98797.95749.64705.44664.84627.42592.82560.75530.93503.14 44, () AIPHPQ187.96210.19229.35245.93260.31272.82283.71293.21301.48308.69314.96 4 S P1097.461061.181027.30995.57965.75937.66911.13886.03862.23839.62818.10 44, 4 ()/AIP H PQSP0.170.200.220.250.270.290.310.330.350.370.38 Scenario4: CompetitiveAligned444, 4 ( ,)/ASP APpQSP 0.830.800.780.750.730.710.690.670.650.630.62

PAGE 47

32 Table2-5Impactofdistributionrange, bUniformDistributionParameter, b 5.008.0011.0014.0017.0020.0023.0026.0029.0032.0035.00 Scenario1: SupplyChain * 1 S P1003.16991.43978.96965.81952.03937.66922.73907.29891.36874.98858.16 ** 222 ( , ) A PpQ243.00237.03231.13225.30219.55213.87208.27202.74197.28191.90186.60 * 22 () H Pw554.60551.06545.88539.06530.60520.51508.78495.42480.42463.78445.51 * 2 S P797.60788.08777.00764.36750.15734.38717.05698.16677.70655.69632.11 ** 222 () H PwSP0.700.700.700.710.710.710.710.710.710.710.70 Scenario2:AIP Coordinatesthe SupplyChain * 2 ** 222 )(,Q APpSP 0.300.300.300.290.290.290.290.290.290.290.30 ** 333 ( , ) A PpQ839.25817.06794.42771.38748.00724.29700.31676.07651.62626.97602.16 * 33 () H PQ136.96143.71150.16156.32162.20167.81173.17178.28183.14187.76192.15 * 3 S P976.21960.76944.57927.70910.19892.10873.48854.35834.76814.73794.31 ** 333 ()/ H PQSP0.140.150.160.170.180.190.200.210.220.230.24 Scenario3:ASP Coordinatesthe SupplyChain *** 3333 (,)/ A PpQSP0.860.850.840.830.820.810.800.790.780.770.76 444, ( , ) ASPAPpQ806.56779.18751.26722.85694.03664.84635.33605.53575.50545.26514.85 44, () AIPHPQ196.60212.25227.70242.96258.00272.82287.41301.76315.86329.71343.32 4 S P1003.16991.43978.96965.81952.03937.66922.73907.29891.36874.98858.16 44, 4 ()/AIP H PQSP0.200.210.230.250.270.290.310.330.350.380.40 Scenario4: CompetitiveAligned444, 4 ( ,)/ASP APpQSP 0.800.790.770.750.730.710.690.670.650.620.60

PAGE 48

33 Figure2-4Impactofpriceelasticityonoverallsupplychain Figure2-5ImpactofpriceelasticityonASPÂ’sexpectedprofit ASP'sExpectedProfit0 200 400 600 800 1000 1200 1.51.61.71.81.922.12.22.32.42.5PriceElasticityofExpectedDemandExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned SupplyChainPerformance0 200 400 600 800 1000 1200 1400 1600 1.51.61.71.81.922.12.22.32.42.5PriceElasticityofExpectedDemandExpectedProfit SupplyChain AIPcoordinates ASPcoordinates CompetitiveAligned

PAGE 49

34 Figure2-6ImpactofpriceelasticityonAIPÂ’sexpectedprofit Figure2-7Impactofcapacitycostonoverallsupplychain AIP'sExpectedProfit0 100 200 300 400 500 600 700 800 1.51.61.71.81.922.12.22.32.42.5PriceElasticityofExpectedDemandExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAlgned SupplyChainPerformance0 200 400 600 800 1000 1200 0.10.20.30.40.50.60.70.80.91PerUnitCapacityCost,cExpectedProfit SupplyChain AIPCorrdinates ASPCoordinates CompetitiveAligned

PAGE 50

35 Figure 2-8 Impact of capacity cost on ASP’s expected profit Figure2-9ImpactofCapacityCostonAIP’sexpectedprofit ASP'sExpectedProfit0 100 200 300 400 500 600 700 800 0.10.20.30.40.50.60.70.80.91PerUnitCapacityCost,cExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned AIP'sExpectedProfit0 100 200 300 400 500 600 0.10.20.30.40.50.60.70.80.91PerUnitCapacityCost,cExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 51

36 Figure2-10Impactofdiseconomyofscaleonoverallsupplychain Figure2-11ImpactofdiseconomyofscaleonASPÂ’sexpectedprofit SupplyChainPerformance0 200 400 600 800 1000 1200 0.050.060.070.080.090.10.110.120.130.140.15DiseconomyofScaleParameter,eExpectedProfit SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned ASP'sExpectedProfit0 100 200 300 400 500 600 700 800 900 1000 0.050.060.070.080.090.10.110.120.130.140.15DiseconomyofScaleParameter,eExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 52

37 Figure2-12ImpactofdiseconomyofscaleonAIPÂ’sexpectedprofit Figure2-13Impactofdistributionrangeonoverallsupplychain AIP'sExpectedProfit0 100 200 300 400 500 600 700 0.050.060.070.080.090.10.110.120.130.140.15DiseconomyofScaleParameter,eExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned SupplyChainPerformance0 200 400 600 800 1000 1200 58111417202326293235DistributionRange,bExpectedProfit SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 53

38 Figure2-14ImpactofdistributionrangeonASPÂ’sexpectedprofit Figure2-15ImpactofdistributionrangeonAIPÂ’sexpectedprofit ASP'sExpectedProfit0 100 200 300 400 500 600 700 800 900 58111417202326293235DistributionRange,bExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned AIP'sExpectedProfit0 100 200 300 400 500 600 58111417202326293235DistributionRange,b ExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 54

39 CHAPTER3 COORDINATIONSTRATEGIESOFAPPLICATIONSERVICESSUPPLYCHAIN: THEQUEUINGEFFECTS 3.1IntroductionoftheASPModelwithQueuingEffects Increasingpressurefromcustomersonspeedtomarketleadstotheemergenceof anewoutsourcingmodel,theApplicationServiceProvider(ASP).TheASPprovidesa network-centricinfrastructurethatwillallowanyusertoaccessvariousapplicationsfrom awiderangeofcomputerplatforms.Byrentingthesoftwareonanasneededbasis,a newdooropensforsmalltomidsizecompaniestostayinbusinessandcompetewith largecorporations.ThisbusinessmodelisaresultofthegrowingInternetinfrastructure, speedycommunicationfunctions,andpowerfulplatforms. ThetypicalfunctionsofanASPincludeprovidingstructureandnetworkservices; datacenterandoperations;applicationmanagementandmaintenance;integration; marketingandchannel(Roddy,1999).Giventhecomplexityofthisbusinessmodel, thereisaneedforstudyofcoordinationissues,pricingmodelsandcapacitymanagement betweeninvolvedparties.Althoughthebenefitsofcommunicationbetweenthe functionalboundariesmayberelativelyeasytoidentify,realizingthesebenefits,and definingacoordinationframeworkundertheinfluenceofqueuingeffectswillrequire newtechniques.Itiswidelyknownthatqueuingeffectsandschedulingarevery importantincomputersystemusage.Thishasbeenreviewedbymanyresearchersinthe fieldofcomputersystemperformanceandschedulingforalongtime.

PAGE 55

40 InthisstudyweanalyzetherelationshipbetweentheApplicationServerProvider (ASP)andtheApplicationInfrastructureProvider(AIPs)withtheinfluenceofqueuing delays.TheAIPoffersacontractforsellingcomputercapacitytotheASP,whichthen usesittoprovidevalue-addedservicessuchaspackagedsoftware(e.g.,,accesstothe ERPsoftware)tothemarket.TheAIPhastodecidehowmuchcomputercapacityto provide,andatwhatpricetosellthiscapacitytotheASPinordertomaximizehis profits.Inthemeantime,theASPhastodecidehowmuchcomputercapacitytoacquire andatwhatpricetoselltheservicestothemarketinordertomaximizeherprofit. However,potentialcustomersconsideringjoiningtheASP’sservicetakeintoaccountthe costcausedbythequeuingdelay,inadditiontothepricechargedbytheASP. Ourresearchdemonstratesthatbyjointlycoordinatingthestrategies,thesupply chainprofitismaximizedcomparedtoindividuallydefinedcoordinationstrategieswith theexistenceofqueuingdelays.Thisresearchalsodefinesaframeworkonstrategic coordinationbetweenASPsandotherinfrastructurepartners,andprovidesguidancefor futurework. Untilrecentlytherehasbeenlittleresearchconsideringcoordinationstrategies betweenAIPandASP,especiallyinrelationtothequeuingeffects.Howeveranumber ofresearchersininformationsystemshaveanalyzedavarietyofmodelstostudythe queuingeffectsforcomputercapacityandpricing.Mendelson(1985)studiedtheeffects ofqueuingdelays,andtheuser’sdelaycosts,onthemanagementofcomputersystemsto maximizeexpectednetvalueofservicesandprofitcenter.Heindicatedthat“computing resourcepricingneednottakethequeuingeffectsintoaccountsincetheseeffectsare

PAGE 56

41 “selfregulating”.Congestionleadstodelaywhichdeteradditionalusersfromjoiningthe system…”(Mendelson,1985,p.313). Mendelson’s(1985)resultdemonstratedthatthepresenceofqueuingdelays aggravatestheproblemofmonopolypricingsincetheprofitcenterstructureprovides incentivetoreducetheavailablecapacityandutilization. Inourresearch,wefurtheranalyzetheimpactofqueuingdelayinrelationtothe supplychaincoordinationstrategies.Therearetwoparties,ASPandAIP,whosegoalis tomaximizeindividualprofitratherthanthatofthewholesupplychain.Ourconclusions alsosupportMendelson’s(1985)self-regulatingsuggestions.Everynewarrivalcauses morewaitingtimeforthemselvesandforothers. Inanotherwork,Cheng(1999)analyzedpricingandcapacitydecisionsof clusteredtwin-computersystemsandconsolidatedsinglecomputersystemsconsidering theeffectofthecostofdelayincomputerprocessing.Hisresearchshowsthatforboth scenarios,optimalarrivalratedecreasesasdelaycostincreases.Heindicatedthat“The optimalpricesfollowanoppositedirectionoftheoptimalarrivalrates.Thatis,alower optimalarrivalrateinducesahigheroptimalpriceandviceversa”(Cheng,1999,p.29). Thereisalsoalimitedamountofresearchinthefieldofpricingmodelsforthe Internetresources.ChengandKoehler(2002)analyzedthebenefitofapplicationservice providersandoptimalpricingpoliciesofweb-enabledapplicationservices.They indicatethattheASPcannotaffectservicecapacityinashortrunproblem.However,if thecapacityisavariable,alongrunproblem,theASPcanincreaseit’sserviceand performancebyincreasingservercapacity.Fromthisstudytheyshowedthat …withalinearcostfunctionanduniformpricereservationdistribution thattheshortrunASPprofitisunimodalinthenumberofsubscribers.

PAGE 57

42 Theoptimalnumberofsubscribersreachesalimitasmarketpotential increases,probablyduetotheperformanceguarantee…(Chengand Koehler,2002,p.24). Alsotheirresearchindicatedthatwhenmarketpotentialincreases,ASPprofitand customerlevelincreases. Theliteraturecontainsasignificantamountofstudywithreferenceto coordinationissuesbetweensupplychainagentsandcapacitydecisions.Ellinger(2000) reviewedrelationshipsbetweenorganizations,cross-functionalcollaboration,effective marketing/logisticsinterdepartmentalintegration,anddistributionserviceperformancein thesupplychain.Hesuggestedthatsuccessintoday’scompetitivemarketplacerelyon theintegrationoftraditionalfunctionalboundariestoprovidebettercustomerservice. Thecoordinationandcommunicationbecomesthemostimportantaspectforthisgoal. Hisstudyshowedtheimportanceofrewardandrecognitiontokeepupthe communicationandcoordination. Ballouetal.(2000)discussedtheevolutionofproductflowsforchannel performanceimprovement.Theydefinedsupplychainmanagementas“…allactivities associatedwiththetransformationandflowofgoodsandservices,includingtheir attendantinformationflows,fromthesourcesofrawmaterialtoendusers…”(Ballou,et al.,2000,p.9). Theyindicatedthatifthebenefitsofchannelaresharedbetweenthemembers,no formalactionisrequiredtodistributeit.Ifthebenefitssharedareunequallydistributed becauseanagentmayormaynotbebetteroffeconomically,thereshouldbea mechanismtosupportthesupplychain.Communicationisthemajormechanismto supportdesiredoutcomeofsupplychaincoordination.Costandotherinformationare usuallynotsharedbetweenthemembers,possiblyduetofearofcorporatesecretsbeing

PAGE 58

43 divulged.Mistrustleadstothebreakdownofthesupplychaincoordination,monopoly structure,andanindividualÂ’sselfinterests.SimilartoBallouetal.Â’sresearch(2000),we useinformationsharingasamajormechanismtosupportdesiredoutcomeoftheASP supplychaincoordinationstrategies. Inanotherwork,SkieraandSpann(1999)analyzedthecompensationofprofit differencesbetweentheoptimalsolutionandsub-optimalcapacitydecisionsfora companyinamonopolisticmarket,whichissellinganon-storableproductandfacing interdependentdemandintwotimeperiods.Hesuggestedthatdefiningtheoptimal pricesbethemostimportantiteminordertomaximizetheprofit.Healsodiscussedwhy suboptimalcapacityhasaminorinfluenceonprofits. InourstudywetakeWengÂ’s(1999)andMendelsonÂ’s(1985)modelsasthe underlyingframework,andrecognizetheimportanceofinformationsharingfrom previousresearch.WengÂ’smodeldoesnotconsiderthequeuingeffects.Instead,Weng (1999)specifiedasupplychainservicelevelrequirement.Thisservicelevelrequirement andtheorder/productionquantitywillinturndeterminethedistributorÂ’sunitsalesprice. Howeverinourmodel,thepriceandcapacitybecomeakeydecisionvariableforthe ASP.Weanalyzetheimpactsofqueuingdelaysonthepriceandcapacityoftheservice, andreviewthecoordinationstrategiesandassociatedpoliciesthatwouldimproveASP supplychaincoordinationdesignandperformance,aswellaseachpartyÂ’sprofitlevelin alongrunproblemsetting. Theremainderofthischapterisorganizedasfollows.Inthenextsection,we presenttheASPsupplychainmodel.InSection3.3.,wedefineandstudythe coordinationstrategiesfortheAIPandASP.Inadditiontotheeffectivenessof

PAGE 59

44 informationsharing,westudytheimpactsofqueuingdelaysonthepriceandcapacityof theservice.InSection3.4.,weexaminetheoptimalpricingpoliciesfortheSupply Chain,AIPandASPbytakingintoaccountthevalueofusers’time,andtheimplications ofcoordinationstrategiesbynumericalexplorations.Finally,thelastchapterofthis thesisprovidesconcludingremarksanddirectionsforfutureresearch. 3.2ApplicationServiceProvidersSupplyChainModelWithQueuingEffects ConsiderasupplychainthatconsistsofanAIPwhoprovidesthecomputer capacitytotheASPatpricewperunitofcapacity,andanASPwhosellsherserviceto themarketatpricepperunitofcapacityinoneperiodsetting.TheAIPoffersacontract ofsellingcomputercapacitytotheASP,whothenusesittoprovideaservicetothe market.Oursettingisbasedonasingleserviceoffering.Alternatively,asinglefirm playstheroleofboththeAIPandASP,ortheAIPandASPjointlydefineagoalfor optimizingthewholesupplychainprofit. Figure3-16OverviewoftheASPinfrastructurewithqueuingdelays 3.2.1InformationSharing InformationsharingisbasedonwhatinformationtheAIPandASPsharetomake theirdecisionsandmaximizetheirindividualprofits.Weconsidertwotypesof AIP w perunitof capacity Capacity, µ Market ASP Arrivalrate, Serviceatprice p

PAGE 60

45 informationsharing:whenAIPcoordinatesthesupplychain,customerarrivalrateand ASP’spricinginformationaresharedfromtheASPtoAIPandtheAIPcoordinates supplychaindecisions.AlternativelywhenASPcoordinatesthesupplychain,theASP approachestheAIPforaquoteofprice-capacityscheduleandtheASPcoordinates supplychaindecisions. 3.2.2TransactionorJobArrival Inourmodel,jobsarriveintocomputersystemrandomly,theyspendrandom amountoftimeandtheyleavethesystem. (poissonrate)isjob’sortransaction’s arrivalratetosystemperunitoftimeandarrivingjobshaveahomogeneousservice requirement.Ifwethink similartothedemand, Q ,fromtheoperationsarea,itis affectedbythevalueofcomputersystemsandpriceofcapacity.Thesystemismodeled asM/M/1queuingsysteminourmodel. µ isacomputercapacitylevelofasingle system,expectedoutputrate(measuredinjobsortransactionsperunitoftime).Inthis study,consider µ asavariable,andtreattheproblemasalongrunproblem.Dueto queuingstructure, µ <,therewillnotbeanyundercapacityconditioninthisproblem. Thetimeanyjobspendsinthesystemincludesactualprocessingandwaitingtime.We denote () Vastheexpectedgrossvalueofthecomputerserviceperunitoftimetoa customer.Withoutconsideringthedelaycostandifthepricepertransactiontoa customeris p ,thenthemarginalvalueofASPserviceisequaltothepricepertransaction, '() Vp = . Whenthecostofdelayisgreaterthanzero,thedelaycostisequalto vT per transaction.Weassumethedelaycostofsystemperunitoftimeperjobis v andthe expectedtimeajobremainsinthesystemfromarrivaltoprocessingiscompletedis T .

PAGE 61

46 Then,theexpectedusercostperjobbecomes p v T + .Theaggregatedelaycostforthe systemis(,) D v T µ = . Inthismodel,weletthedemandbelongtotheclassofisoelasticdemand functionssimilartoMendelson’swork(1985), '()/ Vk=,and 1 ''() k V +=Šwhere 0 < 1 <,andassume 1 / 2 =forsimplificationpurpose. LetLbetheexpectednumberofjobsinthesystemperunitoftime.Then (,)()(/) Lff µ µ ==,with / µ =beingtheutilizationratioofthesystem. FromLittle’slaw, LT =and v Lv T =.Basedonourassumptions,weseethat asMendelson(1985)statedinhisresearch,increasein increasestheexpecteddelay costwiththefollowingtwoways:“Theaddedjobsthemselvesincuradelaycostwhich, toafirstorderapproximation,hasexpectedvalue vT perjob;…callthe“selfregulating”…”(Mendelson,1985,p.315).Basicallyeverynewarrivalcausesmore delaycostforthemselves.Alsohecontinuedwiththefollowingstatement:“Theadded workloadincreasestheexpecteddelaycostinflictedonallcurrentusersby (/) v dWdV. Wecallthisterm“externality”…”(Mendelson,1985,p.315).Inthissituation,every newjobcausesdelaycostforothers.3.2.3ApplicationInfrastructureProvider’sProfitFunctionWeassumethattheAIPprovidescomputercapacitytotheASPatpricewper unitofcomputercapacity.TheAIP’sunitsalepriceisequaltotheASP’sunitpurchase price.TheAIP’sinternalmarginalcostforthecomputercapacityisc.Weanalyzethe coordinationstrategieswiththefollowingtwopricingstructures. IfAIP’sprofitfunctionislinear,theAIP’sexpectedprofitequals

PAGE 62

47 () H Pwc µµµ =Š.(3.23) Secondly,inoursetting,weassumethattheAIP’sprofitfunctionfollows diseconomiesofscale.Thus,theAIP’sexpectedprofitfunctionequals() 2 () HPwce µµµµ =Š+ (3.24) ThefirsttermdescribesthecomputercapacityacquiredbytheASP, µ , multipliedbytheAIP’sunitcapacityprice, w .Thesecondterm,thecoststructureof AIP,hastwoparts.First,thecostofthecapacityforAIPthatisequaltomultiplication ofmarginalcostofcapacitywithtotalcapacity,thenthesecondpartisaboutcost associatedwithdiseconomiesofscaleparameter, e ,thatisgreaterthanzero.Aswe mentioninChapter2,weassumethataveragecostperunitincreasesasthecapacity increasesbeyondthebestoperatinglevel.Increasingcostsresultfromincreasing congestionofhardwareplatform,whichcontributestodifficultyincapacitymanagement, useraccess,privacyprotectionforeachuser,i.e.(Cotton,1975;Selwyn,1970). CurrentlythemostASPsimplementone-to-oneorone-to-fewapplicationdelivery models,ratherthanone-to-manyserviceofferingsinordertoreducethecomplexityof theASPbusinessmodel.Eventhetimesharingisaveryoldmodel,theASPisstillso new,somanyindustryresearchersindicatethattheASPsshouldrevampprocesses, makingthemreliableandscalableinordertoreceiveanybenefitsfromtheeconomiesof scale(Mizoras,2001;Rubens,2001).3.2.4ApplicationServiceProvider’sProfitFunctionServicepricingaffectsthejob’sarrivalratetotheASP.Dependingontheprice scheduleandexpectedwaitingtimes,thecustomerdecideshowtousethesystemand howlongtostay.TheASPcharges p pertransaction(job)arrivingfromthemarketfor

PAGE 63

48 theservice.Intheindustry,themostcommonwayofchargingthisserviceisbasedon peruser,perapplicationandpertimeusage(Davison,2000).Inourmodel,theexpected profitfunctionoftheASP’sisgivenby (,) A Pppw µ µ =Š .(3.25) Amajorpurposeofthisstudyistoexaminevariouscoordinationstrategiesunder theinfluenceofqueuingdelays.TheAIP’sgoalistodecidewhatpricetochargethe ASPinordertomaximizehisprofit.Ontheothersite,ASP’sobjectiveistomaximize herexpectedprofitbydecidinghowmuchcapacitytobuyfromAIPandwhatpriceto chargetothemarket.Thefollowingsectiondiscussestheformsofcoordinatingthe supplychain.3.3AnalysisofCoordinationStrategiesInthissection,wedefineandstudythecoordinationstrategiesfortheAIPand ASP.Inadditiontotheeffectivenessofinformationsharing,westudytheimpactsof queuingdelaysonthepriceandcapacityoftheservice.Weconsiderfourcoordination strategiesincluding(1)overallsupplychaincoordinationstrategy,(2)AIPcoordinates thesupplychain,(3)ASPcoordinatesthecoordinatesthesupplychainand(4)the competitivealignedcoordinationstrategyasfollows.First,weanalyzethese coordinationstrategieswheretheAIP’scoststructure,( i ).Thenthesecondpartofthe analysisincludesthecoordinationstrategieswheretheAIP’sprofitfunctionwith diseconomiesofscale,( j ),wherethesubscript i and j denoteconditiononeandtwo.The objectiveoftheAIPandASParetomaximizetheirindividualexpectedprofitsin additiontowholesupplychain’sexpectedprofit.

PAGE 64

493.3.1CoordinationStrategiesWhenAIP’sExpectedProfitFunctionIsLinearInthissection,wereviewthecoordinationstrategieswhentheAIP’sprofit functionislinearandwithoutdiseconomiesofscale.3.3.1.1Scenario1i:SupplyChainCoordinationStrategyInthisscenario,asinglefirmplaysaroleofboththeAIPandASP.Or,theAIP andtheASPformajointventuretooptimizethesupplychainprofit.WhentheAIPand ASPbelongstothesamefirm,theproblemisverysimilartoNewsvendormodel.The wholesupplychain’sexpectedprofitisthesumoftheexpectedprofitfunctionsofthe AIPandtheASP(SilverandPeterson1975).Proposition3.1.WhenasinglefirmplaysaroleofboththeAIPandASP,the firmneedstoprovidethemaximumcapacity, *2 * 1 1 2 4 k c µ= ,forthearrivalrate, 2 2 * 1 2212 4 k vc ck=Š ,ataprice 2 * 1 2212 2 kvc kv ck p k vckvc c kckŠ =Š inordertomaximizethe profit.Proof.Let1 (,) SPp µ = betheexpectedprofitforthesupplychainthatisthesum oftheexpectedprofitfunctionsoftheAIPandASPasfollows.111 (,)(,)() SPpAPpHP µµµ =+ ,(3.26) where1 (,) APp µ and1 () HP µ aredefinedinEqs.(3.23)and(3.25).Usingthedefinitions andsomealgebra,onehas1(,) S Pppc µ µ =Š (3.27) and '()(,) VpvT µ =+ .

PAGE 65

50 Theprice w perunitofcapacitychargedtotheASPbytheAIPdropsoutinEq. (3.27).Theprice w servestheroleofinternaltransferpriceandhasnoeffectonoverall profit. Tofindtheoptimalsupplychainprofit,1 , m ax(, ) pSPpµ µ where '( )(, ) pVvT µ =Šand µ <,firstorderconditionsrequire 1(,) 0 dSP d µ =and 1(,) 0 dSP d µ µ=.Aftersomealgebra, '( ) 0 V>and '()(,) k v pVvTµ µ =Š=Š Š. Firstorderconditionsleadto2221 ( 1)'(/ ) kvcf µ ŠŠ=(3.28) 22221 1 (1) kcµ ŠŠ=(3.29) Eqs.(3.28)and(3.29)canbesimplifiedasthefollowingwiththeconsiderationof 1 / 2 =. 2 * 1 4 '( ) kvcf =(3.30) *2 * 1 1 2 4 k c µ=(3.31) Aftersomealgebra,fortheM/M/1queuingsystem,alltheseconditionsand assumptionsleadto 2 * 1 2212 4 k vc c kµ=Š , 2 2 * 1 2212 4 k vc ck =Š * 1 2 12 vc k =Š ,and 2 * 1 2212 2 kvc kv ck p k vckvc c kckŠ =Š .

PAGE 66

51 Theoptimalutilizationratio, ,appearstosignificantlydependonthedelaycost ofsystemperunitoftimeperjob, v .Andwhenusers’timeincreases,theutilizationratio andcapacitydecreases.Alsowhentheinternalmarginalcost, c ,increases,utilization ratioandcapacitydecreases. Thetotalsupplychainprofitunderthisscenariowhereasinglefirmplaysarole ofboththeAIPandASPisgivenby111 ( ,)(,)( ) SPpAPpHP µµµ =+1(,) S Pppc µ µ =Š 2 22 ** 111 212 4 2 (,) v ckvcv kck SPp vc kµŠŠ = .(3.32) Theobjectivefunctionoftheoverallsupplychainscenarioisconcaveunder certainconditions.Sincebydefinition,1 ( , ) SPp µ isconcaveonlyif'' 1 ( , ) SPp µ is negativesemi-definite,forall p and µ .3.3.1.2Scenario2i:AIPCoordinatestheSupplyChainInthiscoordinationstrategy,pricesensitivearrivalrateandtheASP’sprice informationaresharedfromASPtotheAIP.AIPcoordinatesthesupplychaindecisions. ForanygivenunitcapacitypricechargedbytheAIP,theASPdeterminesanoptimalunit salespricethatmaximizesherexpectedprofit.Proposition3.2.WhentheAIPcoordinatesthesupplychaindecisions,theASP willorderthecapacity, *22 * 2 2 22212 44 k kvw w wk µ==Š ,fromtheAIP,andcharges

PAGE 67

52 2 * 2 2212 2 kvw kv wk p k vwkvw w kwkŠ =Š .AndtheoptimumcapacityofAIPCoordinationstrategy islowerthantheSupplyChainCoordinationStrategy, ** 2 1 µµ < .Proof.LettheexpectedprofitfortheASPbeasfollows.2(,) A Pppw µ µ =Š (3.33) Tofindtheoptimalexpectedprofit,2 , m ax(, ) pAPpµ µ where '( )(, ) pVvT µ =Š and µ < ,firstorderconditionsrequire 2(,) 0 dAP d µ =and 2(,) 0 dAP d µ µ= .After somealgebra,firstorderconditionsleadto2221 ( 1)'(/ ) kvwf µ ŠŠ= (3.34) 22221 1 (1) kwµ ŠŠ= (3.35) Eqs.(3.34)and(3.35)canbesimplifiedasthefollowingwiththeconsiderationof 1 / 2 =. 2 * 2 4 '( ) kvwf = (3.36) *2 * 2 2 2 4 k w µ= (3.37) WhentheAIP’smarginalcapacitysalepriceishigherthanthemarginalcost, wc > ,wefindthat 12 ** >and ** 12 µµ > . Aftersomealgebra,fortheM/M/1queuingsystem,alltheseconditionsand assumptionsleadto *22 * 2 2 22212 44 k kvw w wk µ==Š , * 2 2 12 vw k =Š ,

PAGE 68

53 2 * 2 2212 2 kvw kv wk p k vwkvw w kwkŠ =Š . Inthisscenario,theacquiredcapacityandASP’spricetomarketissharedwith theAIP.Utilizingthisinformation,AIPdeterminesaunittransferpricethatmaximizes hisprofit.2() H Pwc µµµ =Š (3.38) Noticethat * 2 µ derivedfromProposition3.2isfunctionof w .Whenitis substitutedintoEq.(3.38)becomes2 () H Pw ,afunctionofw.Hence, 2 11/21/2221/23/2 2() 4242 kwkvwkwkvw HPwccŠŠŠŠ=ŠŠ+ .(3.39) Tofindtheoptimalexpectedprofit,2 m ax( ) w H Pw ,firstorderconditionrequires that 1/21/211/21/2 2() 30 222 dHPwkvwckwvw c dwŠŠ=Š++Š= .(3.40) Let * 2 w tobetheoptimalpricefortheAIPderivedfromEq.(3.40).Whenwe definethe * *** * 2 2222 2 (,) H Pwwc µµµ =Š and ****** 2222222 (,) APppw µµ =Š astheoptimalprofits fortheASPandAIPforthisscenario.Hence,thetotalsupplychainprofitequals * ***** 2 22222222 ( ,)(,)(, ) SPpAPpHPp µµµ =+ .(3.41) Consequently,theexpectedprofitsharesoftheAIPandASPare * * 2 22 * * 2 22 ( , ) ( , ) HPw SPp µ µ and * * 2 22 * * 2 22 ( , ) ( , ) APp SPp µ µ .Closeformsolutionsofoptimal * 2 µ , * 2 p and * 2 w aredifficulttoderive.

PAGE 69

54 Inthenextsection,numericalsolutionsofthesevariablesareobtainedtogainfurther insights.3.3.2CoordinationStrategiesWhentheAIP’sExpectedProfitFunctionIncludes DiseconomiesofScaleInthissection,weanalyzethecoordinationstrategieswhentheAIP’sprofit functionincludesdiseconomiesofscale.3.3.2.1Scenario1j:SupplyChainCoordinationStrategySimilartotheSupplyChaincoordinationstrategyintheprevioussection,inthis scenario,asinglefirmplaysaroleofboththeAIPandASP.WhentheAIPandASP belongstothesamefirm,theproblemisverysimilartoNewsvendormodelwithpricing.Proposition3.3.WhenasinglefirmplaysaroleofboththeAIPandtheASP, theprice w servestheroleofinternaltransferpriceandhasnoeffectonoverallprofit.Proof.Let1 ( , ) SPp µ = betheexpectedprofitforthesupplychainthatisthesum oftheexpectedprofitfunctionsoftheAIPandASPasfollows.111 ( ,)(,)( ) SPpAPpHP µµµ =+ ,(3.42) where1 ( , ) APp µ and1 () HP µ aredefinedinEqs.(3.24)and(3.25).Then,onehas 2 1(,) S Pppce µ µµ =ŠŠ .(3.43) Theprice w perunitofcapacitychargedtotheASPbytheAIPdropsoutinEq. (3.43).Theprice w servestheroleofinternaltransferpriceandhasnoeffectonoverall profit.Q.E.D. Tofindtheoptimalsupplychainprofit,1 , m ax(, ) pSPpµ µ where '( )(, ) pVvT µ =Š and µ < ,firstorderconditionsrequire 1(,) 0 dSP d µ =and

PAGE 70

55 1(,) 0 dSP d µ µ= .Aftersomealgebra,firstorderconditionsleadto2221 ( 1)(2)'(/ ) kvcef µ µ ŠŠ=+ (3.44) and 22221 1 (1)(2) kceµµ ŠŠ=+ .(3.45) Eqs.(3.44)and(3.45)canbesimplifiedasthefollowingwiththeconsiderationof 1 / 2 =: 2 ** 1 1 4 (2)'( ) kvcef µ =+ ,(3.46) 2**2 11 * 1 1 4(2) kceµµ =+ . Inthissetting,asweseefromtheaboveequations,utilizationdependsonthe delayandcapacitycharacteristics.Aftersomealgebra,M/M/1settingleadsto() 2* 1 2 * 11 4(2) 1 kvceµ =+ Š (3.47) and 2**2 11 * 1 1 4(2) kceµµ =+ .(3.48) Let * 1 µ betheoptimalcapacity, * 1 betheoptimalarrivalrateand, * 1 p bethe optimalpricetothemarketderivedfromEqs.(3.47)and(3.48).Define * ***** 1 11111111 ( ,)(,)(, ) SPpAPpHPp µµµ =+ astheoptimalsupplychainprofit.Theobjective functionoftheoverallsupplychainscenarioisconcaveundercertainconditions.

PAGE 71

563.3.2.2Scenario2j:AIPCoordinatestheSupplyChainInthiscoordinationstrategy,pricesensitivearrivalrateandtheASP’sprice informationaresharedfromASPtotheAIP.AIPcoordinatesthesupplychaindecisions. Foranygivenunitcapacityprice w chargedbytheAIP,theASPdeterminesanoptimal unitsalespricethatmaximizesherexpectedprofit.Proposition3.4.WhentheAIPcoordinatesthesupplychaindecisions,theASP willorderthecapacity, *22 * 2 2 22212 44 k kvw w wk µ==Š ,fromtheAIP,andcharges 2 * 2 2212 2 kvw kv wk p k vwkvw w kwkŠ =Š .Proof.Let2 ( , ) APp µ betheexpectedprofitfortheASPasfollows.2(,) A Pppw µ µ =Š (3.49) Tofindtheoptimalexpectedprofit,2 , m ax(, ) pAPpµ µ where '( )(, ) pVvT µ =Š and µ < ,firstorderconditionsrequire 2(,) 0 dAP d µ =and 2(,) 0 dAP d µ µ= .Aftersomealgebra,firstorderconditionsleadto2221 ( 1)'(/ ) kvwf µ ŠŠ= (3.50) 22221 1 (1) kwµ ŠŠ= (3.51) Eqs.(3.50)and(3.51)canbesimplifiedasthefollowingwiththeconsiderationof 1 / 2 =:

PAGE 72

57 2 * 2 4 '( ) kvwf = (3.52) *2 * 2 2 2 4 k w µ= (3.53) Aftersomealgebra,fortheM/M/1queuingsystem,alltheseconditionsand assumptionsleadto *22 * 2 2 22212 44 k kvw w wk µ==Š , * 2 2 12 vw k =Š , and 2 * 2 2212 2 kvw kv wk p k vwkvw w kwkŠ =Š . UnderScenario2j,theacquiredcapacityandASP’spricetomarketissharedfrom theASPtotheAIP.Utilizingthisinformation,AIPproviderusesthisinformation, determinesaunittransferpricethatmaximizeshisprofit. 2 2() H Pwce µµµµ =ŠŠ (3.54) Noticethat * 2 µ derivedfromProposition3.4isfunctionof w .Whenitis substitutedintoEq.(3.54)becomes2 () H Pw ,afunctionofw.Hence, 2 211/21/2221/23/2221/23/2 2() 424242 kwkvwkwkvwkwkvw HPwcceŠŠŠŠŠŠ=ŠŠ+ŠŠ .(3.55) Tofindtheoptimalexpectedprofit,2 m ax( ) w H Pw ,firstorderconditionsrequire that 221/23/2231/25/2 2 231/25/2() 13 2 422422 3 220 422 dHPw kwkvwkwkvw cc dw kwkvw eŠŠŠŠ ŠŠ=Š++Š ŠŠ+= .(3.56)

PAGE 73

58 Let * 2 w istheoptimalpricefortheAIPderivedfromEq.(3.56).Define * ***** 2 2 222222(,) H Pwwce µµµµ =ŠŠ and * **** * 2 22222 2 (,) APppw µ µ =Š astheoptimalprofitsfor theASPandAIPfortheScenario2j.Hence,thetotalsupplychainprofitequals * *** 2 22222 ( ,)( ) S PAPpHPwµ=+.(3.57) Consequently,theexpectedprofitsharesoftheAIPandASPare * * 2 22 * 2 ( , ) HPw SP µ and * * 2 22 * 2 ( , ) APp SP µ .3.3.2.3Scenario3j:ASPCoordinatestheSupplyChainInthiscoordinationstrategy,theASPdoesnotcommunicateanycapacity requirementandpricinginformationwiththeAIP.Instead,theASPapproachestheAIP foraquoteofprice-capacityschedule(i.e.,wasafunctionof µ )andcoordinatesthe supplychaindecisions.Inthisscenario,whentheAIPapproachesfortheprice-capacity schedule,theAIPderivestheprice-capacityschedulebyfindingtheoptimalcapacitythat maximizeshisexpectedprofit.Proposition3.5.WhentheASPcoordinatesthesupplychaindecisions,theAIP announcestheprice-capacityschedule,andcharges 33 2 w ce µ =+totheAIPinorderto maximizehisexpectedprofit.Proof.Let3 () HP µ betheexpectedprofitfortheAIPunderthescenario2j,andas follows 2 3() H Pwce µµµµ =ŠŠ.(3.58) Tofindtheoptimalexpectedprofit,3 m ax( ) HPµ µ ,firstorderconditionsrequire

PAGE 74

59 3() 0 dHP d µ µ= .Aftersomealgebra,wefindthatAIP’soptimalcapacity, 3 () 2 w c e µŠ =andunitcapacityprice, 33 2 w ce µ =+. Utilizingthisinformation,theASPdeterminesasalespriceandanordercapacity thosemaximizeherexpectedprofit.TheASP’sexpectedprofitfunctionis3(,) A Pppw µ µ =Š (3.59) Noticethat 3 w derivedfromProposition3.5isfunctionof µ .Whenitis substitutedintoEq.(3.59)becomes3 ( , ) APp µ ,afunctionof p and µ .Hence, 3 3 ( ,)(2 ) APppwpce µ µ µµ =Š=Š+.(3.60) Tofindtheoptimalexpectedprofit,3 , m ax(, ) pAPpµ µ where '( )(, ) pVvT µ =Š and µ < ,firstorderconditionsrequire 3(,) 0 dAP d µ =and 3(,) 0 dAP d µ µ= .Aftersomealgebra,firstorderconditionsleadto2221 ( 1)(4)'(/ ) kvcef µ µ ŠŠ=+ (3.61) 22221 1 (1)(4) kceµµ ŠŠ=+ (3.62) Eqs.(3.61)and(3.62)canbesimplifiedasthefollowingwiththeconsiderationof 1 / 2 =. 2 ** 3 3 4 (4)'( ) kvcef µ =+(3.63) and 2**2 33 * 3 1 4(4) kceµµ =+ .(3.64)

PAGE 75

60 Aftersomealgebra,fortheM/M/1queuingsystem,alltheseconditionsandassumptions lead() 2* 3 2 * 31 4(4) 1 kvceµ =+ Š (3.65) and 2**2 33 * 3 1 4(4) kceµµ =+ .(3.66) Let * 3 µ istheoptimalcapacity, * 3 istheoptimalarrivalrateand, * 3 p isthe optimalpricetothemarketderivedfromEqs.(3.65)and(3.66).Define * ***** 2 3 333333(,) H Pwwce µµµµ =ŠŠand * **** * 3 33333 3 (,) APppw µ µ =Šastheoptimalprofitsfor theASPandAIPfortheScenario2j.Hence,thetotalsupplychainprofitequals * **** 3 333333 ( ,)(, ) SPAPpHPw µµ =+.(3.67) Consequently,theexpectedprofitsharesoftheAIPandASPare * * 3 33 * 3 ( , ) HPw SP µ and * * 3 33 * 3 ( , ) APp SP µ .3.3.2.4Scenario4j:CompetitiveAlignedCoordinationStrategyInthisscenario,theAIPandASPindividuallydeterminetheiroptimalpolicythat maximizesindividualprofits,andthentheycoordinatetheirdecisionstoreachanaligned policy. Let4 ( , ) APp µ betheexpectedprofitfortheASPasfollows.4(,) A Pppw µ µ =Š (3.68)

PAGE 76

61 TofindtheoptimalexpectedprofitoftheASP,4 , m ax(, ) pAPpµ µ where '( )(, ) pVvT µ =Š and µ < ,firstorderconditionsrequire 4(,) 0 dAP d µ =and 4(,) 0 dAP d µ µ= .Aftersomealgebra,wefindthat *22 * 4 4, 22212 44ASP kkvw wwk µ==Š as giveninProposition3.4.Giventhesameperunitcapacityprice w, theAIPmaximizes it’sprofitfunction,4 m ax( ) HPµ µ ,firstorderconditionsrequire 4() 0 dHP d µ µ= asgivenin Proposition3.5.Aftersomealgebra,wefindthattheAIP’soptimalcapacity, * 4, () 2 AIP w c e µŠ =.Themutuallyagreeablepolicyimpliesthat * * * 4 ,4, 4 ASPAIP µµµ ==(3.69) Inthisscenario,bydefinition * 4,() 1 0 when 0 2 AIPdw e d weµ =>> ,* 4, A I P µisastrictly increasingfunctionof w and * 2 4, 35/2() 3 0whenand0 24 ASPdw kkv kv d w ww µ=Š+<> ,* 4, A S P µis astrictlydecreasingfunctionof w .Thusthereisauniquesolutioninthisscenario. Let * 4 w betheoptimalpricefortheAIPderivedfromEq.(3.69).Define * ***** 2 4 444444(,) H Pwwce µµµµ =ŠŠ and * **** * 4 44444 4 (,) APppw µ µ =Š astheoptimalprofitsfor theASPandAIPforthisscenario.Hence,thetotalsupplychainprofitequals * ***** 4 44444444 ( ,)(,)(, ) SPpAPpHPp µµµ =+ .(3.70) Consequently,theexpectedprofitsharesoftheAIPandASPare * * 4 44 * * 4 44 ( , ) ( , ) HPw SPp µ µ and * * 4 44 * * 4 44 ( , ) ( , ) APp SPp µ µ .Closeformsolutionsofoptimal * 4 µ , * 4 p and * 4 w aredifficulttoderive.In

PAGE 77

62 thenumericalexplorationssection,numericalsolutionsofthesevariablesareobtainedto gainfurtherinsights.3.4NumericalExplorationsTodrawmoremanagerialinsightfromthesemodels,weexamineaseriesof computationalresults.Further,weexploretheimpactofthreekeyparametersonthe supplychainperformanceunderthetwoconditionswithfourdifferentscenarios, including(1)delaycostofthecomputersystemperunitoftimeperjob, v ,(2)perunit capacitycostoftheAIP, c ,(3)diseconomyofscaleparameterofprovidingthecapacity, e . We first select a set of baseline parameters for the supply chain model, see Table 3-6. Foreachscenario,wevaryoneparameteratatimeoverarangeofvaluesandcalculate ninestatistics–thewholesupplychain’sprofit,theAIP’sprofit,theASP’sprofit, percentofAIP’sprofitagainstthatofthesupplychain,percentoftheASP’sprofit againstthatofthesupplychain,capacity,arrivalrate,utilizationratioandmarketprice. TheresultsaregiveninTable3-8toTable3-15. Inouranalysis,wefirstexaminethecoordinationstrategieswheretheAIP’s expectedprofitfunctionislinear,withoutdiseconomiesofscale.Wethenanalyzethe coordinationstrategieswheretheAIP’sexpectedprofitfunctioniswithdiseconomiesof scale.Inboth,westudytheimpactofqueuingdelaysonmarketprice,arrivalrateand capacityoftheservice.Inaddition,weexaminethecoordinationstrategiesandthe associatedpoliciesthatwouldimproveASPsupplychaincoordinationdesignand performanceinadditiontoeachparty’sperformance. Thirty-twofiguresarecreatedforbothscenariostoanalyzethequeuingaffects and supply chain performance by exploring three parameters, resulting in Figure 3-17 to Figure 3-48. The first group of figures, Figure 3-17 to Figure 3 -25, examines the impact

PAGE 78

63 ofdelayandcapacitycostsonthesupplychain,utilizationratio,capacity,arrivalrateand marketpricewhentheAIP’sexpectedprofitfunctioniswithoutdiseconomiesofscale. The second group of figures, Figure 3-26 to Figure 3-48, analyzes the effect of delay and capacitycosts,anddiseconomyofscalewhentheAIP’sexpectedprofitfunctionincludes diseconomiesofscale. Severalimportantfindingsarederivedfromthenumericalanalysis.First,forall possible combination of parameters in Figure 3-17 to Figure 3-21 and Figure 3-26 to Figure 3-32 the delay cost impacts the supply chain’s expected profit, utilization ratio, capacityandarrivalratenegatively.Underallcoordinationscenarios,theseitems decreaseasthedelaycostincreases,asthemarketpriceincreases.Inotherwords,when thereisdelay,therearefewernewarrivalstothesystem.Thereisareverserelationship betweenthedelaycostandtheutilizationratio.Delayleadstolessnewarrivals,thus causeslessutilizationratio.Thentheorganizationreducestheavailablecapacity.Also themarketpricefollowstheoppositedirectionofthearrivalrate.Whenthearrivalrate decreasesthemarketpriceincreasesandviceversa.Surprisinglytheimpactsofthedelay costandcapacitycostsarehighertothewholesupplychainperformancewhenthe coordinationstrategyisthewholesupplychainorcompetitivealigned.Oneprobable interpretationofthisresultisthefollowing.Inthedecentralizedstrategies,theimpactsof thedelayandcapacitycostsmighthavebeensharedbetweentheinvolvedparties.The marketpriceisthelowest,andthecapacityandthearrivalratearethehighestwhenthe supply chain is coordinated by the AIP. From, Figure 3-22, Figure 3-33 and Figure 3-34, alsowhendelaycostincreasesexpectedprofitshareoftheASPdecreasesandexpected profitshareoftheAIPincreases.Basicallydelaycostimpactsmoresignificantlytothe

PAGE 79

64 playerwhoisclosertothemarket. Secondly, we observe from Figure 3-23, Figure 3-24 and Figure 3-35 to Figure 338 that the e xpected profits and utilization ratio decrease under all c oordina tion strategies astheunitcapacitycost,c,increases.Wediscoverthattheimpactofcapacitycosttothe ASPisthelowestwhentheAIPcoordinatesthesupplychain.Anditisviseversawhen theASPcoordinatesthesupplychain. Th irdly, from Figure 3 -26, Figure 3 -29 to Figure 3 -32, Figure 3-35, Figure 3 -38 and Figure 3-41, for all combination of parameters, the competitive aligned coordination strategygeneratesthesameutilizationratioandtheexpectedprofitwiththesupply chain’scoordinationstrategy.Theoverallsupplychainperformance,utilizationratio, capacityandarrivalratearethehighestwhenthesupplychainiscoordinatedasa competitivealigned.Wediscoveradecentralizedcoordinationmechanismtoachievethe samegoalofmaximizingthewholesupplychain’sperformance.Theclosest performanceisreceivedwhensupplychainiscoordinatedbytheASPinsteadoftheAIP. Thisfindingseemstosuggestthatintheabsenceofcompetitivealignedandacentralized system,itisbettertolettheplayerwhoisclosertothemarket,coordinatethesupply chain.AnotherfindingisthatthemarketpriceisthelowestwhentheASPcoordinates. ThecapacityishigherwhentheASPcoordinatescomparedtotheAIPcoordinates.The ASPsimplydoesnothavetheincentiveinthiscasetobetterpredictthemarketdemand. TheASPkeepsthecapacityashighaspossible.Wealsonoticetheeffectofthecapacity relateddiseconomiesofscaletotheoptimumperformancesandcapacitiesofeachplayer. From Figure 3-17, Figure 3-27 and Figure 3-28 we find that whoever coordinates thesupplychainreceivesthegreaterprofitthantheotherplayer’scoordinationstrategy.

PAGE 80

65 Whoevercoordinatesthesupplychainexploitstheinformationsharedfromtheother partnerbyincludingtheinformationintheobjectivefunction. From Figure 3-41, the diseconomy of scale parameter affects the whole supply chain expected profit negatively under all coordination strategies. From Figure 3-42, the expectedprofitoftheAIPdecreaseswhenthediseconomyofscaleincreasesunderthe AIP’scoordinationstrategy,inthemeantimetheAIP’sexpectedprofitincreasesunder theASP’sandcompetitivealignedstrategies.Theimpactofdiseconomiesofscaletothe utilizationratioandcapacitywhentheAIPcoordinatesthesupplychain.Themarket priceisnotaffectedbythediseconomyofscalesignificantlywhentheASPcoordinates the supply chain as it is shown in Figure 3-46 to Figure 3-48. Finally, from Figure 3 -42 to Figure 3 -48, when there is a diseconomy of scale, the AIPincreasestheunitsaleprice, w ,inordertokeephisexpectedprofitsharehigh.Price increasecauseslessarrivalsandlesscapacityneeds.

PAGE 81

66 Table3-6SummaryofnotationforModel2 Serviceparameters: poissonarrivalrateofjobs(transactions)tothesystemperunitoftime µ servicerateoftheApplicationServiceProvider( µ < ) utilizationratioofthesystem( / µ = ) v delaycostofsystemperunitoftimeperjob Revenueandcosts: w AIP’sunitcapacityprice c AIP’sinternalmarginalcostforthecapacity pA SP’spriceperjob e diseconomiesofscalecostparameterforAIP(e>0) HP AIP’sprofitfunction AP ASP’sprofitfunction SP supplychainprofitfunction () VgrossvalueoftheASPservicetothemarketperunitoftimewhenthearrivalrate is . '() VmarginalvalueofASPservice Table3-7BaselineparametersfornumericalexplorationsforModel2 ParametersBaselineValues PerunitcapacitycostoftheAIP, c 1.00 Demandfunctionparameter,0.50 Delaycostofthecomputersystemperunitof timeperjob, v 0.20 Demandfunctionparameter, k 1.00 Diseconomyofscaleparameterofproviding thecapacity, e 0.10

PAGE 82

673.4.1NumericalExplorations–Condition1:AIP’sExpectedProfitFunctionis LinearTheresultsoftheexperimentalanalysisforthefirstconditionwhentheAIP’s expectedprofitfunctionislinearareillustratedinthissection.

PAGE 83

68 Table3-8Impactofdelaycost,v(perunitoftimeperjob)whentheAIPhasalinearcostfunctionCapacityCostParameter c 1.001.001.001.001.001.001.001.001.001.001.00 Demandfunctionparameter 0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.040.060.080.100.120.140.160.180.200.220.24 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 µ1 *0.15000.12750.10860.09190.07680.06290.05000.03790.02640.01550.0051 1 *0.09000.06510.04720.03380.02360.01580.01000.00570.00280.00100.0001 1 *0.60000.51010.43430.36750.30720.25170.20000.15150.10560.06190.0202 p 1 *2.66672.96043.30253.72084.25544.97356.00007.601910.472117.150750.4949 Scenario1.1:SupplyChain SP10.09000.06510.04720.03380.02360.01580.01000.00570.00280.00100.0001 µ2 *0.04450.03990.03590.03200.02810.02420.02030.01610.01180.00720.0025 2 *0.02160.01550.01120.00810.00560.00380.00240.00140.00070.00020.0000 2 *0.48580.38830.31270.25150.20000.15650.11910.08650.05800.03260.0102 p 2 *5.05525.57566.19796.97097.99989.385811.388714.559020.220333.6513100.8566 w2 *1.65281.55931.47631.40071.33331.27041.21241.15901.10911.06341.0205 HP 20.02900.02230.01710.01280.00940.00660.00430.00260.00130.00050.0001 AP 20.03570.02420.01660.01130.00750.00480.00290.00160.00080.00030.0000 SP20.06470.04650.03360.02410.01690.01140.00720.00420.00200.00070.0001 HP 2/SP20.44840.48020.50780.53220.55550.57620.59520.61330.62900.64630.6626 Scenario1.2:AIPCoordinates AP 2/SC20.55160.51980.49220.46780.44450.42380.40480.38670.37100.35370.3374

PAGE 84

69 Table3-9Impactofcapacitycost, c (perunitofcapacity)whentheAIPhasalinearcostfunctionCapacityCostParameter c 0.200.300.400.500.600.700.800.901.001.101.20 Demandfunctionparameter 0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.200.200.200.200.200.200.200.200.200.200.20 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 µ1 *3.751.420.680.370.210.130.080.050.030.010.00 1 *2.250.720.290.140.070.030.020.010.000.000.00 1 *0.600.510.430.370.310.250.200.150.110.060.02 p 1 *0.530.891.321.862.553.484.806.8410.4718.8760.59 Scenario1.1:SupplyChain SP10.450.220.120.070.040.020.010.010.000.000.00 µ2 *1.10660.44350.22410.12770.07810.04940.03160.01990.01180.00600.0017 2 *0.53710.17220.07010.03210.01560.00770.00380.00170.00070.00020.0000 2 *0.48530.38820.31260.25110.20000.15640.11900.08650.05800.03300.0103 p 2 *1.01341.67282.47953.49284.80146.57509.119813.107220.220336.5334119.9406 w2 *0.33110.46780.59060.70100.80010.88950.97011.04321.10911.16871.2243 HP 20.14510.07440.04270.02570.01560.00940.00540.00280.00130.00040.0000 AP 20.17780.08050.04140.02250.01250.00690.00370.00180.00080.00020.0000 SP20.32290.15500.08410.04820.02810.01620.00900.00460.00200.00060.0001 HP 2/SP20.44930.48020.50790.53320.55570.57660.59570.61350.62900.64030.6585 Scenario1.2:AIPCoordinates AP 2/SC20.55070.51980.49210.46680.44430.42340.40430.38650.37100.35970.3415

PAGE 85

70 Figure3-17ImpactofdelaycostonoverallsupplychainwhentheAIPhasalinearcost function Figure3-18ImpactofdelaycostonutilizationratiowhentheAIPhasalinearcost function SupplyChainPerformance0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.040.060.080.100.120.140.160.180.200.220.24 DelayCostParameter, vExpectedProfit SupplyChain AIPCoordinates UtilizationRatio0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.04 0.06 0.08 0.10 0.12 0. 1 4 0. 1 6 0 . 1 8 0 . 20 0.22 0.24DelayCostParameter, vUtilizationRatio SupplyChain AIPCoordinates

PAGE 86

71 Figure3-19ImpactofdelaycostoncapacitywhentheAIPhasalinearcostfunction Figure3-20ImpactofdelaycostonmarketpricewhentheAIPhasalinearcostfunction Capacity0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.040.060.080.100.120.140.160.180.200.220.24 DelayCostParameter, vCapacity SupplyChain AIPCoordinates MarketPrice0 20 40 60 80 100 120 0.040.060.080.100.120.140.160.180.200.220.24 DelayCostParameter, v MarketPrice SupplyChain AIPCoordinates

PAGE 87

72 Figure3-21ImpactofdelaycostonarrivalratewhentheAIPhasalinearcostfunction Figure3-22ImpactofdelaycostonexpectedprofitsharewhentheAIPhasalinearcost function ExpectedProfitShare-AIPCoordinates0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.700 . 0 4 0 . 0 6 0 . 0 8 0 .1 0 0 .1 2 0 .1 4 0 . 1 6 0 . 1 8 0 .2 0 0 .2 2 0 .2 4DelayCostParameter, vExpectedProfitShare AIP'sProfitShare-AIP Coordinates ASP'sProfitShare-AIP Coordinates ArrivalRate0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.040.060.080.100.120.140.160.180.200.220.24 DelayCostParameter, vArrivalRate SupplyChain AIPCoordinates

PAGE 88

73 Figure3-23ImpactofcapacitycostonoverallsupplychainwhentheAIPhasalinear costfunction Figure3-24ImpactofcapacitycostonutilizationratiowhentheAIPhasalinearcost function SupplyChainPerformance0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfit SupplyChain AIPCoordinates UtilizationRatio0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, c UtilizationRatio SupplyChain AIPCoordinates

PAGE 89

74 Figure3-25ImpactofcapacitycostonexpectedprofitsharewhentheAIPhasalinear costfunction ExpectedProfitShare-AIPCoordinates0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfitShare AIP'sProfitShare-AIP Coordinates ASP'sProfitShare-AIP Coordinates

PAGE 90

75 3.4.2NumericalExplorations–Condition2:AIP’sExpectedProfitFunction IncludesDiseconomiesofScale TheresultsoftheexperimentalanalysisforthesecondconditionwhentheAIP’s expectedprofitfunctionincludesthediseconomiesofscaleareillustratedinthissection.

PAGE 91

76 Table3-10Impactofdelaycost, v (perunitoftimeperjob)whentheAIP’scostfunctionincludesdiseconomiesofscale(for Scenario2.1andScenario2.2)CapacityCostParameter c 1.001.001.001.001.001.001.001.001.001.001.00 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.040.060.080.100.120.140.160.180.200.220.24 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 1.001.001.001.001.001.001.001.001.001.001.00 µ1 *0.09820.08560.07460.06440.05480.04580.03700.02870.02020.01220.0042 1 *0.05520.04020.02940.02110.01480.01000.00630.00370.00180.00060.0001 1 *0.56240.46980.39400.32810.26970.21800.17080.12830.08760.05120.0170 p 1 *3.32383.66464.06364.56875.22806.09887.36159.283312.911521.018660.0979 Scenario2.1:SupplyChain SP10.07580.05440.03930.02800.01950.01300.00820.00470.00230.00080.0001 µ2 *0.03780.03420.03100.02770.02460.02120.01780.01420.01050.00640.0022 2 *0.01770.01270.00920.00660.00460.00310.00200.00110.00060.00020.0000 2 *0.46900.37130.29640.23610.18680.14480.10940.07880.05280.02940.0090 p 2 *5.51956.08296.76707.63598.754710.323112.561616.130722.368937.5469114.6674 w2 *1.76221.64701.54711.45871.37781.30591.23921.17861.12151.07061.0230 HP 20.02740.02100.01600.01200.00870.00600.00390.00230.00120.00040.0000 AP 20.03120.02090.01420.00960.00630.00400.00240.00130.00060.00020.0000 SP20.05860.04190.03020.02150.01500.01010.00640.00360.00180.00060.0001 HP 2/SP20.46710.50050.52950.55580.57850.60080.62010.63890.65220.67150.6936 Scenario2.2:AIPCoordinates AP 2/SP20.53290.49950.47050.44420.42150.39920.37990.36110.34780.32850.3064

PAGE 92

77 Table3-11Impactofdelaycost,v(perunitoftimeperjob)whentheAIP’scostfunctionincludesdiseconomiesofscale(for Scenario2.3andScenario2.4)CapacityCostParameter c 1.001.001.001.001.001.001.001.001.001.001.00 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.040.060.080.100.120.140.160.180.200.220.24 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 1.001.001.001.001.001.001.001.001.001.001.00 µ3 *0.07840.06870.06010.05220.04460.03740.03040.02360.01680.01010.0035 3 *0.04250.03070.02220.01590.01100.00740.00460.00270.00130.00040.0001 3 *0.54150.44680.36990.30470.24760.19750.15280.11310.07650.04380.0143 p 3 *3.73994.12824.59365.17445.94076.97048.463610.753215.014124.768771.5502 w3 *1.15691.13751.12021.10431.08921.07471.06071.04721.03361.02021.0070 HP 30.00620.00470.00360.00270.00200.00140.00090.00060.00030.00010.0000 AP 30.06810.04860.03480.02460.01700.01130.00700.00400.00190.00070.0001 SP30.07430.05330.03840.02740.01900.01270.00800.00460.00220.00080.0001 HP 3/SP30.08280.08860.09400.09940.10460.11010.11570.12240.12810.13570.1512 Scenario2.3:ASPCoordinates AP 3/SP30.91720.91140.90600.90060.89540.88990.88430.87760.87190.86430.8488 µ4 *0.09820.08580.07460.06440.05490.04590.03710.02860.02020.01210.0040 4 *0.05530.04030.02940.02110.01480.01000.00630.00360.00180.00060.0001 4 *0.56250.47000.39370.32810.27020.21850.17100.12760.08760.05070.0164 p 4 *3.32353.66064.06714.56865.21676.08217.35179.340812.915621.232662.3308 w4 *1.19641.17041.14881.12861.10971.09061.07371.05701.04051.02411.0077 HP 40.00960.00730.00550.00410.00300.00210.00140.00080.00040.00010.0000 AP 40.06610.04720.03370.02380.01640.01090.00680.00390.00180.00060.0001 SP40.07580.05440.03930.02800.01950.01300.00820.00470.00230.00080.0001 HP 4/SP40.12730.13330.14110.14790.15450.15800.16630.17440.18210.18810.1813 Scenario2.4:CompetitiveAligned AP 4/SP40.87270.86670.85890.85210.84550.84200.83370.82560.81790.81190.8187

PAGE 93

78 Table3-12Impactofcapacitycost,c(perunitofcapacity)whentheAIP’scostfunctionincludesdiseconomiesofscale(forScenario 2.1andScenario2.2)CapacityCostParameter c 0.200.300.400.500.600.700.800.901.001.101.20 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.200.200.200.200.200.200.200.200.200.200.20 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 1.001.001.001.001.001.001.001.001.001.001.00 µ1 *0.20420.17140.14080.11300.08790.06630.04780.03250.02020.01050.0031 1 *0.06170.04850.03680.02690.01860.01220.00730.00390.00180.00060.0001 1 *0.30230.28330.26160.23820.21170.18370.15350.12110.08760.05300.0178 p 1 *2.62092.91043.28633.77124.44335.36666.73278.935712.911522.257268.9706 Scenario2.1:SupplyChain SP10.07930.06050.04490.03230.02220.01450.00890.00490.00230.00070.0001 µ2 *0.14090.11240.08780.06680.04960.03580.02500.01680.01050.00540.0016 2 *0.03690.02670.01860.01230.00780.00460.00250.00130.00060.00020.0000 2 *0.26170.23750.21180.18460.15670.12890.10180.07640.05280.03010.0097 p 2 *3.28543.78624.44455.33296.56038.308810.919915.020022.368940.2023127.5385 w2 *0.68140.72670.77670.83110.88890.94861.00851.06631.12151.17581.2259 HP 20.04800.03530.02540.01770.01190.00760.00460.00250.00120.00040.0000 AP 20.02510.01940.01440.01030.00690.00440.00260.00140.00060.00020.0000 SP20.07310.05470.03980.02790.01880.01200.00720.00390.00180.00060.0001 HP 2/SP20.65630.64550.63730.63270.63200.63510.64140.64720.65220.66510.6708 Scenario2.2:AIPCoordinates AP 2/SP20.34370.35450.36270.36730.36800.36490.35860.35280.34780.33490.3292

PAGE 94

79 Table3-13Impactofcapacitycost,c(perunitofcapacity)whentheAIP’scostfunctionincludesdiseconomiesofscale(forScenario 2.3andScenario2.4)CapacityCostParameter c 0.200.300.400.500.600.700.800.901.001.101.20 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.200.200.200.200.200.200.200.200.200.200.20 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 1.001.001.001.001.001.001.001.001.001.001.00 µ3 *0.12600.10850.09200.07620.06170.04840.03640.02580.01680.00900.0027 3 *0.03140.02540.01990.01500.01090.00750.00470.00270.00130.00040.0000 3 *0.24960.23370.21690.19750.17700.15450.13020.10400.07650.04670.0159 p 3 *3.52413.87434.30374.88165.63146.67698.208210.656315.014125.473377.5199 w3 *0.45190.51700.58390.65240.72340.79680.87280.95161.03361.11811.2054 HP 30.01590.01180.00850.00580.00380.00230.00130.00070.00030.00010.0000 AP 30.05390.04210.03210.02370.01690.01140.00710.00400.00190.00060.0001 SP30.06970.05390.04060.02960.02070.01370.00850.00470.00220.00070.0001 HP 3/SP30.22750.21830.20830.19650.18420.17080.15670.14180.12810.11300.0996 Scenario2.3:ASPCoordinates AP 3/SP30.77250.78170.79170.80350.81580.82920.84330.85820.87190.88700.9004 µ4 *0.20420.17110.14030.11290.08800.06600.04780.03250.02020.01050.0030 4 *0.06180.04840.03670.02690.01860.01210.00730.00390.00180.00060.0001 4 *0.30240.28290.26120.23800.21200.18340.15350.12130.08760.05300.0177 p 4 *2.62052.91543.29353.77614.43785.38016.73168.924112.915622.274369.2180 w4 *0.60840.64280.68220.72590.77620.83360.89570.96521.04051.12101.2061 HP 40.04170.02940.01990.01280.00780.00450.00230.00110.00040.00010.0000 AP 40.03760.03110.02500.01950.01450.01010.00660.00380.00180.00060.0001 SP40.07930.06050.04490.03230.02220.01450.00890.00490.00230.00070.0001 HP 4/SP40.52600.48570.44320.39540.34910.30690.25840.21810.18210.14990.1235 Scenario2.4:CompetitiveAligned AP 4/SP40.47400.51430.55680.60460.65090.69310.74160.78190.81790.85010.8765

PAGE 95

80 Table3-14Impactofdiseconomyofscale, e (perunitofcapacity)whentheAIP’scostfunctionincludesdiseconomiesofscale(for Scenario2.1andScenario2.2)CapacityCostParameter C 1.001.001.001.001.001.001.001.001.001.001.00 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.200.200.200.200.200.200.200.200.200.200.20 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 0.200.300.400.500.600.700.800.901.001.101.20 µ1 *0.02490.02410.02340.02280.02230.02170.02120.02070.02020.01980.0194 1 *0.00250.00240.00230.00220.00210.00200.00190.00180.00180.00170.0016 1 *0.10150.09930.09730.09550.09390.09220.09060.08910.08760.08630.0850 p 1 *10.955511.222111.482411.736211.960212.206612.447412.682312.911513.136413.3555 Scenario2.1:SupplyChain SP10.00270.00260.00250.00250.00240.00240.00230.00230.00230.00220.0022 µ2 *0.01140.01130.01120.01100.01090.01080.01060.01050.01050.01030.0102 2 *0.00060.00060.00060.00060.00060.00060.00060.00060.00060.00050.0005 2 *0.05670.05610.05550.05500.05440.05390.05340.05280.05280.05190.0514 p 2 *20.741320.973021.202821.430721.656821.881122.103522.368922.368922.766222.9853 w2 *1.11231.11371.11511.11641.11771.11891.12011.12151.12151.12361.1247 HP 20.00130.00120.00120.00120.00120.00120.00120.00120.00120.00120.0011 AP 20.00070.00070.00070.00070.00070.00060.00060.00060.00060.00060.0006 SP20.00200.00200.00190.00190.00190.00180.00180.00180.00180.00180.0017 HP 2/SP20.63580.63850.64120.64380.64630.64870.65110.65440.65220.65810.6603 Scenario2.2:AIPCoordinates AP 2/SP20.36420.36150.35880.35620.35370.35130.34890.34560.34780.34190.3397

PAGE 96

81 Table3-15Impactofdiseconomyofscale, e (perunitofcapacity)whentheAIP’scostfunctionincludesdiseconomiesofscale(for Scenario2.3andScenario2.4)CapacityCostParameter C 1.001.001.001.001.001.001.001.001.001.001.00 Demandfunctionparameter0.500.500.500.500.500.500.500.500.500.500.50 DelayCostParameter v 0.200.200.200.200.200.200.200.200.200.200.20 Demandfunctionparameter k 1.001.001.001.001.001.001.001.001.001.001.00 DiseconomyofScaleParameter e 0.200.300.400.500.600.700.800.901.001.101.20 µ3 *0.02350.02220.02130.02030.01940.01860.01800.01730.01680.01620.0157 3 *0.00230.00210.00190.00180.00170.00150.00140.00140.00130.00120.0011 3 *0.09750.09380.09110.08790.08510.08250.08030.07810.07650.07430.0726 p 3 *11.462811.976012.376412.867813.342713.807514.219414.656715.014115.488615.8830 w3 *1.00941.01331.01701.02031.02331.02611.02871.03121.03361.03561.0377 HP 30.00010.00010.00020.00020.00020.00020.00030.00030.00030.00030.0003 AP 30.00250.00240.00230.00230.00220.00210.00200.00200.00190.00190.0018 SP30.00260.00260.00250.00250.00240.00230.00230.00220.00220.00220.0021 HP 3/SP30.04160.05740.07190.08370.09420.10350.11240.12010.12810.13390.1402 Scenario2.3:ASPCoordinates AP 3/SP30.95840.94260.92810.91630.90580.89650.88760.87990.87190.86610.8598 µ4 *0.02480.02410.02340.02280.02220.02170.02120.02070.02020.01980.0194 4 *0.00250.00240.00230.00220.00210.00200.00190.00180.00180.00170.0016 4 *0.10120.09920.09730.09540.09370.09220.09050.08910.08760.08630.0850 p 4 *10.990611.243811.493111.738511.980212.203312.452812.683912.915613.138013.3616 w4 *1.00981.01441.01871.02281.02671.03011.03391.03731.04051.04361.0466 HP 40.00010.00020.00020.00030.00030.00030.00040.00040.00040.00040.0005 AP 40.00250.00240.00230.00220.00210.00210.00200.00190.00180.00180.0017 SP40.00270.00260.00250.00250.00240.00240.00230.00230.00230.00220.0022 HP 4/SP40.04570.06640.08590.10430.12160.13580.15330.16790.18210.19490.2075 Scenario2.4:CompetitiveAligned AP 4/SP40.95430.93360.91410.89570.87840.86420.84670.83210.81790.80510.7925

PAGE 97

82 Figure3-26ImpactofdelaycostonoverallsupplychainwhentheAIPÂ’scostfunction includesdiseconomiesofscale Figure3-27ImpactofdelaycostonAIPÂ’sexpectedprofitwhentheAIPÂ’scostfunction includesdiseconomiesofscale SupplyChainPerformance0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080.04 0.06 0. 0 8 0 . 1 0 0 . 1 2 0 . 1 4 0 . 16 0.18 0.20 0.22 0.24DelayCostParameter, vExpectedProfit SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned AIP'sExpectedProfit0.00 0.01 0.01 0.02 0.02 0.03 0.030 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 0 . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0 . 2 0 0 . 2 2 0 . 2 4DelayCostParameter, vExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 98

83 Figure3-28ImpactofdelaycostonASPÂ’sexpectedprofitwhentheAIPÂ’scostfunction includesdiseconomiesofscale Figure3-29ImpactofdelaycostonutilizationratiowhentheAIPÂ’scostfunction includesdiseconomiesofscale ASP'sExpectedProfit0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0. 2 2 0. 2 4DelayCostParameter, vExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned UtilizationRatio0.00 0.10 0.20 0.30 0.40 0.50 0.600 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 0 . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0 . 2 0 0 . 2 2 0 . 2 4DelayCostParameter, v UtilizationRatio SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 99

84 Figure3-30ImpactofdelaycostoncapacitywhentheAIPÂ’scostfunctionincludes diseconomiesofscale Figure3-31ImpactofdelaycostonmarketpricewhentheAIPÂ’scostfunctionincludes diseconomiesofscale Capacity0.00 0.02 0.04 0.06 0.08 0.10 0.120.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0. 2 2 0. 2 4DelayCostParameter, vCapacity SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned MarketPrice0 20 40 60 80 100 120 1400 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 0 . 1 2 0.14 0.16 0.18 0.20 0.22 0.24DelayCostParameter, v MarketPrice SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 100

85 Figure3-32ImpactofdelaycostonarrivalratewhentheAIPÂ’scostfunctionincludes diseconomiesofscale Figure3-33ImpactofdelaycostonAIPÂ’sexpectedprofitsharewhentheAIPÂ’scost functionincludesdiseconomiesofscale ArrivalRate0.00 0.01 0.02 0.03 0.04 0.05 0.060.04 0.06 0.08 0. 1 0 0. 1 2 0.14 0.16 0.18 0. 2 0 0. 2 2 0. 2 4DelayCostParameter, vArrivalRate SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned AIP'sExpectedProfitShare0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.800. 0 4 0 . 0 6 0.08 0.10 0.12 0.14 0. 1 6 0 . 18 0.20 0.22 0.24DelayCostParameter, vExpectedProfitShare AIP'sProfitShare-AIP Coordinates AIP'sProfitShare-ASP Coordinates AIP'sProfitShareCompetitiveAligned

PAGE 101

86 Figure3-34ImpactofdelaycostonASPÂ’sexpectedprofitsharewhentheAIPÂ’scost functionincludesdiseconomiesofscale Figure3-35ImpactofcapacitycostonoverallsupplychainwhentheAIPÂ’scost functionincludesdiseconomiesofscale SupplyChainPerformance0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfit SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned ASP'sExpectedProfitShare0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.000. 0 4 0 . 06 0.08 0.10 0.12 0 . 1 4 0.16 0.18 0.20 0. 2 2 0 . 24DelayCostParameter, vExpectedProfitShare ASP'sProfitShare-AIP Coordinates ASP'sProfitShare-ASP Coordinates ASP'sProfitShareCompetitiveAligned

PAGE 102

87 Figure3-36ImpactofcapacitycostonAIPÂ’sexpectedprofitwhentheAIPÂ’scost functionincludesdiseconomiesofscale Figure3-37ImpactofcapacitycostonASPÂ’sexpectedprofitwhentheAIPÂ’scost functionincludesdiseconomiesofscale AIP'sExpectedProfit0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned ASP'sExpectedProfit0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfit AIPCoordinates ASPCoordinates CompetitiveAligned

PAGE 103

88 Figure3-38ImpactofcapacitycostonutilizationratiowhentheAIPÂ’scostfunction includesdiseconomiesofscale Figure3-39ImpactofcapacitycostonAIPÂ’sexpectedprofitsharewhentheAIPÂ’scost functionincludesdiseconomiesofscale UtilizationRatio0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, c UtilizationRatio SupplyChain AIPCoordinates ASPCoordinates CompetitiveAligned AIP'sExpectedProfitShare0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfitShare AIP'sProfitShare-AIP Coordinates AIP'sProfitShare-ASP Coordinates AIP'sProfitShareCompetitiveAligned

PAGE 104

89 Figure3-40ImpactofcapacitycostonASPÂ’sexpectedprofitsharewhentheAIPÂ’scost functionincludesdiseconomiesofscale Figure3-41ImpactofdiseconomiesofscaleonoverallsupplychainwhentheAIPÂ’s costfunctionincludesdiseconomiesofscale SupplyChainPerformance0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterExpectedProfit SupplyChain ASPCoordinates AIPCoordinates CompetitiveAligned ASP'sExpectedProfitShare0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.20.30.40.50.60.70.80.91.01.11.2 CapacityCostParameter, cExpectedProfitShare ASP'sProfitShare-AIP Coordinates ASP'sProfitShare-ASP Coordinates ASP'sProfitShareCompetitiveAligned

PAGE 105

90 Figure3-42ImpactofdiseconomiesofscaleonAIPÂ’sexpectedprofitwhentheAIPÂ’s costfunctionincludesdiseconomiesofscale Figure3-43ImpactofdiseconomiesofscaleonASPÂ’sexpectedprofitwhentheAIPÂ’s costfunctionincludesdiseconomiesofscale AIP'sExpectedProfit0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterExpectedProfit ASPCoordinates AIPCoordinates CompetitiveAligned ASP'sExpectedProfit0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterExpectedProfit ASPCoordinates AIPCoordinates CompetitiveAligned

PAGE 106

91 Figure3-44ImpactofdiseconomiesofscaleonutilizationratiowhentheAIPÂ’scost functionincludesdiseconomiesofscale Figure3-45ImpactofdiseconomiesofscaleoncapacitywhentheAIPÂ’scostfunction includesdiseconomiesofscale UtilizationRatio0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameter UtilizationRatio SupplyChain ASPCoordinates AIPCoordinates CompetitiveAligned Capacity0.00 0.01 0.01 0.02 0.02 0.03 0.03 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterCapacity SupplyChain ASPCoordinates AIPCoordinates CompetitiveAligned

PAGE 107

92 Figure3-46ImpactofdiseconomiesofscaleonmarketpricewhentheAIPÂ’scost functionincludesdiseconomiesofscale Figure3-47ImpactofdiseconomiesofscaleonAIPÂ’sexpectedprofitsharewhenthe AIPÂ’scostfunctionincludesdiseconomiesofscale MarketPrice0 5 10 15 20 25 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameter MarketPrice SupplyChain ASPCoordinates AIPCoordinates CompetitiveAligned AIP'sExpectedProfitShare0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterExpectedProfitShare AIP'sProfitShare-AIP Coordinates AIP'sProfitShare-ASP Coordinates AIP'sProfitShareCompetitiveAligned

PAGE 108

93 Figure3-48ImpactofdiseconomiesofscaleonASPÂ’sexpectedprofitsharewhenthe AIPÂ’scostfunctionincludesdiseconomiesofscale ASP'sExpectedProfitShare0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.20.30.40.50.60.70.80.91.01.11.2 DiseconomyofScaleParameterExpectedProfitShare ASP'sProfitShare-AIP Coordinates ASP'sProfitShate-ASP Coordinates ASP'sProfitShareCompetitiveAligned

PAGE 109

94 CHAPTER4 DUOPOLISTICPRICEANDCAPACITYCOMPETITIONOFAPPLICATION SERVICEPROVIDERSWITHTHEQUEUINGEFFECTS 4.1IntroductionofDuopolisticPriceandCapacityCompetitions Price,speedandqualityarethemostimportantdimensionsofanyserviceand productionindustries.Companiesneedtousetheweightofeachofthesecomponentsin ordertocompete,stayinbusinessandbeprofitable.Recently,theconceptofapplication serviceprovidersisbecomingpopular.Byincorporatingmanyresourceswithanetworkcentricinfrastructure,theseinformationtechnologycompaniesprovidevalueadded servicestotheendusersmuchcheaper,fasterandmorereliable.EventheASPmarket behavedmuchsmallerthanwhatitwasexpectedtofor2001-2002,analysisindicatesthat thisismerelyatemporarilystall,andcorporationscanbeprofitableifitisdeliveredwith properexecution(Atick,2001).GartnerResearchindicatedthatusersÂ’expectationsfrom theASPsarereliability,stability,financialviability,adaptability,flexibility,security, supportandspeedyservice(Jester,2000).OneofthemajordifferencesbetweenASP andsomeoftheotheroutsourcingmodelsisthateventhenew-customerincrementalcost isnotsmallbecauseofadditionalhardware,softwareandsupportrequiredwithsome customizationcost,ASPisalwayscheaperthandoingitbythemselvesforanycustomer (Williams,2001).BecauseofanumberofefficiencyreasonsintheASPindustry,the configurationmodelispreferredcomparedtothecustomizationmodel.Thatiswhyin ourresearch,weassumeastandardserviceoffering,e.g.,theEnterpriseResource Planningapplication.

PAGE 110

95 Itiswidelyknownthatwaitingtimeandpriceareveryimportantinthe Internet/networkarena.Becauseofthelowsearchcost,itisveryeasytofindanew serviceproviderwhenauserisnotsatisfiedwiththeservice. Anumberofpapershavebeendevotedtotheduopolisticprice,capacity,quality andcustomizationtypeofcompetitions.Inthisstudyweanalyzeduopolisticpriceand capacitycompetitionoftwoserviceproviderswiththeinfluenceofqueuingdelays.We considertwoserviceproviderswhoselltheirvalue-addedservicestothemarketand competeforcustomers.Bothserviceprovidersneedtodecidehowmuchcapacityto haveandwhatpricetochargeinordertomaximizetheirprofitandmarketshare.In additiontoserviceproviderÂ’sdecisionprocess,potentialcustomersconsideringjoining theASPÂ’sservicetakeintoaccountthecostcausedbythequeuingdelay,inadditionto thepricechargedbytheASP. Inparticular,weshowthatthereisnodirecteffectofthedelaycostonthearrival rate.Ifafirmhasahighercapacity,thenhe/sheprovidesfasterservicewithahigher price. Asweindicateearlier,speedandpriceoftheInternetserviceplayasignificant roleinanyusersdecisionprocess.Queuingnetworkmodelshavebeenusedtosolve modelsofcomputersystems,communicationnetworksandmanufacturingsystemsfor manyyears.Inthecomputersystemqueuingmodel,eachservicerequestoriginatedbya customerisqueuedatthetime-sharedcomputersystem(SiaandHo,1997,p.196).Some oftheearlyworkisontheusagequeuingmodelsfortheschedulingproblemsofthe computersystems(Michel,1974;Rasch,1970).Theyreviewedthebenefitofusingthe feedbackorprioritymodelsintheschedulingoftime-sharedcomputersystems.Inhis

PAGE 111

96 research,Mendelson(1985)reviewedtheeffectsofqueuingdelaysanduser’srelated costsonthemanagementofcomputingresources.Whencomputingsystemssetpricesto covertheircosts,suchdelaycostrecoverywouldleadtounder-utilizationofresources. However,ifthesystemisdefinedasaprofitcenter,thereisadangerofmonopoly pricing.Inourresearch,weanalyzetheprofitcentermaximizationwithrelationtoeach firm’sprofitfunction. Inanotherwork,LiandLee(1994)studiedthecompetitionoftwoservice providersbasedonprice,qualityanddeliverytimewithdifferentiatedprocessingrates. Theyindicatedthat“Intheequilibrium,thefirmwithahigherprocessingratealways enjoysapricepremium,and,further,enjoysalargermarketsharewhenitsopponentalso hasadequateprocessingratetoserveallthecustomersalone”(LiandLee,1994,p.633). Theyusedacustomerpreferencefunctionthatincludescost,qualityandtime withcertainreservationvalues.Ifthevaluethatisprovidedbythefirmislowerthanthe user’sexpectation,thatuserdoesnotjointhefirm. Ourresearchusesthedelaycostforanindicationoflowperformanceandquality, ratherthananalyzingthedelivery-timeandqualityasseparatecomponents.This researchshowsthatthespeedyservicedoesgiveacompetitortheadvantageofprice premiumandmarketshare. ApaperbySo(2000)advancedtheimpactofusingtimeguaranteeson competition.Inhisresearch,heindicatedthat,whenallfactorsareequal,thehigh capacityfirmsprovidebettertimeguaranteeswhilethelowcapacityfirmsprovidelower pricebecauseoftheloweroperatingcost.Basedonthetimeorpricesensitivity,the customerspicktheappropriateserviceproviders.Ifafirmdominatestheotherwithboth

PAGE 112

97 ahighercapacityandloweroperatingcost,thedominatingfirmoffersabetterpriceand deliverytime.Thisthesisusestime,priceandexternalattractionfactorsinthespecific marketsharefunction,andalinearcoststructure.Theprobabilityofmeetingtheservice deliverytimeguaranteeistobegivenandfixed.Inourresearch,wealsoassumethatthe marketsizeisfixedandgiven.Inotherwords,thepriceandservicespeeddecisionsdo notaffecttheoverallmarketsize,theyaffectonlytheresultingmarketshareofeach serviceprovider. WedefineanequilibriumfunctionbydefiningtheusercostastotalofASPÂ’s priceandthewaitingcost.Basically,userscanusetheslowerASPwithalowerpriceor jointhefasterASPwithahigherprice.Wedonotdefineanyreservationvaluethat impactstheusersÂ’decision,morerealistically,inourmodelusersjoiningoneofthe firms.OurconclusionalsosupportLiandLee(1994),andSoÂ’s(2000)research.Afirm withahighercapacityreceivesthelargermarketshareandchargesahigherprice. Inourstudywetakesomeoftheearlierworkastheunderlyingframework.We analyzetheimpactofpriceandcapacitydecisionsintheduopolisticcompetitionsetting, andreviewtheimpactofqueuingdelaysontheprice,capacityandarrivalrates.Inthis study,wereviewthebehaviorandperformanceofthecompetitionfromseveral perspectives.Intheshortrunproblem,thecapacitiesarefixed,andinthelongrun problem,capacitiesaredecisionvariablesinadditiontopricedecisions. Theremainderofthispaperisorganizedasfollows.Inthenextsection,we presentthemodelofduopolisticcompetitionwithinfluenceofqueuingdelays.Section 4.2.1.and4.2.2.examinethevariouscompetitionstrategies,priceandcapacity.In section4.3.,weanalyzetheoptimalpricingandcapacitydecisionsofASPsbynumerical

PAGE 113

98 explorations.Finally,Chapter5ofthisthesisprovidesconcludingremarksanddirections forfutureresearch. 4.2ModelofDuopolisticCompetitionwithInfluenceofDelayCosts ConsideranASPmarketthatconsistsoftwoserviceproviders,ASP1andASP2, who sell their value added services to the market and compete for customers. Figure 4-49 showsthemarketconditionofthismodel. Figure4-49OverviewoftheduopolisticcompetitionsofASPs Inourmodel,jobsarriveintothecomputersystemrandomly,theyspendrandom amountoftimeandtheyleavethesystem.Themarketischaracterizedasarrivalrate injobsperunitoftime(poissonrate)andarrivingjobshaveahomogeneousservice requirementovertheirvaluationoftheERPservice.Thetimeanyjobspendsinthe systemincludesactualprocessingandwaitingtime.Withoutconsideringthedelaycost andifthepricepertransaction(thejob-by-jobpricing)toacustomeris p ,thenthe marginalvalueofASPserviceisequaltothepricepertransaction,'() Vp = . Weassumetheconstantdelaycostperunitoftimeofspendingtimeinthesystem is v andtheexpectedtimeajobremainsinthesystemfromarrivaltoprocessingis completedis T .Then,theexpectedusercostperjobbecomes p v T + .FortheM/M/1 Market ASP1 1 1 1 ,, bp ASP2 2 2 2 ,, bp 1 2

PAGE 114

99 system, 1/() T µ =Š .Assumethatthecustomer’spreferenceoncostandwaitingtime istoassumeatime-independentvalueV.Thus,attheequilibrium,customers(jobs)are indifferentbetweenASP1andASP2whichleadstothefollowingequilibriumequation. 12 1 12211 VpvVpv µ µ Š+=Š+ŠŠ, 12 1 12 2 11 pvpv µ µ +=+ ŠŠ .(4.71) Weassumethatthemarketsize, ,isfixedandgiven.Inotherwords,the pricingandcapacitydecisionsoftheASPsaffectonlytheresultingmarketshareofthe eachfirm, i={1,2 } i i =,nottheoverallmarketsize.Hencethe equals = + 2 1 (4.72) where 0 1 ,0 2 , 11 µ >and 22 µ >.(4.73) Customerschoosetheservicesbasedonthevalueofcomputersystemsandthe priceofcapacity.ThesystemismodeledasM/M/1queuingsysteminthisstudy. 1 µ and 2 µ aretheprocessingratesofeachoftheserviceprovidersmeasuredinjobsor transactionsperunitoftime.Weassumethatthecapacityofeachoftheservice providersisgreaterthantheindividualdemand, 11 µ > and 22 µ >,sothatthesystem hasasteadystate. Servicepricingaffectsthejob’sarrivalratetothesystem.Dependingontheprice scheduleandexpectedwaitingtimes,thecustomerdecideswhethertousethesystemand whichserverprovidertojoin.TheASP1andASP2charge 1 p and 2 p perjob.Inthe

PAGE 115

100 industry,themostcommonwayofchargingthisserviceisbasedonperuser,per applicationandpertimeusage(Davison,2000).Inourmodel,theexpectedprofit functionoftheASP’sisgivenby () i iii i A Ppp==where i={1,2} fortheshort-runproblemand () i iiiii i A Pppb µ ==Šwhere i={1,2} forthelong-runproblem. i b isthe marginalcapacitycostofthe ASPi.Inthelong-runsetting,thefirsttermgivesthe expectedrevenueofthecomputerservicewhilethesecondtermdescribestheexpected costoftheservicefortheASP.TheASP’sobjectiveistomaximizetheirindividual expectedprofitsbydecidingwhatprice 12 (,) p p tochargetothemarket.Inthelong-run problem,theASPsalsoneedtodecidehowmuchcapacitytheyneedtohave 1 2 (,) µµ . Customerschoosetheserviceprovidersbasedontheirpricesandtheperformanceofthe systemswhichimpactsonthevalueoftheservice. Amajorpurposeofthispaperistoexaminethebehaviorofvariousduopolistic competitionsbetweentwoASPsundertheinfluenceofqueuingdelays.Welookattwo cases,oneasashort-runproblemandtheotherasalong-runproblem.Intheshort-run problem,theASP’sobjectiveistomaximizeherexpectedprofitbydecidingwhatprice tosell.Inthelong-runproblem,ASPsalsoneedtodecidehowmuchcapacitytohavein additiontopricedecision.Thefollowingsectiondiscussestwocasesingreaterdetail.4.2.1PriceCompetitionofASPsInthissection,wedefineandstudytheduopolisticpricecompetition.Inaddition totheeffectivenessofcompetitionstrategy,westudytheimpactofqueuingdelaysonthe price,arrivalrateandmarketshare.Consideragamebetweentwoserviceprovidersin whichbothchoosetheirprices, 1 p and 2 p ,wherethecapacitiesaregivenas 1 µ and 2 µ

PAGE 116

101 respectively.Inthissetting,priceistheonlydecisionvariable.AndtheASPsarenot identical.4.2.1.1ApplicationServiceProvider1’sshort-runproblem(giventhefixed capacity)Withagivenfixedcapacity,ASP1’smaximizationproblemis()1 1 11maxpp=s.t.Eqs.(4.71),(4.72),and(4.73). SubstitutingEq.(4.72)intoEq.(4.71)leadsto () 12 1 12111 pvpv µ µ +=+ ŠŠŠ .(4.74) Then,() 1 1 1121 2 11 1 vv pp µ µ =+Š ŠŠŠ (4.75) SolvingthemaximizationproblemofASP1isequivalenttosolvingthefollowing problem() 111 121 2111 max vv p µ µ =+Š ŠŠŠ(4.76) s.t.Eq.(4.73). Asweseefromtheaboveequation,theprofitoftheASP1dependsontheprice decisionoftheASP2andthecapacityparametersofbothserviceproviders.Inthis study,customersareawareofbothproviders’prices. Evenweknowthatthecapacityofeachoftheserviceprovidersneedstobe greaterthantheindividualdemand, 11 µ > and 22 µ > inorderthesystemhasasteady state,ifwecandefinethemaximizationproblemasthefollowingway

PAGE 117

102() 111 121 2111 max vv p µ µ =+Š ŠŠŠs.t. 11 µ and0 1 . TofindtheoptimalASP1’sprice,arrivalrateandprofit,wedefinetheKuhnTuckerconditionsas() ()() () 2 1 211 22 11 21 0 v v pxyµ µ µ µŠ +ŠŠ+= Š ŠŠ()111 0 xµŠ=11 0 y= 11 µ ,0 1 ,1 0 y ,1 0 x . FromtheQueuingtheorem,weknowthat 11 µ < .Thisleadsto1 0 x = inorder tosatisfythesecondcondition.InadditionforASP1tobeprofitable1 0 > and1 0 y = . Thenaftersomealgebra,() ()() () 2 1 2 22 11 21 0 v v pµ µ µ µŠ +Š= Š ŠŠ .(4.77) FromEq.(4.77)wefindtheASP1’sarrivalrateisintermsofpriceofASP2,the capacitiesofASP1andASP2,andtheunitdelaycostparameter,* 1212 ( ,,, ) pv µµ,and theoptimumpriceofASP1.Basically,bothprices,ASP1’sandASP2’s,effectthe customer’sdecision,arrivalrate.4.2.1.2ApplicationServiceProvider2’sshort-runproblem(giventhefixed capacity)SimilartotheASP1’sproblem,theobjectiveoftheASP2istomaximizethe expectedprofitoftheservice.Thus,

PAGE 118

103()2 2 22maxpp= s.t.Eqs.(4.71),(4.72),and(4.73). Aftersomealgebra,substitutingEq.(4.72)intoEq.(4.71)leadsto() 12 1 22 2 11 pvpv µ µ +=+ ŠŠŠ .(4.78) Then() 2 2 2212 1 22 2 vv pp µ µ =+Š ŠŠŠ .(4.79) SolvingtheproblemASP2isequivalenttosolvingthefollowingproblem() 222 212 1 222max vv p µ µ =+Š ŠŠŠ(4.80) s.t.Eq.(4.73). LikewisefortheASP2,tofindtheoptimalASP2’sprofit,weassumethat 22 µ < and2 0 > ,andwefindthefirstorderconditionof 2 intermsofthearrivalrateas()()()() ()() () 122 222 1 22 22 121 0 vv vv pµ µ µ µŠŠŠ ŠŠŠ +Š= Š ŠŠandaftersimplifications() ()() () 1 2 1 22 22 12 0 v v pµ µ µ µŠ +Š= Š ŠŠ .(4.81) FromEq.(4.81)wefindtheoptimumarrivalrateofASP2,* 2112 ( ,,, ) pv µµ,and theoptimumpricethatwillmaximizetheexpectedprofitofASP2.SimilartotheASP1’s problem,ASP2’sarrivalratesignificantlydependsonthepricedecisionofASP1. Consequently,theexpectedmarketsharesoftheASP’sandtheutilizationratioswith

PAGE 119

104 respecttothewholemarketdemandandtheirindividualcapacitiesare * ** 1 21 1 , , µ and * 2 2 µ .Wefurtheranalyzetheinsightsrespectivetothemarketsharesoftheservice providersinthenumericalanalysissection.Proposition4.1.When 12 µ µ << (orlikewise 21 µ µ << ),thereexistsa uniqueNashequilibrium.Proof.WesolvethefollowingfoursystemequationstofindtheNash equilibriumofthepricecompetitionproblem.Thesesystemequationsare Eq.(4.71), 12 1 12 2 11 pvpv µ µ +=+ ŠŠ , Eq.(4.72), = + 2 1 , thefirstorderconditionof 1 intermsofthearrivalrate, 1 , Eq.(4.77),() ()() () 2 1 2 22 11 21 0 v v pµ µ µ µŠ +Š= Š ŠŠ , andthefirstorderconditionof 2 intermsofthearrivalrate, 2 , Eq.(4.81)() ()() () 1 2 1 22 22 12 0 v v pµ µ µ µŠ +Š= Š ŠŠ where1 0 > ,2 0 > , 11 µ > and 22 µ > . SubstitutingEqs.(4.72),(4.77)and(4.81)intoEq.(4.71),wegetthefollowing equation,() () ()() 11 21 22 11 21 0 µ µ µ µŠ+Š Š += Š ŠŠ.(4.82)

PAGE 120

105 Aftersomealgebra,wedefinetheEq.(4.82)as()()() ()32222 1 1211212121 1 222322 212121122234342 220. f µµ µµµµ µ µ µµµµµµµµµ=ŠŠ+ŠŠŠŠŠ++ ŠŠ+Š+Š++= When1 0 = ,()()()() 2 2 121120fµµµµ==Š+ŠŠand 12 µµ <+ ,then()1 00 f=> ,()21 0 µŠ>,thus()12 0. µŠ>Hence,() 1 1 0 df d >. Thisshowsthat() 1 fhasauniquerealroot, * 1 .Therefore,when 12 µ µ << , thereexistsauniquesolutiontothesystemofequations,i.e.auniqueNashequilibrium. Q.E.D. Evenwecanonlyproofthispropositionforagivencondition, 12 µ µ << ,we cancomputetheoptimalserviceproviders’pricesandcorrespondingarrivalrates, * * * 1 2 1 , , ppand * 2 ,numerically.WecanonlyprooftheNashequilibriumforagiven rangeanalytically.

PAGE 121

106Lemma4.1.When 21 µ µ >> ,onehas 1 12 2 µ µ +<+ and 1 12 2 µ µ Š<Š . Inthefollowingprocess,weproofthisbycontradiction.Proof.WereviewthevalueofEq.(4.82)forthreeconditions,when 2121 , >< and 21 = .SubstitutingEq.(4.72)intoEq.(4.82)leadsto,() () 2 12 11 2122µ µ µµŠŠ =ŠŠ(4.84) where 21 µ µ >> ,21 µµ +> , 12 µ > (fromthepreviousproposition),1 0 > ,2 0 > , 11 µ > and 22 µ > .Thefollowingshowsthat() () 2 12 11 2122 1 µ µ µµŠŠ =<ŠŠ,then 1 22 1 µ µ Š<Š and 1 12 2 µ µ Š<Š .Q.E.D. Table4-16ProofbycontradictionforLemma1LeftsideofEq.(4.84)RightsideofEq.(4.84) () () 2 12 11 2122 1 µ µ µµŠŠ =>ŠŠ 21 > 1 22 1 µ µ Š>ŠThisisnotpossible 1 12 2 µ µ Š>ŠThisispossible 21 < 1 22 1 µ µ Š>ŠThisispossible 1 12 2 µ µ Š>ŠThisisnotpossible 21 = 1 22 1 µ µ Š>ŠThisisnotpossible 1 12 2 µ µ Š>ŠThisisnotpossible () () 2 12 11 2122 1 µ µ µµŠŠ =<ŠŠ 21 > 1 22 1 µ µ Š<ŠThisispossible 1 12 2 µ µ Š<ŠThisispossible 21 < 1 22 1 µ µ Š<ŠThisispossible 1 12 2 µ µ Š<ŠThisispossible 21 = 1 22 1 µ µ Š<ŠThisispossible 1 12 2 µ µ Š<ŠThisispossible () () 2 12 11 2122 1 µ µ µµŠŠ ==ŠŠ 21 > 1 22 1 µ µ Š=ŠThisisnotpossible 1 12 2 µ µ Š=ŠThisisnotpossible 21 < 1 22 1 µ µ Š=ŠThisispossible 1 12 2 µ µ Š=ŠThisisnotpossible 21 = 1 22 1 µ µ Š=ŠThisisnotpossible 1 12 2 µ µ Š=ŠThisisnotpossible

PAGE 122

107Observation4.2.Whenthereisapricecompetitionbetweenthetwoservice providers,if 21 µµ > andthereisaNashequilibrium,then 21 > . Whilethereexistsnoclosedformsolutionfortheabovefoursystemequations, Observation4.2statesthatwecanobservefromthenumericalanalysisthatASPwitha highercapacityenjoysthelargermarketsharewithahigherpricethanthecompetitor. Thedifficultyofderivingaclosed-formsolutionof *** 1 21 , , ppand * 2 areillustratedas follows.Fromtheequations,* 1212 ( ,,, ) pv µµand* 2112 ( ,,, ) pv µµarethequadratic formscomplicatethepossibilityofaclosed-formsolution.Especially,iftheprocessing timeisimportantforthecustomer,becauseofhavinghighercapacity,ASP2hasan advantageofprocessingfasterthanhiscompetitor.Proposition4.3.When 21 µ µ >> , 21 pp > .Proof.Fromtheequilibriumequation,Eq.(4.71),andLemma4.1,weknowthat 12 1122 11 pvpv µ µ +=+ ŠŠand 1 12 2 µ µ Š<Š .Then 21 pp > .Q.E.D. BasicallytheASPwhohasthelargercapacitychargesthehigherpricethanhis opponent.Whenaproviderhaslargercapacity,thiscausesahigheroperatingcost,then thepriceincreases.Ifthepricecomponentismoreimportantthantheprocessingrate,in thiscaseASP1hasthelowerpriceadvantage.Observation4.4.Whenthereisapricecompetitionbetweentwoservice providers,thearrivalratefollowsthesamedirectionoftheserviceprovider’scapacity, 1 1 0 d d µ> and 2 2 0 d d µ> .

PAGE 123

108 Aftersomealgebra , wefindthe 1 1 d d µ and 2 2 d d µ withthefollowingprocess.When wedefinethe() () 11 1 111 0 dfdf d ddd µµ== ,thenwefindthefirstorderconditionofthe ASP1’sarrivalrateas () ( )()() 222 12111222 1 2222 1 112121212142222 6234342 d dµµµµµµ µ µµµµµµ µ µ +ŠŠ++ŠŠ+=ŠŠ+ŠŠŠŠŠ++. Whilethereexistsnoclosedformsolutionforthe 11 / d d µ ,observation4.4statesthat wecancomputetheoptimalserviceproviders’pricesandcorrespondingarrivalrates, *** 121 , , ppand * 2 ,numericallyforsomerangeofparameters,and * 1 isastrictly increasingfunctionof 1 µ ,and * 2 isastrictlyincreasingfunctionof 2 µ .Whenthe capacityoftheserviceproviderincreases,thearrivalrateofthatserviceprovider increases.Proposition4.5.When 21 µ µ >> , * 1 p isastrictlydecreasingfunctionof 1 µ .Proof.FromEqs.(4.72),(4.77)and(4.81),let() ()() () 1 2 1 22 22 12v v pµ µ µ µŠ =Š+ Š ŠŠ and() ()() () 2 1 2 22 11 21v v pµ µ µ µŠ =Š+ Š ŠŠ bethe pricesofASP1andASP2.Whenwetakethefirstorderconditionsof 1 p and 2 p with respectto 1 µ and 2 µ ,aftersomealgebrawefindthat ()() () ()() () ()() 112 1 233 1 1212122 vv dp v d µ µ µ µµµŠŠŠ =Š+= ŠŠŠŠŠŠ and

PAGE 124

109 ()() () ()() () ()() 221 2 233 2 2121212 vv dp v d µ µ µ µµµŠŠŠ =Š+= ŠŠŠŠŠŠ . When1 µ < ,then * 1 1 0 dp dµ< .Q.E.D. Fromthenumericalanalysisweobservethat * 2 2 0 dp dµ< .Thispropositionindicates thatwhenthecapacityoftheserviceprovide rsdecreases,unitservicepriceperusage increasesduetoincreasingcongestion.Proposition4.6.Thereisnoimpactofthedelaycostofthecomputersystemper unitoftimeperjob, v ,onthearrivalrate.Thereisnodirectrelationshipbetweenthe delaycostandthearrivalrate.Itonlyeffectstothepriceoftheservice.Proof.Whenwesolvethefoursystemequations,Eqs.(4.71),(4.72),(4.77)and (4.81)aftersomealgebra,thedelaycostofthecomputersystemperunitoftimeperjob, v, dropsoutinEq.(4.82),() () ()() 11 21 22 11 21 0 µ µ µ µŠ+Š Š += Š ŠŠ.Thatis, v hasno directeffectonthearrivalrateofserviceproviders.Proposition4.7.Thedelaycostofthecomputersystemaffectsthepriceofthe service.Theserviceprovider’spricefollowsthesamedirectionofdelaycost.Proof.AsweknowfromtheProposition4.6,thereisnodirecteffectofthedelay costonthearrivalrate.WhenwereviewtheEq.(4.71), 12 1 12 2 11 pvpv µµ +=+ ŠŠ , thevaluesof() 11 µ Šand() 22 µ Šdonotchange.Higherdelaycostleadstohigher prices.Thepriceofthedelaycostaffectsthepriceofbothserviceproviders.

PAGE 125

1104.2.2CapacityCompetitionofASPsInthissetting,consideraduopolisticcapacitycompetitionbetweentwoASPs. Consideragamebetweentwoserviceprovidersinwhichbothchoosetheirprices, 1 p and 2 p ,andcapacityparameters, 1 µ and 2 µ simultaneously.4.2.2.1ApplicationServiceProvider1’slong-runproblemTheobjectiveoftheASP1istomaximizetheexpectedprofitoftheservice,as given()11 11111 ,maxppbµ µ =Š s.t.Eqs.(4.71),(4.72),and(4.73)where b1isthemarginalcapacitycostofASP1. SubstitutingEq.(4.72)intoEq.(4.71),andthenEq.(4.75)intotheaboveASP1’s long-runproblemleadsto() 1111 12111 , 2111max vv pbµ µ µµ=+ŠŠ ŠŠŠ(4.85) s.t.Eq.(4.73). Evenweknowthatthecapacityofeachoftheserviceprovidersneedstobe greaterthantheindividualdemand, 11 µ > and 22 µ > inorderthesystemhasasteady state,ifwecandefinethemaximizationproblemasthefollowingway() 1111 12111 , 2111max vv pbµ µ µµ=+ŠŠ ŠŠŠs.t. 11 µ ,0 1 and1 0 µ . TofindtheoptimalASP1’sprice,arrivalrateandprofit,wedefinetheKuhnTuckerconditionsas

PAGE 126

111() ()() () 2 1 211 22 11 21 0 v v pxyµ µ µ µŠ +ŠŠ+= Š ŠŠ ,() 1 112 2 11 0 v bxy µŠ++= Š,()111 0 xµŠ=,11 0 y= ,21 0 yµ= and 11 µ ,0 1 ,1 0 y ,1 0 x . FromtheQueuingtheorem,weknowthat 11 µ < .Thisleadsto1 0 x = inorder tosatisfythethirdcondition.InadditionforASP1tobeprofitable1 0 > ,1 0 µ> ,1 0 y = and2 0 y = .ThisleadstoEq.(4.77),() ()() () 2 1 2 22 11 21 0 v v pµ µ µ µŠ +Š= Š ŠŠ and() 1 1 2 11 0 v b µŠ= Š.(4.86) Thus,ASP1’soptimalcapacityequalsto * ** 1 11 1v b µ =+ (4.87) FromEqs.(4.77)and(4.87)wefindtheASP1’sarrivalrateintermsofpriceof unitpriceofASP2,thecapacitiesofASP1andASP2,andtheunitdelaycostparameter,** 1212 ( ,,, ) pv µµ,thentheoptimumpriceandcapacityoftheASP1.4.2.2.2ApplicationServiceProvider2’slong-runproblemSimilartotheASP1’sproblem,theobjectiveoftheASP2istomaximizethe expectedprofitoftheservice.Thus,()22 22222 ,maxppbµ µ =Š s.t.Eqs.(4.71),(4.72),and(4.73),where b2isthemarginalcapacitycostofASP2.

PAGE 127

112 SubstitutingEq.(4.72)into(4.71),andthenEq.(4.79)intoASP2’slong-run problemleadsto() 2222 21222 , 1222max vv pbµ µ µµ=+ŠŠ ŠŠŠ(4.88) s.t.Eq.(4.73). LikewiseforASP2,afterassuming2 0 > and2 0 µ> ,firstorderconditionsof 2 intermsofthearrivalrate, 2 ,andthecapacity, 2 µ ,leadstoEq.(4.81),() ()() () 1 2 1 22 22 12 0 v v pµ µ µ µŠ +Š= Š ŠŠ and() 2 2 2 22 0 v b µŠ= Š .(4.89) Thus,ASP2’soptimalcapacityequals * ** 2 22 2v b µ =+ .(4.90) FromEqs.(4.81)and(4.90)wefindtheASP2’sarrivalrateintermsofpriceof unitpriceofASP1,thecapacitiesofASP1andASP2,andtheunitdelaycostparameter,** 2121 ( ,,, ) pv µµ. WesolvethefollowingsystemofsixequationstofindtheuniqueNash equilibriumofthecapacitycompetitionproblem.Thesesystemequationsare Eq.(4.71), 12 1 12 2 11 pvpv µ µ +=+ ŠŠ , Eq.(4.72), = + 2 1 , thefirstorderofconditionsof 1 intermsofthearrivalrate, 1 ,andthecapacity, 1 µ ,

PAGE 128

113 Eqs.(4.77)and(4.87),() ()() () 2 1 2 22 11 21 0 v v pµ µ µ µŠ +Š= Š ŠŠ , * ** 1 11 1v b µ =+ , andthefirstorderconditionsof 2 intermsofthearrivalrate, 2 ,andthecapacity, 2 µ , Eqs.(4.81)and(4.90),() ()() () 1 2 1 22 22 12 0 v v pµ µ µ µŠ +Š= Š ŠŠ and * ** 2 22 2v b µ =+ . Closeformsolutionsofoptimal ***** 12121 , ,,, pp µ and * 2 µ aredifficulttoderiveforASP1 andASP2.Inthenumericalanalysissection,wefurtheranalyzethesevariablestogain furtherinsights.Proposition4.8. * 1 µ isastrictlydecreasingfunctionof 1 b and * 2 µ isastrictly decreasingfunctionof 2 b , * 1 1 0 d dbµ< and * 2 2 0 d dbµ< ,andincreasingfunctionofunitdelay cost, v .Proof.WhenwereviewtheEq.(4.87), * ** 1 11 1v b µ =+ ,andEq.(4.90), * ** 2 22 2v b µ =+ ,andthefirstandsecondorderconditionsoftheseequationsintermsof 1 , vb and 2 b ,wefindthatthecapacityoftheserviceprovidersfollowthesamedirection oftheunitdelaycost.Whenthemarginalcapacitycostsincreases,increasingoperating costdirectstheASPstodecreasetheircapacities.Q.E.D.4.3NumericalExplorationsforCapacityCompetitionofASPsInthissection,weexamineaseriesofcomputationalresultstoillustratethe behaviorofourmodel.Further,weexploretheimpactofthreekeyparametersonthe arrivalrate,utilizationratio,marketpriceandprofitoftheASPs,including(1)the

PAGE 129

114 capacitiesoftheASPs,(2)thedelaycostofthecomputersystemperunitoftimeperjob, v,and(3)themarginalcapacitycosts, 1 b and 2 b .Wefirstselectasetofbaseline parameters for the model, see Table 4-18. For each scenario, we vary one parameter at a time over a range of values and c alcula te statistics. The results a re given in Table 4-19 to Table 4 -29. In our analysis, we first examine the duopolistic p rice competition in the short-runproblemsetting.Wethenanalyzethelong-runproblem,thecapacity competitionofserviceproviders.BecauseoftheMathematicalpackage,e.g.,Maple6, generatesoverlymessyandnon-meaningfulsolutionsforoptimalarrivalrate,priceand capacity,soitisverydifficulttoanalyzethismodelwithcomparativestatics. Twenty-fourfiguresarecreatedforbothcasestoanalyzethequeuingeffectsand service providers’ performance by exploring three parameters, resulting in Figure 4-50 to Figure 4 -75. The first group of figures, Figure 4-50 to Figure 4-65, examine the impact of capacityoftheASPsandtheunitdelaycostofthecomputersystemfortheprice competitionproblem.Thisincludesthreescenarios,including(1)whenthecapacityof eachoftheserviceprovidersislessthanthemarketdemand,i.e.,1 < and2 b ,(2) whenthecapacityofeachoftheserviceprovidersisgreaterthanthemarketdemand,i.e.,1 > and2 > and(3)whenoneoftheproviders’capacitiesislesswhiletheother’s isgreaterthanthemarketdemand,i.e.1 < and2 .Underallscenariosforprice competitionproblem,whenthecapacityoftheprovidersincreasesthemarketprice decreases,andthearrivalrateofthatserviceproviderincreases. Inthefirstscenario,wesetthecapacityofASP1as1 6 = ,andthemarket parametersat 7 =,thenstudydifferentcaseswiththeninevaluesof 2 (7,6.75,6.5,

PAGE 130

115 6.25,6,5.75,5.5,5.25and5)forASP2andv(0.1,0.2,0.3,0.4and0.5),andcomputethe equilibriumprices,thearrivalrates,profitsandutilizationoftheASPs.Several importantfindingsarederivedfromthisstudy.FromFigure4-50toFigure4-53,all otherfactorsbeingequal,theserviceproviderwithahighercapacityhasthelarger demand,salespriceandprofit.Thereisareverserelationshipbetweenthecapacityand themarketprice.DecreasingthecapacityfurtherdecreasesthearrivalrateoftheASP andincreasesthepriceoftheservice.Whenthecapacityislow,congestioncauses higherprice.Whenthecapacityishigherbecauseofcompetition,ASPstrytokeepthe pricelowinordertoreceivethehigherdemand.Highercapacityfirmhasthehigher profit.Whilethehighcapacityfirmcompeteswithfasterprocessingrate,thelow capacityfirmcompeteswithhislowerprice. In the second and third scenarios, Figure 4-54 to Figure 4-61, we compute the equilibriumprices,thearrivalrates,profitsandutilizationoftheASPswhenthecapacity ofeachoftheserviceprovidersisgreaterthanthemarketdemand,i.e.,1 > and2 > ,andwhenoneoftheproviders’capacitiesislesswhiletheother’sisgreaterthan themarketdemand,i.e.1 < and2 .Weobserveverysimilarbehaviorwiththe scenarioone.Whenwecomparetheresultsfromeachscenario,wenoticethatthe overallprofit,utilizationratioandpricearemuchlowerinscenariotwothanothers.Too muchexcesscapacitycausesadditionalcostandlowerutilization. Under all scenarios, Figure 4 -62 and Figure 4 -63, there is no impact of the d elay costofthecomputersystemperunitoftimeperjob,v,onthearrivalrateandutilization ratioinanytheabovescenarios.Thereisnodirectrelationshipbetweenthedelaycost andthearrivalrate.Alsothemarketpricefollowssamedirectionoftheunitdelaycost.

PAGE 131

116 Inotherwords,whentheunitdelaycostincreases,thepriceoftheservicealsoincreases, Figure 4-64 and Figure 4-65, ASPs increase the capacity to decrease the impact of delay costtothemarket.Whenbothofthefirmsareidentical, 12 = ,theNashequilibrium solutionissymmetric, ** 12 pp =and ** 12 =. In the second part of the analysis, Figure 4 -66 to Figure 4 -7 5, we review the impactofthedelaycostofthecomputersystemandthemarginalcapacitycostsfor capacitycompetitionproblem.Whenthefirm’smarginalcapacitycostsarethesame,the Nashequilibriumsolutionissymmetric, ** 12 = , ** 12 pp =and** 12 /2 ==. Inthefirstscenario,wesetthemarginalcapacitycostofASP1as1 1 b = ,the marketparametersat 7 =andtheunitdelaycostat 0.1 v =,thenstudydifferentcases withthefivevaluesof 2 b (1.2,1.1,1,0.9and0.8)forASP2,andcomputethe equilibriumprices,thearrivalrates,profits,utilizationsandthecapacitiesoftheASPs. Several imp ortant findings are derived from th is study. Figure 4 -66 to Figure 4 -69, all otherfactorsbeingequal,similartothepricecompetitionproblem,theserviceprovider withahighercapacityhasthelargerdemand,salespriceandprofit.Thereisadirect relationshipbetweenthemarginalcapacitycostandthemarketprice.Decreasingthe marginalcapacitycostfurtherdecreasesthemarketprice.Whenthemarginalcapacity costishigh,ASPschargehigherpriceinordertobeprofitable.Highercapacityfirmhas thehigherprofit.Whilethehighcapacityfirmcompeteswithherfastprocessingrate, thelowcapacityfirmcompeteswithherlowprice. Also from Figure 4-71 to Figure 4-75, when the marginal capacity costs are not thesame,lowmarginalcapacitycostreceiveshigherarrivalwhenthedelaycost increases.BecauseASP1canincreasetheircapacitylimitmuchcheaperthantheASP2,

PAGE 132

117 marketpriceandcapacityfollowthesamedirectionwiththedelaycost,whenthedelay costincreasesthemarketpriceandthecapacityincreases,soalsotheprofitofASPs decreases.Finally,wediscoverthatifallofthemarketconditionsaresymmetric includingthemarginalcapacitycost,thereisnoeffectofdelaycostonthepriceorarrival rate,ASPsneedtoincreasecapacitiesinordertoservethecustomers.

PAGE 133

118 Table4-17SummaryofnotationforModel3 Serviceparameters: job’sortransaction’s(totalmarket)arrivalratetothesystemperunitoftime (poissonrate),fixed µ acomputercapacitylevelofsinglesystem,expectedoutputrate(measuredinjobs ortransactionsperunitoftime)whenthesystemisfullyused( µ < ) relativeutilizationrateofthesystem( / µ = ) 12 , µµ ASP1andASP2’scapacitiesinthepricecompetitionproblem ** 12 , µµ ASP1andASP2’soptimumcapacitiesinthecapacitycompetitionproblem ** 12 , ASP1andASP2’soptimumarrivalrates Revenueandcosts: v delaycostofsystemperunitoftimeperjob 12 , bb ASP1andASP2’sinternalmarginalcostforthecapacity 12 , pp A SP1andASP2’spriceperunitofcapacityusagetothemarketfortheservice 12 , A SP1andASP2’sprofitfunctions Table4-18BaselineparametersfornumericalexplorationsforModel3 ParametersBaselineValues Delaycostofthecomputersystemperunitof timeperjob, v 0.10 CapacityofASP1, 1 µ 6.00 CapacityofASP2, 2 µ 7.00 TotalMarketArrivalRate, 7.00 MarginalcapacitycostofASP1, 1 b 1.00 MarginalcapacitycostofASP2, 2 b 1.00

PAGE 134

119 Table4-19Impactofdelaycost, v ,andcapacitywhenmu1=6
PAGE 135

120 Table4-20Impactofdelaycost,v,andcapacitywhenmu1=10>lambda=7,mu2> lambda=7(Scenario2:mu2isincreasing,visincreasing)vlambdamu1lambda1mu2lambda2p1p2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 0.17103.5000103.50000.01660.01660.05800.05800.50000.50000.35000.3500 0.17102.7061154.29390.00740.01180.02020.05070.38660.61340.27060.2863 0.17102.0371204.96290.00410.01000.00840.04970.29100.70900.20370.2481 0.17101.4871255.51290.00240.00910.00360.04990.21240.78760.14870.2205 0.17101.0328305.96720.00150.00850.00150.05040.14750.85250.10330.1989 0.17100.6540356.34600.00080.00800.00050.05100.09340.90660.06540.1813 0.17100.3347406.66530.00040.00770.00010.05160.04780.95220.03350.1666 0.17100.0629456.93710.00010.00750.00000.05210.00900.99100.00630.1542 0.27103.5000103.50000.03310.03310.11600.11600.50000.50000.35000.3500 0.27102.7061154.29390.01490.02360.04030.10150.38660.61340.27060.2863 0.27102.0371204.96290.00820.02000.01680.09950.29100.70900.20370.2481 0.27101.4871255.51290.00490.01810.00730.09990.21240.78760.14870.2205 0.27101.0328305.96720.00290.01690.00300.10090.14750.85250.10330.1989 0.27100.6540356.34600.00170.01610.00110.10200.09340.90660.06540.1813 0.27100.3347406.66530.00080.01550.00030.10310.04780.95220.03350.1666 0.27100.0629456.93710.00010.01500.00000.10410.00900.99100.00630.1542 0.37103.5000103.50000.04970.04970.17400.17400.50000.50000.35000.3500 0.37102.7061154.29390.02230.03550.06050.15220.38660.61340.27060.2863 0.37102.0371204.96290.01230.03010.02510.14920.29100.70900.20370.2481 0.37101.4871255.51290.00730.02720.01090.14980.21240.78760.14870.2205 0.37101.0328305.96720.00440.02540.00450.15130.14750.85250.10330.1989 0.37100.6540356.34600.00250.02410.00160.15300.09340.90660.06540.1813 0.37100.3347406.66530.00120.02320.00040.15470.04780.95220.03350.1666 0.37100.0629456.93710.00020.02250.00000.15620.00900.99100.00630.1542 0.47103.5000103.50000.06630.06630.23200.23200.50000.50000.35000.3500 0.47102.7061154.29390.02980.04730.08060.20300.38660.61340.27060.2863 0.47102.0371204.96290.01650.04010.03350.19890.29100.70900.20370.2481 0.47101.4871255.51290.00980.03620.01450.19980.21240.78760.14870.2205 0.47101.0328305.96720.00590.03380.00600.20180.14750.85250.10330.1989 0.47100.6540356.34600.00330.03220.00220.20400.09340.90660.06540.1813 0.47100.3347406.66530.00160.03090.00050.20620.04780.95220.03350.1666 0.47100.0629456.93710.00030.03000.00000.20820.00900.99100.00630.1542 0.57103.5000103.50000.08280.08280.28990.28990.50000.50000.35000.3500 0.57102.7061154.29390.03720.05910.10080.25370.38660.61340.27060.2863 0.57102.0371204.96290.02060.05010.04190.24870.29100.70900.20370.2481 0.57101.4871255.51290.01220.04530.01820.24970.21240.78760.14870.2205 0.57101.0328305.96720.00730.04230.00760.25220.14750.85250.10330.1989 0.57100.6540356.34600.00410.04020.00270.25510.09340.90660.06540.1813 0.57100.3347406.66530.00190.03870.00060.25780.04780.95220.03350.1666 0.57100.0629456.93710.00030.03750.00000.26030.00900.99100.00630.1542

PAGE 136

121 Table4-21Impactofdelaycost, v ,andcapacitywhenmu1=6= lambda=7(Scenario3:mu2isincreasing,visincreasing)vlambdamu1lambda1mu2lambda2p1p2ASP1ASP2 la mbda1/ lambda lambda2 /lambda lambda1 /mu1lambda2/mu2 0.1763.336173.66390.07700.08460.25680.30980.47660.52340.55600.5234 0.1763.25817.53.74190.06640.07630.21640.28540.46540.53460.54300.4989 0.1763.183483.81660.05830.06990.18560.26680.45480.54520.53060.4771 0.1763.11228.53.88780.05190.06490.16170.25230.44460.55540.51870.4574 0.1763.044493.95560.04680.06080.14250.24060.43490.56510.50740.4395 0.1762.98009.54.02000.04260.05750.12690.23100.42570.57430.49670.4232 0.1762.9189104.08110.03910.05460.11410.22300.41700.58300.48650.4081 0.1762.860710.54.13930.03610.05220.10330.21620.40870.59130.47680.3942 0.1762.8055114.19450.03350.05020.09410.21040.40080.59920.46760.3813 0.2763.336173.66390.15400.16910.51370.61960.47660.52340.55600.5234 0.2763.25817.53.74190.13280.15250.43270.57080.46540.53460.54300.4989 0.2763.183483.81660.11660.13980.37130.53370.45480.54520.53060.4771 0.2763.11228.53.88780.10390.12980.32340.50460.44460.55540.51870.4574 0.2763.044493.95560.09360.12170.28510.48120.43490.56510.50740.4395 0.2762.98009.54.02000.08520.11490.25390.46200.42570.57430.49670.4232 0.2762.9189104.08110.07820.10930.22810.44600.41700.58300.48650.4081 0.2762.860710.54.13930.07220.10450.20650.43240.40870.59130.47680.3942 0.2762.8055114.19450.06710.10030.18820.42080.40080.59920.46760.3813 0.3763.336173.66390.23100.25370.77050.92940.47660.52340.55600.5234 0.3763.25817.53.74190.19920.22880.64910.85620.46540.53460.54300.4989 0.3763.183483.81660.17500.20980.55690.80050.45480.54520.53060.4771 0.3763.11228.53.88780.15580.19470.48500.75690.44460.55540.51870.4574 0.3763.044493.95560.14040.18250.42760.72180.43490.56510.50740.4395 0.3762.98009.54.02000.12780.17240.38080.69300.42570.57430.49670.4232 0.3762.9189104.08110.11720.16390.34220.66900.41700.58300.48650.4081 0.3762.860710.54.13930.10830.15670.30980.64860.40870.59130.47680.3942 0.3762.8055114.19450.10060.15050.28240.63120.40080.59920.46760.3813 0.4763.336173.66390.30790.33821.02731.23910.47660.52340.55600.5234 0.4763.25817.53.74190.26560.30510.86541.14150.46540.53460.54300.4989 0.4763.183483.81660.23330.27970.74261.06740.45480.54520.53060.4771 0.4763.11228.53.88780.20780.25960.64671.00920.44460.55540.51870.4574 0.4763.044493.95560.18730.24330.57010.96240.43490.56510.50740.4395 0.4762.98009.54.02000.17040.22990.50780.92400.42570.57430.49670.4232 0.4762.9189104.08110.15630.21860.45630.89200.41700.58300.48650.4081 0.4762.860710.54.13930.14440.20890.41310.86480.40870.59130.47680.3942 0.4762.8055114.19450.13420.20060.37650.84160.40080.59920.46760.3813 0.5763.336173.66390.38490.42281.28421.54890.47660.52340.55600.5234 0.5763.25817.53.74190.33200.38131.08181.42690.46540.53460.54300.4989 0.5763.183483.81660.29160.34960.92821.33420.45480.54520.53060.4771 0.5763.11228.53.88780.25970.32450.80841.26150.44460.55540.51870.4574 0.5763.044493.95560.23410.30410.71261.20300.43490.56510.50740.4395 0.5762.98009.54.02000.21300.28730.63471.15500.42570.57430.49670.4232 0.5762.9189104.08110.19540.27320.57031.11490.41700.58300.48650.4081 0.5762.860710.54.13930.18050.26120.51641.08100.40870.59130.47680.3942 0.5762.8055114.19450.16770.25080.47061.05200.40080.59920.46760.3813

PAGE 137

122 Table4-22.Impactofdelaycost,vwhenmu1=lambda,mu2>lambda(Scenario5:mu1 =10>lambda=7,mu2>lambda=7,visincreasing)vlambdamu1lambda1mu2lambda2p1P2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 0.17102.7061154.29390.00740.01180.02020.05070.38660.61340.27060.2863 0.27102.7061154.29390.01490.02360.04030.10150.38660.61340.27060.2863 0.37102.7061154.29390.02230.03550.06050.15220.38660.61340.27060.2863 0.47102.7061154.29390.02980.04730.08060.20300.38660.61340.27060.2863 0.57102.7061154.29390.03720.05910.10080.25370.38660.61340.27060.2863 Table4-24Impactofdelaycost, v whenmu1lambda(Scenario6:mu1 =6lambda=7,visincreasing)vlambdamu1lambda1mu2lambda2p1P2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 0.1763.25817.53.74190.06640.07630.21640.28540.46540.53460.54300.4989 0.2763.25817.53.74190.13280.15250.43270.57080.46540.53460.54300.4989 0.3763.25817.53.74190.19920.22880.64910.85620.46540.53460.54300.4989 0.4763.25817.53.74190.26560.30510.86541.14150.46540.53460.54300.4989 0.5763.25817.53.74190.33200.38131.08181.42690.46540.53460.54300.4989

PAGE 138

123 Table4-25Impactofdelaycost, v whenmu1=mu2lambda(Scenario8:mu1=mu2 =10>lambda=7,visincreasing)vlambdamu1Lambda1mu2lambda2p1p2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 0.17103.5000103.50000.04450.02190.15560.07660.50000.50000.35000.3500 0.27103.5000103.50000.08890.04380.31120.15320.50000.50000.35000.3500 0.37103.5000103.50000.13340.06570.46680.22990.50000.50000.35000.3500 0.47103.5000103.50000.17780.08760.62240.30650.50000.50000.35000.3500 0.57103.5000103.50000.22230.10950.77800.38310.50000.50000.35000.3500

PAGE 139

124 Figure4-50Impactofcapacityonarrivalrate(Scenario1) Figure4-51Impactofcapacityonutilizationratio(Scenario1) ArrivalRate3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 7.06.86.56.36.05.85.55.35.0 ASP2'sCapacity, mu2(mu1=6)ArrivalRate lambda2 lambda1 UtilizationRatio0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 7.06.86.56.36.05.85.55.35.0 ASP2'sCapacity, mu2(mu1=6)UtilizationRatio lambda2/mu2 lambda1/mu1

PAGE 140

125 Figure4-52Impactofcapacityonprice(Scenario1) Figure4-53Impactofcapacityonprofit(Scenario1) Price0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 7.06.86.56.36.05.85.55.35.0 ASP2'sCapacity, mu2(mu1=6)Price p2 p1 Profit0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 7.06.86.56.36.05.85.55.35.0 ASP2'sCapacity, mu2(mu1=6)Profit ASP2 ASP1

PAGE 141

126 Figure4-54Impactofcapacityonarrivalrate(Scenario2) Figure4-55Impactofcapacityonutilizationratio(Scenario2) ArrivalRate0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 10.015.020.025.030.035.040.045.0 ASP2'sCapacity, mu2(mu1=10)ArrivalRate lambda2 lambda1 UtilizationRatio0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0.36 10.015.020.025.030.035.040.045.0 ASP2'sCapacity, mu2(mu1=10) UtilizationRatio lambda2/mu2 lambda1/mu1

PAGE 142

127 Figure4-56Impactofcapacityonprice(Scenario2) Figure4-57Impactofcapacityonprofit(Scenario2) Price0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 10.015.020.025.030.035.040.045.0 ASP2'sCapacity, mu2(mu1=10)Price p2 p1 Profit0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 10.015.020.025.030.035.040.045.0 ASP2'sCapacity, mu2(mu1=10)Profit ASP2 ASP1

PAGE 143

128 Figure4-58Impactofcapacityonarrivalrate(Scenario3) Figure4-59Impactofcapacityonutilizationratio(Scenario3) ArrivalRate0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 7.07.58.08.59.09.510.010.511.0 ASP2'sCapacity, mu2(mu1=6)ArrivalRate lambda2 lambda1 UtilizationRatio0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 7.07.58.08.59.09.510.010.511.0 ASP2'sCapacity, mu2(mu1=6)UtilizationRatio lambda2/mu2 lambda1/mu1

PAGE 144

129 Figure4-60Impactofcapacityonprice(Scenario3) Figure4-61Impactofcapacityonprofit(Scenario3) Price0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 7.07.58.08.59.09.510.010.511.0 ASP2'sCapacity, mu2(mu1=6)Price p2 p1 Profit0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 7.07.58.08.59.09.510.010.511.0 ASP2'sCapacity, mu2(mu1=6)Profit ASP2 ASP1

PAGE 145

130 Figure4-62Impactofunitdelaycostonarrivalrate(Scenario4) Figure4-63Impactofunitdelaycostonutilizationratio(Scenario4) ArrivalRate3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 0.10.20.30.40.5 Unitdelaycost, vArrivalRate lambda2 lambda1 UtilizationRatio0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.10.20.30.40.5 Unitdelaycost, vUtilizationRatio lambda2/mu2 lambda1/mu1

PAGE 146

131 Figure4-64Impactofunitdelaycostonprice(Scenario4) Figure4-65Impactofunitdelaycostonprofit(Scenario4) Price0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.10.20.30.40.5 Unitdelaycost, vPrice p2 p1 Profit0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 0.10.20.30.40.5 Unitdelaycost, vProfit ASP2 ASP1

PAGE 147

132 Table4-27Impactofunitcapacitycost, b whenb1NEb2,b2decreasing(Scenario1:b1 NEb2,b2isdecreasing)b1b2Vlambdamu1lambda1mu2lambda2p1p2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 11.20.174.10613.51344.02573.48662.20922.19243.65562.81330.50190.49810.85560.8661 11.10.174.09943.50724.05633.49282.10452.09593.28152.85870.50100.49900.85550.8611 110.174.09163.50004.09163.50002.00002.00002.90842.90840.50000.50000.85540.8554 10.90.174.08083.49004.13453.51001.89661.90402.53832.96200.49860.50140.85520.8490 10.80.174.07193.48194.18133.51811.79171.81042.16673.02430.49740.50260.85510.8414 Table4-28Impactofdelaycost, v whenb1NEb2, v isincreasing(Scenario2:b1NE b2, v isincreasing)b1b2Vlambdamu1lambda1mu2lambda2p1p2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 11.20.174.10613.51344.02573.48662.20922.19243.65562.81330.50190.49810.85560.8661 11.20.274.35823.51924.24243.48082.21332.18913.43082.52870.50270.49730.80750.8205 11.20.374.55213.52394.40833.47612.21652.18643.25862.31040.50340.49660.77410.7885 11.20.474.71583.52794.54793.47212.21932.18423.11362.12620.50400.49600.74810.7634 11.20.574.86033.53154.67073.46852.22182.18222.98601.96400.50450.49550.72660.7426 Table4-29Impactofdelaycost, v whenb1=b2, v isincreasing(Scenario3:b1=b2= 1, v isincreasing)b1b2Vlambdamu1lambda1mu2lambda2p1p2ASP1ASP2 lambda1/ lambda lambda2/ lambda lambda1/ mu1 lambda2/ mu2 110.174.09163.50004.09163.50002.00002.00002.90842.90840.50000.50000.85540.8554 110.274.33673.50004.33673.50002.00002.00002.66332.66330.50000.50000.80710.8071 110.374.52473.50004.52473.50002.00002.00002.47532.47530.50000.50000.77350.7735 110.474.68323.50004.68323.50002.00002.00002.31682.31680.50000.50000.74730.7473 110.574.82293.50004.82293.50002.00002.00002.17712.17710.50000.50000.72570.7257

PAGE 148

133 Figure4-66Impactofunitcapacitycostonarrivalrate(Scenario1) Figure4-67Impactofunitcapacitycostonutilizationratio(Scenario1) ArrivalRate3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 1.21.11.00.90.8 ASP2'sunitcapacitycost, b2(b1=1)ArrivalRate lambda2 lambda1 UtilizationRatio0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.95 0.98 1.00 1.21.11.00.90.8 ASP2'sunitcapacitycost, b2(b1=1)UtilizationRatio lambda2/mu2 lambda1/mu1

PAGE 149

134 Figure4-68Impactofunitcapacitycostonprice(Scenario1) Figure4-69Impactofunitcapacitycostonprofit(Scenario1) Price1.500 1.600 1.700 1.800 1.900 2.000 2.100 2.200 2.300 2.400 2.500 1.21.11.00.90.8 ASP2'sunitcapacitycost, b2(b1=1)Price p2 p1 Profit2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 1.21.11.00.90.8 ASP2'sunitcapacitycost, b2(b1=1)Profit ASP2 ASP1

PAGE 150

135 Figure4-70Impactofunitdelaycostoncapacity(Scenario1) Figure4-71Impactofunitdelaycostonarrivalrate(Scenario2) ArrivalRate3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 0.10.20.30.40.5 Unitdelaycost, vArrivalRate lambda2 lambda1 Capacity0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 1.21.11.00.90.8 ASP2'sunitcapacitycost, b2(b1=1)Capacity mu2 mu1

PAGE 151

136 Figure4-72Impactofunitdelaycostonutilizationratio(Scenario2) Figure4-73Impactofunitdelaycostonprice(Scenario2) UtilizationRatio0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0.10.20.30.40.5 Unitdelaycost, vUtilizationRatio lambda2/mu2 lambda1/mu1 Price2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 0.10.20.30.40.5 Unitdelaycost, vPrice p2 p1

PAGE 152

137 Figure4-74Impactofunitdelaycostonprofit(Scenario2) Figure4-75Impactofunitdelaycostoncapacity(Scenario2) Profit1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 0.10.20.30.40.5 Unitdelaycost, vProfit ASP2 ASP1 Capacity0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 0.10.20.30.40.5 Unitdelaycost, vCapacity mu2 mu1

PAGE 153

138 CHAPTER5 CONCLUSIONSANDDIRECTIONSFORFUTURERESEARCH Inthisresearch,weanalyzeoneoftheIToutsourcingmodels,theApplication ServiceProviders,andstudyanapplicationservicessupplychainconsistingofone ApplicationServiceProvider(ASP)andoneApplicationInfrastructureProvider(AIP). TheAIPsuppliesthecomputercapacitytotheASPthatinturnssellsthevalue-added applicationservicestothemarketbyusingarental-pricingmodel.Themarketis characterizedbyaprice-sensitiverandomdemand.TheASPÂ’sobjectiveistodetermine theoptimalpriceofitsservicetothemarketandtheoptimalcapacitytopurchasefrom theAIP.TheAIPÂ’sgoalontheotherhandistomaximizeitsprofitfromsellingthe capacitytotheASP. Inthefirstmodel,weexaminethesupplychainÂ’sperformanceunderfour differentcoordinationstrategiesinvolvingriskandinformationsharingbetweentheASP andtheAIP.Inthefirstscenario,asinglefirm(oracentralplanner)playstheroleof boththeAIPandtheASPtoachievethegoalofoptimizingthesupplychainasawhole. Inthesecondcoordinationscenario,theprice-sensitiverandomdemandinformationand theASPÂ’spricingandorderquantitydecisionsaredisclosedtothecomputercapacity provider,AIP.TheAIPcoordinatesthesupplychainandbearstheriskofover-and under-capacitycosts.Inthethirdscenario,theASPdoesnotcommunicateanymarket demandinformationanditspricingdecisionswiththecomputercapacityprovider,the AIP.InsteadtheASPapproachestheAIPforaquoteofprice-quantityscheduleand coordinatesthesupplychaindecisions.TheASPbearstheriskofover-andunder-

PAGE 154

139 capacitycostofthesupplychain.Finallyinthe“competitivealigned”scenario,boththe ASPandtheAIPoptimizetheirownprofitfunctionsandthencomebacktonegotiatea mutuallyagreeablepolicy. Throughextensivenumericalexplorations,wefindseveralkeymanagerial insightsfromoutmodelreiteratedasfollows.First,thecompetitivealignedcoordination strategygeneratesthesameperformance(expectedprofit)forthewholesupplychainas forthecasewherethesupplychainiscoordinatedbyacentralplanner.Inotherwords, thecompetitivealignedcoordinationstrategyisaneffectivedecentralizedmechanismto achievethesamegoalofmaximizingtheoverallsupplychainperformance.Inthe mutuallyagreeablepolicy,thecomputercapacitytheASPagreestobuyandtheAIP agreestosellbecomesthecapacitythatmaximizesthewholesupplychain’s performance.Absentthecompetitivealignedmechanism,wefindthatthewholesupply chain’sexpectedprofitwhentheASPcoordinatesthesupplychain,isbetterthanthe scenariowheretheAIPcoordinatesthesupplychain.Thisfindingseemstosuggestthat itisbettertolettheplayerclosertothemarketcoordinatethesupplychain. Second,weobservethatwhoevercoordinatesthesupplychainrealizesgreater profitthanwhentheotherpartnercoordinatesthechain.Moreover,whoevercoordinates thesupplychainachievesgreaterprofitthantheotherpartner.Themanagerial implicationisthatwhoevercoordinatesthesupplychainexploitstheinformationshared fromtheotherpartnerbyincludingtheinformationintheobjectivefunction. Inthesecondmodelweextendtheproblemtoanalyzerelationshipsbetweenone ASPandoneAIPundertheinfluenceofqueuingdelaysinordertomaximizeeach party’sexpectedprofitinadditiontothoseofthewholesupplychain.Also,potential

PAGE 155

140 customersconsideringjoiningtheASPÂ’sservicewilltakeintoaccountthecostcausedby thequeuingdelay,inadditiontothepricechargedbytheASP.Weexaminethesupply chainÂ’sandeachpartyÂ’sexpectedprofitunderfourcoordinationstrategies;supplychain, AIP,ASP,andcompetitivealigned.First,weanalyzethemodelwheretheAIPÂ’s expectedprofitfunctionislinear.Wethenstudythequeuingaffectsandinformation sharingwhentheAIPÂ’sexpectedprofitfunctionincludesdiseconomiesofscale.Inthis model,theinformationsharingincludescustomerarrivalrate,ASPÂ’sunitpriceandAIPÂ’s quoteofprice-capacityschedule.Inthismodel,jobsarriveintothecomputersystem randomly,theyspendrandomamountoftimeandtheyleavethesystem.Thearrivalrate isaffectedbythevalueofcomputersystemsandpriceofcapacity. Ourapproachshowsthatunderallcoordinationscenarios,thesupplychainÂ’s expectedprofit,utilizationratio,capacityandarrivalratedecreaseasthedelaycost increases.Inotherwords,whenthereisadelay,therearefewernewarrivalsthesystem, andthesystemislessused.Surprisinglytheimpactsofthedelaycostandcapacitycosts arehighertothewholesupplychainperformancewhenthecoordinationstrategyisthe wholesupplychainorcompetitivealigned.Oneprobableinterpretationofthisresultis thefollowing.Inthedecentralizedstrategies,theimpactsofthedelayandcapacitycosts mighthavebeensharedbetweentheinvolvedparties. Thirdimportantconclusionwehaveisthatmanagingthecoordinationstrategy playsasignificantroleontheexpectedprofitshare.Ourresultssuggestthatwhenthe pricingscheduleislinearbetweentheAIPandtheASP,ifasinglefirmisnotplayinga roleofboththeAIPandtheASP,theAIPhasthepowerofcoordinatingthesupply chain.ThereisadoublemarginalizationproblemincaseoftheASPÂ’sandcompetitive

PAGE 156

141 alignedcoordinationstrategieswhentheexpectedprofitfunctiondoesnotinclude diseconomyofscale.IftheAIPÂ’sexpectedprofitfunctionincludesthediseconomyof scale,theAIPandtheASPmaximizetheirexpectedprofitinadditiontothewhole supplychainwhentheycoordinatewithanalignedstrategy.Also,thisresearchpointout thatSupplyChainandAlignedCoordinationStrategiesgeneratethesameexpectedtotal supplychainprofitandutilizationratioofthesystem.Inotherwords,thecompetitive alignedcoordinationstrategyisaneffectivedecentralizedmechanismtoachievethe samegoalofmaximizingtheoverallsupplychainperformance.Intheabsenceof competitivealignedstrategy,theperformanceofthewholesupplychain,capacityand arrivalratesarehigheriftheASPcoordinatesthesupplychaininsteadoftheAIP coordinates.Similartothefirstmodel,itisbettertolettheplayerwhoisclosertothe marketcoordinatethesupplychain. Whenthecostoftheserviceincludesthecostcausedbyqueuingdelayandcostis chargedbytheASP,whoevercoordinatesthesupplychainrealizesgreaterprofitwhen theotherpartnercoordinates.Basicallywhoevercoordinatesthesupplychain,includes thesharedinformationintheobjectivefunction. Thethirdmodelanalyzesduopolisticpriceandcapacitycompetitionof applicationserviceproviderswiththeinfluenceofqueuingdelays.Weconsiderasupply chainmechanismthatconsistsoftwoserviceproviderswhosellstheirvalue-added servicestothemarketandcompeteforcustomers.Bothserviceprovidersneedtodecide howmuchcapacitytohaveandwhatpricetochargeinordertomaximizetheirprofits andmarketshares.Aswementioninthesecondmodel,potentialcustomersconsidering

PAGE 157

142 joiningtheASPÂ’sservicetakeintoaccountthecostcausedbythequeuingdelay,in additiontothepricechargedbytheASP. WeexaminetheASPscompetitionundertwostrategies;shortrunwhenthe capacitiesarefixed,andinthelongrunproblemasthecapacitiesarealsodecision variablesinadditiontopricedecisions.Inourmodel,weassumethatthetotalmarket sizeisfixedandgiven.Inotherwords,thepricingandcapacitydecisionsoftheASPs affectonlytheresultingmarketshareofeachfirm,nottheoverallmarketsize.Alsojobs arriveintothecomputersystemrandomly,theyspendrandomamountoftimeandthey leavethesystem.Thearrivalrateisaffectedbythevalueofcomputersystemsandprice ofcapacity.Oneofthemajordifferencefromthepastresearchthatwedonotdefineany reservationvaluethatimpactÂ’stheuserÂ’sdecision,usersneedtojoinoneoftheservice providers.Alsoourequilibriumisbasedonunitcostoftheserviceforacustomerrather thanthevalueoftheservice. Ourapproachshowsthatinthepricecompetitionproblem,afirmwithahigher capacityreceivesthelargermarketshareandchargesahigherprice.Whenthehigher capacityfirmcompeteswithhisfasterprocessingrate,thelowercapacityfirmcompetes withhislowerprice.Underallscenariosforpricecompetitionproblem,whenthe capacityoftheprovidersincreases,themarketpricedecreases,andthearrivalrateofthat serviceproviderincreases.Decreasingthecapacityfurtherdecreasesthearrivalrateof theASPandincreasesthepriceoftheservice.Whenthecapacityislow,congestion causeshigherprice.Inparticular,weshowthatthereisnodirecteffectofthedelaycost onthearrivalrate.Whentheunitdelaycostincreases,thepriceoftheservicealso increases.

PAGE 158

143 Fromthecapacitycompetitionproblem,weobservethatsimilartotheprice competitiongame,theASPwiththehighercapacityreceivesthehigherdemand.When thecapacitycostishigh,theASPchargeshighertobeprofitable.Finally,wediscover thatifallofthemarketconditionsaresymmetricincludingthemarginalcapacitycost, thereisnoeffectofdelaycostonthepriceorarrivalrate,ASPsneedtoincrease capacitiesinordertoservethecustomers. Extensionsofthisstudycouldfocusonseveralaspects.First,thebasicmodels studiedinthisresearchcouldbeextendedtoexaminedifferentcoststructuresoftheAIP andASP,setupcost,diseconomyofscale.Second,althoughwehaveonlyanalyzedthe duopolisticcompetitionofserviceproviders,thesecompetitionscanbestudiedforN serviceprovidersforinthemulti-stagegames.Alsotheimpactofcapacityrelated diseconomyofscalescanbefurtheranalyzed.

PAGE 159

144 APPENDIXA ANALYTICALPROOFOFCONCAVITITYOFSUPPLYCHAINPROFIT FUNCTIONINTHERISKANDINFORMATIONSHARINGOFAPPLICATION SERVICESSUPPLYCHAIN TheobjectivefunctionoftheoverallsupplychainscenarioinChapter2is concaveundercertainrathergeneralconditions.Sincebydefinition,1 ( , ) S PpQ is concaveonlyif1 ( , ) S PpQ isnegativesemi-definite,forall p and Q. TheHessianmatrix1 ( , ) S PpQ isnegativesemi-definiteifandonlyif i) 1 2(,) 0 dSPpQ dQ and 1 2(,) 0 dSPpQ dp ii) 1111 1 22(,)(,)(,)(,) (,)0 dSPpQdSPpQdSPpQdSPpQ SPpQ dQdpdQdpdpdQ =Š (Madden,1986).The Asweknowthatthesupplychain’sprofitfunctionis () 2 1 22 ()()2() 4 (,) 42 ()()() 44 Q pkdpbbcrdpb pberk SPpQQ bb rpdpbkdpb bb +Š+ŠŠŠŠ ŠŠ+Š=+ ŠŠŠŠ+ +Š . WhenwetakethefirstandsecondorderconditionsoftheprofitfunctionrespectivetopandQleadto 1(,)222 2 444 ()()() , 222 dSPpQpQrQkQ eQ dQbbb p dpbrdpbkdpb c b bbŠ =Š+Š Š+ŠŠŠ+ +ŠŠ+

PAGE 160

145 1 2 1 2(,)222 2 whereand, 0 444 (,) 0 dSPpQprk eprek dQbbb dSPpQ dQ Š =Š+Š , 1(,)2() 4222 dSPpQ Q dpbprk d Qdpbbb b ŠŠ+Š =++Š , 2 1 2 (,) (()) 42 ()()()() 224dSPpQQQ dpbpkr dpbb p rdpbkdpbdpb bbb Š =+Š+Š+Š ŠŠŠŠ+ŠŠ ++Š , 1(,)21 (()), 42dSPpQQ d pbpkr dpdQbb Š =+Š+Š+Š 22 1 2(,) 2()()2() 2224dSPpQ Q dpbprkdpb dpbbbb ŠŠŠŠŠŠŠ =+Š+ , 1 2(,) 0 dSPpQ dp . ThentheHessianmatrix1 (,) S PpQ isnegativesemi-definite, 1111 1 22(,)(,)(,)(,) (,)0 dSPpQdSPpQdSPpQdSPpQ SPpQ dQdpdQdpdpdQ =Š . ThedeterminantofthisHessianmatrixisfoundtobepositive,1 (,)0 SPpQ , 1 2(,) 0 dSPpQ dQ and 1 2(,) 0 dSPpQ dp where and,0 prek ,then1 (,) S PpQisa concavefunction.

PAGE 161

146 APPENDIXB PROOFOFTHEPROPOSITIONSFORTHEDUOPOLISTICPRICEAND CAPACITYCOMPETITIONOFAPPLICATIONSERVICEPROVIDERSWITHTHE QUEUINGEFFECTS Inthissection,weprovidetheanalyticalsolutionofthepropositionsweuseinthe Chapter4.Proposition4.1.Forsomerangeofparameters,whenthesecondorder conditionsof 1 and 2 arelessthanzero, () ()() () 2 2 11 233 1 11 212 20 v vµ µ µ µŠ =ŠŠ< Š ŠŠ and () ()() () 2 1 22 233 2 22 122 20 v vµ µ µ µŠ =ŠŠ< Š ŠŠ ,theproceduregivenconvergestothe uniqueNashequilibriumsolutionfortheduopolisticpricecompetitionproblem.When twofirmsarecompetingforthemarketdemand,thereexistsauniqueoptimalprices ( ** 12 , pp )andarrivalrates( ** 12 , )thatmaximizestheprofitfunction() ** 111 , p and() ** 222 , p ingivencapacities 1 µ and 2 µ .Proof.WesolvethefollowingfoursystemequationstofindtheuniqueNash equilibriumofthepricecompetitionproblem.Thesesystemequationsare Eq.(4.1), 12 1 12 2 11pvpv µ µ +=+ ŠŠ , Eq.(4.2), = + 2 1 , thefirstorderconditionof 1 intermsofthearrivalrate, 1

PAGE 162

147 Eq.(4.7),() ()() () 2 1 2 22 11 21 0 v v pµ µ µ µŠ +Š= Š ŠŠ , andthefirstorderconditionof 2 intermsofthearrivalrate, 2 Eq.(4.11),() ()() () 1 2 1 22 22 12 0 v v pµ µ µ µŠ +Š= Š ŠŠ whereEq.(4.3)0 1 , 0 2 , 11 µ > and 22 µ > . SubstitutingEqs.(4.2),(4.7)and(4.11)intoEq.(4.1),wegetthefollowing equationintermsofASP1’sarrivalrate.Thus, 12 1 12 2 11pvpv µ µ +=+ ŠŠ ,() ()() () () ()() () 12 21 2222 1 12 2 2211 122111vv vv vvµµ µµ µ µ µµ µµŠŠ Š++=Š++ ŠŠ ŠŠ ŠŠŠŠ() () ()() () 1 2 22 1121 11 212 2 11 0 µ µ µµ µ µŠ Š Š++Š= ŠŠŠ Š ŠŠand() () ()() 11 21 22 11 21 0 µ µ µ µŠ+Š Š += Š ŠŠ.(4.12) Aftersomealgebra,wedefinetheEq.(4.12)as()()()()()() ()()2 2 111212111 32222 1 2112121211 222322 2121211220 =234342 220gµµµµ µµ µµµµ µ µ µµµµµµµµµ=Š+ŠŠŠ+ŠŠ= Š+Š++ŠŠŠŠ++ Š+Š+Š++= thenifwechangethesignof() 1 g,()() 11 fg=Šand()()() ()32222 1 1211212121 1 222322 212121122234342 220.f µµ µµµµ µ µ µµµµµµµµµ=ŠŠ+ŠŠŠŠŠ++ ŠŠ+Š+Š++=

PAGE 163

148 When1 0 = ,() ()() ()()() 2 22322 1212121122 2 2 2112 2 2 2112022fa ===++ =+ =+ and 12 <+ ,then()1 00 f=> ,thus()21 0 >and()12 0. >Hence,() 1 1 0 df d >. FigureB-1Plotoftheequilibriumfunctionforgivenparameters,() 1 ffor12 7,0.1,6,10 v==== and1 7to7 = .

PAGE 164

149 FigureB-2Plotoftheequilibriumfunctionwhenthearrivalrateiszero,()1 00 f=for 12 µ µ <<1 7,2,2, v === 1 5to6.9999 µ= and2 7.1111to100 µ= .

PAGE 165

150 LISTOFREFERENCES Atick,J.(2001,July/August).AfutureforASPs?BiometricTechnologyToday , 7-8. Ballou,R.H.,Gilbert,S.M.,&Mukherjee,A.(2000).NewManagerial ChallengesfromSupplyChainOpportunities.IndustrialMarketingManagement,29 ,718. Bernard,A.(2000,October27).InvestorpreferenceshiftsfromASPstoAIPs. ASPNews.com . Braunstein,A.(1999).ThestateofASPs.RobertFrancesGroup . Cachon,G.P.(1998).Competitivesupplychaininventorymanagement.Tayur, S.,Ganeshan,R.,&Magazine,M.(Ed.),Quantitativemodelsforsupplychain management(pp.112-146).Boston:KluwerAcademicPublishers. Chen,F.,Federgruen,A.,&Zheng,Y-S.(2001).Coordinationmechanismsfora distributionsystemwithonesupplierandmultipleretailers.ManagementScience,47 (5), 693-708. Cheng,H.K.(1999).Pricingandcapacitydecisionsofclusteredtwin-computer systemssubjecttobreakdowns.DecisionSupportSystems,25 ,19-37. Cheng,H.K.,&Koehler,G.J.(2002).Optimalpricingpoliciesofweb-enabled applicationservices.DecisionSupportSystems (Forthcoming). Cotton,I.W.(1975).Microeconomicsandthemarketforcomputerservices. ComputingSurveys,7 (2),95-111. Crofts,M.R.,&Swatman,P.A.(2001).Informationsystemsoutsourcing:doinhousesystemanalystholdirreplaceableknowledge?SchoolofManagementInformation Systems,DeakinUniversity (Workingpaper). Davison,D.(2000,June12).ASPpricingparameters.ServiceManagement Strategies.MetaGroup . Dodson,C.T.J.,&Gonzalez,E.A.(1995).Experimentsinmathematicsusing maple .NewYork:Springer-VerlagBerlinHeidelberg.

PAGE 166

151 Ellinger,A.E.(2000).Improvingmarketing/logisticscross-functional collaborationinthesupplychain.IndustrialMarketingManagement,29 ,85-96. Erenguc,S.S.,Simpson,N.C.,&Vakharia,A.J.(1999).Integrated production/distributionplanninginsupplychains:aninvitedreview.EuropeanJournalof OperationalResearch ,115,219-236. Frequentlyaskedquestions.(1999).ASPIndustryConsortium . Heck,A.(1993).Introductiontomaple .NewYork:Springer-VerlagBerlin Heidelberg. Ingene,C.,&Parry,M.(1995).Coordinationandmanufacturerprofit maximization:Themultipleretailerchannels.JournalofRetailing,71 ,129-151. Jester,R.(2000,December11).WhatdouserswantfromASPs?Gartner Advisory,DataquestPerspective . Jueland,A.,&Shugan,S.(1983).Managingchannelprofits.MarketingScience, 2 ,239-272. Kumar,K.R.,Loomba,A.P.S.,&Hadjinicola,G.C.(2000).Marketingproductioncoordinationinchannelsofdistribution.EuropeanJournalofOperations Research,126 ,189-217. Li,L.,&Lee,Y.S.(1994,May).Pricinganddelivery-timeperformanceina competitiveenvironment.ManagementScience,40 (5),633-647. MacLennan,B.(2000,October27).Corioaddsstructureashostingpartner. InternetNews–ASPNews. Madden,P.(1986).Concavity&optimizationinmicroeconomics .NewYork: BasilBlackwellInc. Maoz,M.(2000,June28).CRM-capableASPs:valuabletothosethatchoose wisely.GartnerAdvisory . Mason,R.P.,&Grieser,T.(2000,June).WorldwideMSPmarketforecastand analysis,2000-2004.IDCFlash . McKie,S.(1999,November).OutsourcingwithASPsintheinternetage. BusinessFinance,61 . Mendelson,H.(1985).Pricingcomputerservices:queuingeffects. CommunicationsoftheACM,3 ,312-321. Mendelson,H.(1987).Economiesofscaleincomputing:Grosch’slawrevisited. CommunicationsoftheAssociationforComputingMachinery,30 ,1066-1072.

PAGE 167

152 Michel,J.A.,&CoffmanJR,E.G.(1974,April).Synthesisofafeedback queueingdisciplineforcomputeroperation.JournaloftheAssociationforComputing Machinery ,21(2),329-339. Mizoras,A.(2001,September21).ASPsheretostay.IDC-CIOAnalystCorner . Moorthy,K.(1987).Managingchannelprofits:comment.MarketingScience,6 , 375-379. Muse,D.(2001,October11).Whatmakesatop20ASP?ASPNews.com . OÂ’Reilly,J.(2001,June).CostsavingsleadsreasonsforASPpurchase,new marketstudyfinds.ASPIndustryOrg . Patnayakuni,R.,&NainikaS.(2001).WhyLicensewhenyoucanrent ?San Diego,CA:ACM2001. Paulak,E.,&Terdiman,R.(2000,June22).CRMASPservices:isithosting, ASPsoroutsourcing?GartnerAdvisory . Rasch,P.J.(1970,January).Aqueueingtheorystudyofround-robinscheduling oftime-sharedcomputersystems.JournaloftheAssociationforComputingMachinery, 17 (1),131-145. Redfern,D.(1996).Themaplehandbook .NewYork:Springer-VerlagBerlin Heidelberg. Roddy,D.J.(1999).TheInternet-basedASPmarketplace,renaissanceofthe value-addednetwork.DeloitteResearch . Rubens,P.(2001,September19).Infrastructuresoftwarevendorscaughtina catch-22.ASPNews.com . Rubens,P.(2001,October24).WhatÂ’ssobadaboutabadeconomy? ASPNews.com . Rutherford,E.(2000,June26).ABCsofASPs.CIOOutsourcingResearch Center . Selwyn,L.(1970,June).Ecomiesofscaleincomputerusage,initialtestsand implicationsforthecomputerutility.(Doctoraldissertation,SloanSchoolof Management,MIT,1970).ProjectMACTech.ReportTR-68 . Sia,C.-L.,&andHo,Y.S.(1997).Predictivecapacityplanning:aproactive approach.InformationandSoftwareTechnology,39 ,195-204. Silberschatz,A.,Peterson,J.L.,&Galvin,P.B.(1991).Operatingsystem concepts (3rded.).Massachusetts:Addison-WesleyPublishing.

PAGE 168

153 Silver,E.A.,&Peterson,R.(1975).Decisionsystemsforinventorymanagement andproductionplanning .USA:JohnWiley&SonsInc.. Skiera,B.,&Spann,M.(1999).Theoryandmethodology–theabilityto compensateforsuboptimalcapacitydecisionsbyoptimalpricingdecisions.European JournalofOperationalResearch,118 ,450-463. So,C.K.(2000).Priceandtimecompetitionforservicedelivery.Manufacturing andServiceOperationsManagement,2 (4),392-409. TheASPnewstop20-Octoberupdate.(2001,October9).ASPNews.com . TheASPs’ImpactontheITIndustry:AnIDC-WideOpinion.(1999, September).InternationalDataCorporation . TheStateoftheASPIndustry.(2000,July1).Corio . Thomas,D.J.,&Griffin,P.M.(1996).Coordinatedsupplychainmanagement. EuropeanJournalofOperationalResearch,94 ,1-15. Wainewright,P.(1999).Packagedsoftwarerental:thenet’skillerapp .London, England:FarleitLimited. Wendland,R.(1999,July).ApplicationserviceprovidersareportbyDurlacher Research.DurlacherResearch . Weng,K.(1995).Channelcoordinationandquantitydiscounts.Management Science,41 (9),1509-1522. Weng,Z.K.(1999).Manufacturinganddistributionsupplychainmanagement: alliancesandcompetition.MarketingScienceInstituteReport, 99-117. Williams,A.(2001,August).ASPsandcustomization.ASPnews.com .

PAGE 169

154 BIOGRAPHICALSKETCH HalukDemirkanwasborninAksaray,Turkey.HereceivedtheBachelorof SciencedegreeinmechanicalengineeringfromIstanbulTechnicalUniversityin1991 andtheMasterofEngineeringdegreeinindustrialengineeringfromtheUniversityof Floridain1995.HeiscurrentlywiththeDepartmentofDecisionandInformation SciencesoftheUniversityofFlorida.Hisresearchinterestsfocusonmanagementof informationsystems,electroniccommerce,supplychainmanagement,project management,decisionsupportsystemsanddatamanagement.Inadditiontohisstudy,he hasworkedasaBusinessIntelligenceTechnicalPrincipleconsultantinanumberof firms.HeisamemberofAlphaPiMuIndustrialEngineeringHonorSociety,Project ManagementInstitute,InstituteforOperationsResearchandtheManagementSciences, AssociationforInformationSystemsandtheAmericanSocietyforQuality.