The effect of activity-based costing on traditional operations research models

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The effect of activity-based costing on traditional operations research models
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by Diana I. Angelis.
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THE EFFECT OF ACTIVITY-BASED COSTING
ON TRADITIONAL OPERATIONS RESEARCH MODELS












By


DIANA I. ANGELS


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA

1996


UNIVERSITY C- FrL -A UL":IS






















I dedicate this work to my husband, Jim, who kept me going through this long journey,

to my daughters, Alix and Kris, who bring joy and laughter to every day,

and to my parents, Judith and Jaime, who inspired me by example.
















ACKNOWLEDGMENTS


I wish to thank Dr. Chung-Yee Lee for creating the opportunity for students to

expand their horizons into new topics not normally associated with engineering and for

patiently and ceaselessly encouraging and guiding me in this endeavor. I am indebted to

him and to the other members of my committee, Dr. Barney L. Capehart, Dr. Douglas

A.T. Snowball and in particular, Dr. D. Jack Elzinga, for his valuable comments and

support. I also wish to thank Dr. B.D. Sivazlian for his personal interest in my academic

success and spiritual well-being. Finally, I would like to acknowledge the financial

support of the National Science Foundation, IBM Corporation and the College of

Engineering.














TABLE OF CONTENTS


ACKNOW LEDGM ENTS ........................................ ............................................ iii

LIST OF TABLES ........................................................................................................ vii

LIST OF FIGURES............................................................................................ viii

ABSTRACT................................................................................................................... ix

CHAPTERS

1 INTRODUCTION ..................................................................................................... 1

Activity-Based Costing ..................................................... ... ........................
Example......................................................... ................................................... 6
Decision M making with ABC .............................................................................9

2 LITERATURE REVIEW ................................................................................ 12

Development of ABC............................................................. .......................... 12
Case Studies and Applications.......................................................................... 15
Lim stations of ABC ......................................................................................... 16
Operations Research M odels.......................................................... ................... 19
Economic Order Quantity............................ ............................................... 19
Investment Analysis.......................................................................................... 19
Analytical Hierarchy Process .................................................. ................ 21
Break-even Analysis....................................................................................... .. 21
Pricing and Product M ix.................................................................................. 22
Product Design .................................................... ................................. 22
The Engineering Perspective ................................................................................ 23

3 ECONOM IC ORDER QUANTITY...................................................................... 24

Introduction............................................................................................................. 24
The Inventory M odel ........................................................................................... 25
Single Product.................................................................................................... 30
Setup Costs ....................................................... ................................................... 31
Number of Clerks as the Cost Driver............................................................... 31
M multiple Products......................................................................................... 33








Fixed and Variable Setup Costs ..........................................................................40
Inventory Costs........................................................................................................44
Number of W arehouses as Cost Driver...................................... ................ 45
Conclusion......................................................................................................... 47

4 INVESTM ENT ANALY SIS .............................................................................. 49

Activity-based Investment ..................................................... ........................... 49
Non-financial Considerations.................................................................... 51
Decision M odel.................................................................................................. 52
Cost Im pact ................................................................................................. 54
Perform ance Impact...................................................... ............................. 62
Choosing Investment Alternatives ................................................................. 64
Conclusion............................................................................................................... 66

5 DETERMINISTIC SCHEDULING.................................. ........................... 68

Cost Considerations.............................................................................................. 68
Cost Parameters................................................................................................. 69
Schedule Dependent Cost Drivers ................................................... ............... 72
Setup Tim e .................................................................................................. 73
Number of Setups ......................................................................................... 73
Cost Improvements............................................................................................ ..... 74
Cost M inimization...........................................................................................75
Conclusion............................................................................................. ........ ........... 76

6 COST/SCHEDULE ANALYSIS ...................................................... .. .............. 77

Traditional M odel......................................................................................... 77
ABC M odel ........................................................................... .. ........................ 79
Conclusion ......................................................................................................... 82

7 PRODUCT M IX................................................................................................. 84

Traditional M odel ............................................................................................... 84
Volume-Related Fixed Costs........................................................................... 85
ABC M odel .................................................................................. ..................... 87
Conclusion................................................................................................... 89

8 BREAK-EVEN ANALYSIS.................................................................... 91

Traditional M odel................................................................................................. 91
ABC M odel ............................................... ........................................... ........... 94
Example............................................... ...................................................... 96
Step Function Fixed Costs.............................................................................. 99
Conclusion....................... ................................................................................ 100








9 CONCLUSION AND FURTHER RESEARCH.................................................... 102

Conclusion........................................................................................................ 102
Cost Parameters ....................................................... ............................... 102
Indirect Costs................................................................................................... 103
Problem Structure ........................................ ............................................ 103
Further Research........................ ............... 104
Location Models ............................ .......................................... ........ 104
Network Models ....................................... ....... 107
Other Areas.............. .......................................................................... 109

LIST OF REFERENCES................................................ ........................................ 110

BIOGRAPHICAL SKETCH ....................................................................... 118














LIST OF TABLES

Tabk lep

1-1 Overhead costs............................................................................................... 7

1-2 Traditional Overhead Allocation................................................................... 7

1-3 Resource Drivers............................................................................................ 8

1-4 Allocation of Resources to Activities............................................................ 8

1-5 Activity Drivers.............................................................................................. 8

1-6 Allocation of Activities to Products................................................. ............. 9

4-1 Cost Savings ................................................................................................ 58

4-2 Resource Driver Usage ............................................................................ 60

4-3 ABC Cost Allocation for Machine A ............................................ ........... 60

4-4 ABC Cost Allocation for Machine B ............................ ............ ........... 61

4-5 Performance Measures ............................................................................... 64

6-1 Cost Driver Consumption........................................................................... 97

6-2 Allocation of Fixed Costs to Products ...................................... .............. 98














LIST OF FIGURES

Figure age

Figure 1-1. Activity-based Cost Allocation........................................................... 5

Figure 3-1. Cost vs. Order Quantity.................................................................... 36

Figure 4-1. Cost and Performance Impact of Investments........................ ............. 53

Figure 4-2. Allocation of Cost Impact to Activities .................................... ........... 56

Figure 4-3. AHP Priority Weights for Goals and Activities.......................................... 59

Figure 4-4. Cost Impact for Example.............................................. ...................... 62

Figure 4-5. Performance Impact for Example.......................................... .............. 65

Figure 4-6. Cost vs. Performance............................................................................ 65

Figure 5-1. Lateness Penalty Function................................................................... 70

Figure 7-1. Activity Cost When by > d ....................................................................... 81

Figure 7-2. Activity Cost When by < d ....................................................................... 82















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


THE EFFECT OF ACTIVITY-BASED COSTING
ON TRADITIONAL OPERATIONS RESEARCH MODELS

By

Diana I. Angelis

August, 1996

Chairman: Chung-Yee Lee
Major Department: Industrial and Systems Engineering


Activity-based Costing (ABC) was originally developed to improve product

costing in complex manufacturing environments. The concepts of ABC have been

extended to management through Activity-based Management (ABM) and are widely

accepted in the management and accounting fields; however, little research has been done

on the effects of this new accounting system on the operations research models

traditionally used by industrial engineers. ABC is a valuable tool that not only eliminates

product cost distortion, but can also provide important information about the

manufacturing process.

The cost accounting system is used to allocate the costs of operation to

departments, activities and products. Thus it provides the values for the parameters used

in engineering decision models and can affect the results of these models. More

importantly, the way in which costs are allocated defines the mathematical formulation of

the objective function in these models. ABC methodology, with its emphasis on activities









and non-volume-based cost drivers, can significantly change the assumptions made in

decision models. This in turn can change the objective function and/or the structure of

traditional operations research models.

We examine the effect of ABC on inventory lot size (economic order quantity),

investment analysis, deterministic scheduling, project management (cost/schedule analysis)

and production (product mix and break even analysis). In each case we seek to discover

how industrial engineers can use the information provided by ABC to revise and improve

these quantitative models. The primary objective is to show how the assumptions made by

the accounting system are critical to the formulation of operations research models.

Without this insight, the results predicted by these models may not be optimal and may not

be validated by the financial results reported in the accounting system.














CHAPTER 1
INTRODUCTION


Activity-Based Costing

Over the past decade, many companies have revised their cost systems significantly

as they reorganized to become more competitive in an environment that demands high

quality, excellent service and reasonable prices (Mecimore and Bell, 1995). These new

cost systems are founded on activity-based costing (ABC). Although activity-based

costing was developed primarily to improve product costing, it can also provide valuable

information about the manufacturing process. This is important to industrial engineers

who work with these processes on a daily basis. While many industrial engineers might

not feel that the cost accounting system is relevant to their work, the fact is that the cost

accounting system provides the values for the parameters used in industrial engineering

decision models. If the values are distorted or incorrect, then the decisions will be

erroneous. In today's competitive environment, costing errors can lead to significant

losses and it is imperative that management understand the true cost of doing business.

ABC provides management with this information.

Cost accounting is concerned with the allocation of costs within the business

environment. In manufacturing the focus is on the allocation of costs to products. This

information is used by management in three ways: planning, reporting and controlling. In

each case how costs are traced to products can significantly influence the outcome of

decisions. For years organizations have operated under the assumption that cost

information was accurate because it was precise, when in fact, many cost systems were

providing misleading and inaccurate information.









Traditionally, materials, labor and manufacturing overhead are allocated to

products based on the number of labor or machine hours or direct material dollars

consumed. Although this simple, one-stage allocation scheme (from resources to

products) can distort product cost, it made sense when it was first developed, since labor

and materials often represented the majority of the manufacturing cost, while overhead

was a small fraction of the cost. This was true in labor intensive manufacturing

environments that produced a narrow range of products. Thus the effort and expense of

collecting and processing data manually could hardly be justified to correct minor cost

distortions.

Kaplan (1989) notes that traditional accounting control procedures stressed

adherence to centrally determined standards, in accordance with the principles of scientific

management. Extensive reports on the deviations of actual costs from the standards were

prepared monthly, but the information used to prepare the standards and reports was

crude, due to the expense of collecting data. Accounting systems allocated overhead

based on data that was already being collected for other purposes: direct labor quantities

as reported on payroll time cards and material usage as reported in purchase orders.

In the past 20 years many companies have experienced significant changes in their

cost structure (Hardy and Hubbard, 1992). As the cost of the manufacturing process has

increased, the relative importance of raw (direct) materials has decreased. At the same

time, complex technology requires a complex support system and the cost of overhead, or

indirect expense, has increased dramatically. For example, one leading semiconductor

company had overhead costs that were 1400% of direct labor cost (Mangan, 1995). As a

result, overhead has become the dominant cost component of many products. Traditional

cost accounting has failed to properly address these changes, which can lead to significant

distortions in product cost, particularly if the allocation base is unrelated to the actual

consumption of resources. Activity-based Costing was developed to address this issue.









As early as 1963 Peter Drucker warned of the dangers of using traditional product

costing to guide marketing decisions; however, costing products using activity-based

costing was infeasible before the advent of modern computer technology and software.

As the cost of information processing decreased and the capabilities of personal

computers increased, companies began to experiment with new approaches to

management accounting systems. During the 1970s and early 1980s companies such as

Schrader Bellows, John Deere, Hewlett-Packard and Union Pacific used ABC to obtain

better product cost information to guide them in pricing and product mix decisions. Robin

Cooper formally defined the concepts and principles of activity-based costing in a series of

articles in the late 1980s. Other authors, such as H. Thomas Johnson, Robert S. Kaplan

and Peter B. B. Tumey also made significant contributions.

Activity-based Costing, as the name suggests, traces costs to cost objects

(products, customers, etc.) through activities. This is in contrast to traditional cost

accounting which traces costs directly to products. Activities, rather than products,

consume resources and the demand for those activities in the manufacturing process

determines how the costs are allocated to the individual cost objects. Resources include

all the costs recorded by the accounting system in carrying out daily business, such as

salaries, materials and overhead (rent, utilities, insurance, advertising, etc.). Activities are

procedures that are carried out in order to manufacture a product or provide a service.

The business processes can be broken down into activities. Typically, activities are

grouped by function and the grouping is referred to as an activity center. Cost objects are

the final result of the business process.

The two-stage cost assignment from resources to activities and then from activities

to cost objects is based on multiple cost drivers, such as number of setups, square footage

of warehouse space, number of purchase orders, machine hours, number of parts, number

of defects, etc. Cost drivers are the bases used to make cost assignments and can be

resource drivers or activity drivers, depending on whether we are allocating resource costs









to activities or activity costs to products, respectively. Cost drivers are selected to reflect

the cause-and-effect relationships in the manufacturing process. While traditional cost

accounting allocates costs to products using volume cost drivers, ABC recognizes that

costs may be driven by other factors, such as complexity.

Direct labor and materials can be allocated the same way under either traditional

cost accounting or ABC, but overhead allocation is much more sophisticated under ABC,

since it allows for multiple cost drivers. As a result, the ABC product costs can be

radically different from those of the traditional cost accounting system. For example,

traditional accounting will undercost a complex low volume product, subsidizing its cost

by allocating most of the overhead to high-volume, standard products. The result can lead

to incorrect decisions about product mix, pricing and process improvement. ABC is able

to provide a more refined and "accurate" view of process costs thanks to the wide-spread

use of computer technology in the manufacturing environment. This enables companies to

economically compile the multiple cost driver information needed for the ABC system.

If we look at the allocation rates used in any cost accounting system (including

ABC) we note that they are stated in terms of dollars per unit. The numerator is the cost

of resources or activities (in dollars) and the denominator is some measure of how the

resource or activity is consumed (for example, time, number of parts, dollars, etc.). In

ABC, the denominators used to allocate resource dollars to activities are called resource

drivers and those used to allocate activity dollars to products are called activity drivers.

Figure 1-1 illustrates how ABC allocates costs to products (or cost objects).






SSome authors limit the use of the term "cost driver" to the causal events that influence
the quantity of work (see Raffish and Turey, 1991). We use it in a more general sense,
referring to the mechanism of cost assignment (as most authors do) because causal events
are very often used as the resource and activity drivers in the ABC system.

























Figure 1-1. Activity-based Cost Allocation


Let the dollar amount of each resource cost pool k be Cad. Then the total cost of


resources to be assigned to products (or any other cost objects) will be 2 C, = C. The
k

actual amounts are usually obtained from the accounting records, such as the general

ledger, or the operating budget for each department. The first step is to assign the

resource dollars in each department to the activities performed in that department. Each

cost pool within the department will use a different resource driver or allocation base to

distribute Cka. For example, if we want to allocate fuel costs, we might use number of

gallons as our allocation base. Let ri be the amount of resource k driver (allocation base)

consumed by activity (the number of gallons consumed by each activity). Then the total


allocation base for resource k is rV = rk (the total number of gallons used by the

department) and the allocation rate for resource k will be C, I rk (dollars/gallon). The

dollar amount allocated from resource k to activity j is calculated as C,( r = Cg.
do k *


Resources (k)

Resource
Drivers

Activities 0) C

Activity
Drivers


Products (i)








We do this for all the resources to arrive at the cost of the activities. Thus each activity
has a total dollar cost of Y'i C = C4 .

Next we will allocate the cost of each activity to the products that demand that

activity. Suppose the activity is material transfer, which includes fuel costs, as well as

other resource costs. We might choose to allocate the costs of this activity based on the

number of trips. Let a, be the amount of activity driver (trips) consumed by product i

(for simplicity, assume each trip can only accommodate one type of product). Then the


total activity driver (total number of trips) for activity is Xa1i = a, and the allocation

rate for activity j is C, / a, (dollars/trip). The cost of activity allocated to product i is

calculated as C, i a = Ci and the total cost of product i will be Cc, = C, .

Note that it is possible (and often necessary) to allocate the cost of one or more

activities to other activities rather than directly to products. This will be the case for

support activities or departments such as maintenance or personnel. In this case the total

cost of some activities would include not only Ci dollars, but also some CAJI dollars

(where the cost of activity j had been allocated to activity i).


Example

The following is an example of how ABC can significantly change product costing.

Suppose a company manufactures four products: A, B, C and D. The products differ in

batch sizes (volume). Table 1-1 shows the resources used in one period (this example is

limited to overhead resources, since direct materials and labor are assumed to be allocated

directly to the product).








Table 1-1. Overhead costs


Table 1-2 shows the allocation of these resources directly to each product using a

traditional cost accounting system based on machine hours.


Table 1-2. Traditional Overhead Allocation
Product Volume Mach hours O/H rate Allocation Cost/Unit

A 10 5 $56.82 $284 $28.40

B 100 50 $ 56.82 $ 2,841 $ 28.40

C 10 15 $ 56.82 $ 852 $ 85.20

D 100 150 $ 56.82 $ 8,523 $ 85.20

Total 220 $ 12,500


Suppose that four activities consume the resources: transporting parts to and from

the machines, setting up the machines, machining the parts and administration. Table 1-3

shows the resource drivers and Table 1-4 shows how the overhead is allocated to each of

these activities. In Table 1-5 we show the activity drivers and Table 1-6 shows how the

costs of the activities are allocated to each of the products. Note the significant

differences in the cost per unit of products A and C. Such changes in product cost are

typical when an ABC system is implemented and a more accurate allocation of overhead is

made.








Table 1-3. Resource Drivers
Resource Driver Transp Setup Mach Adm Total

Benefits # of people 1 2 4 1 8

Electricity Watts 100 800 100 1000

Supplies Dollars 700 300 1000

Gasoline Gallons 400 400

Rent Sq. feet 100 1700 200 2000



Table 1-4. Allocation of Resources to Activities
Resource Transp Setup Mach Adm Total

Benefits 375 750 1,500 375 3,000

Electricity 500 4,000 500 5,000

Supplies 700 300 1,000

Gasoline 500 500

Rent 150 2,550 300 3,000

Total ($) 1,025 1,950 8,050 1,475 12,500



Table 1-5. Activity Drivers
Activity Driver A B C D Total

Transportation no. trips 3 2 5 10 20

Setup no. setups 2 3 2 3 10

Machining mach. hours 5 50 15 150 220

Administration # of parts 2 2 3 3 10








Table 1-6. Allocation of Activities to Products
Product Transp Setup Mach Adm Total Cost/Unit

A 154 390 182 295 1,021 102.10

B 103 585 1,830 295 2,813 28.13

C 256 390 549 443 1,638 163.80

D 512 585 5,489 442 7,028 70.28

Total ($) 1,025 1,950 8,050 1,475 12,500


This example serves to illustrate how low-volume (relative to machine hours)

products such as A and C can be underpriced by the traditional cost accounting system.
The ABC analysis showed that these products, although requiring relatively little

machining, still needed a significant portion of the other activities. This could be the case

if the product is very complex or requires special handling. The old accounting system

was in essence subsidizing the low-volume products by allocating the overhead based on

machine hours, when in fact, much of the overhead was independent of machine hours.


Decision Making with ABC

Although ABC was originally developed to improve product costing, its real

strength lies in its analysis of the business process and the focus on activities required to

manufacture the product or provide a service. This focus on activities has been extended

to management in a philosophy known as activity-based management (ABM). The goal of
ABM is continuous improvement and this is achieved by managing activities rather than

departments or divisions. In developing an ABC model, management must first identify,

analyze and understand the activities involved in the business process. This is the key to

process improvement. ABM uses the information provided by ABC to identify value-









added and non-value-added activities and to improve manufacturing processes and

product design.

For industrial engineers, that means using ABC to improve our decision models.

As we will see in this research, insights gained from ABC analysis can improve the results

of traditional operations research models. Activity-based costing allows decision makers

to accurately trace overhead and to determine the real causes of overhead. This

information can be used to eliminate or improve activities that consume excessive amounts

of overhead. ABC also highlights and quantifies the impact of design decisions on

overhead costs, which can dramatically affect the final cost of products. Knowing this

information ahead of time allows engineers to improve product and process design.

We will look at how ABC affects some of the traditional decision models used by

industrial engineers to control and improve processes. We assume that the cost

parameters used in these models are derived from accounting records. This is a very

reasonable assumption since the alternative is to estimate the values without any

consideration of the actual costs of manufacturing. Even if cost parameters are based on

previous experience or benchmarking, the values are credible only if they were originally

derived from the actual costs collected in the accounting system. Given this assumption,

we will look at how ABC may change the value of these parameters and thus the results of

the model. We will also see how the ABC methodology, with its emphasis on activities

and non-volume-based cost drivers, may also change the model assumptions and therefore

the objective function or the formulation.

As we examine a variety of operations research models, we will see that the

underlying theme in each of the chapters is the fact that ABC makes it possible to build

better models by providing accurate information about indirect costs. These costs have

traditionally been treated by accountants as "fixed" with the cost accounting system

spreading them out over products based on volume or some volume-related driver. The

result has been not only inaccurate product cost information, but misleading decision









models. This is because the decision models depend on the information provided by the

cost accounting system. If accurate information about indirect costs is not available from

the cost accounting system, then the decision models will also be lacking. In fact, most of

the operations research models that we examined had this common flaw: indirect costs

were treated as "fixed" and were either excluded completely from the model, or

introduced in a very primitive fashion, assuming that they varied as a percentage of

volume.

We will provide insight into how industrial engineers can use the information

provided by ABC to improve and revise these models. The primary objective is to show

how the assumptions made by the accounting system are critical to the outcome of the

decision model and must therefore be considered by the industrial engineer in formulating

these models. Moreover, if the assumptions made by the accounting system and the

decision model are not the same, management may be frustrated in its efforts to improve

the manufacturing process because the results predicted by the model may not be realized

in the financial results reported by the accounting system and used to measure

management performance.













CHAPTER 2
LITERATURE REVIEW


Development of ABC

The concept of activity-based costing has been prevalent in accounting journals

since the late 1980s when it was first defined and popularized. Since then, hundreds of

articles have been written on the subject, mostly in business journals, the majority of them

being either of a descriptive nature or case studies. Relatively few articles have explored

the implications of ABC on areas outside product costing and process improvement and

even fewer have ventured outside the field of accounting to look at the affect of ABC on

industrial engineering models.

In the 1960s, General Electric developed activity cost analysis in order to obtain

better information for managing indirect costs. The technique traced each indirect activity

in the company to one output of a particular department. The outputs caused other

departments to engage in activities. The goal of the analysis was to determine the

approximate percentage of time each employee spent on indirect activities and to trace the

primary cause of each activity to the output of a department. However, GE did not

extend this concept to product costing (General Electric, 1964).

In 1963 Peter Drucker warned of the dangers of using traditional product costing

to guide marketing decisions and recognition of problems with traditional cost accounting

grew during the 1970s. Driven by the availability of low-cost semiconductor technologies

ABC began to appear in the late 1970s as a solution to product cost distortion. The idea

of using cost drivers for product costing was initially implemented by consulting firms

during the 1970s and early 1980s for companies such as Schrader Bellows, John Deere









and Union Pacific to obtain better product cost information to guide them in pricing and

mix decisions (Johnson, 1992). Berlant, Browning and Forster (1990) describe an

activity-based system implemented at Hewlett-Packard based on an off-line accounting

system developed by the manufacturing department.

In the early 1980s articles began to appear in the literature highlighting the

problems with traditional product costing and formalizing the concepts of ABC. Miller

and Vollman (1985) describe a "hidden factory" that incurs overhead costs that are not

controlled by the cost accounting system. They suggested using drivers other than volume

to allocate overhead. Brimson (1986) noted that most accounting systems did not provide

the information necessary to manage automated manufacturing systems and Seed (1984)

described changes needed in cost accounting systems in order to provide more reliable

product cost information in advanced manufacturing environments.

In their book Relevance Lost: The Rise and Fall of Management Accounting

(1987), Johnson and Kaplan called for major changes in the way organizations measure

and manage costs. They noted that management accounting information is driven by the

procedures and cycles of the organization's financial reporting system which makes it too

aggregated and distorted to be relevant for planning and control decisions. They observed

that financial accounting systems produce short-term profit pressures that can lead to a

decrease in investment in the long-run. Monthly accounting statements can signal

increased profits even when the long-term economic health of the firm has been

compromised. They argued that new accounting systems were needed to take advantage

of the reduced costs of collecting, processing, analyzing and reporting information brought

about by the computing revolution. Computers used in automated factories can provide

timely and relevant managerial information that can be used to develop more accurate,

timely and effective reporting and controlling systems.

Cooper and Kaplan (1988a) discuss how product costs are distorted by the

traditional cost accounting systems used by several manufacturing firms (the paper is









based on information gained from studying more than 20 firms). They argue that marginal

costing, long advocated by economists and accountants for product decisions, is rejected

in practice because of the long-term commitments required to implement such decisions.

However, the full cost information provided by traditional systems is not accurate and may

also lead to incorrect decisions. They suggest that product costing must take into account

the cost of complexity and transactions as well as volume. Robin Cooper formally defined

the concepts and principles of activity-based costing in a series of articles titled "The Rise

of Activity-Based Costing" in the late 1980s (1988a,b, 1989a,b). He identified diversity

(in volume, size, complexity and other drivers) as the cause of bias in volume-based cost

systems and developed a model to examine the relationship between the cost of

measurement and accuracy in developing the optimal cost system and the factors affecting

these parameters. He discussed factors that should be considered when designing an ABC

system, including how many and what kind of cost drivers should be used based on

sensitivity analysis. He also illustrated the concepts with five case studies.

Cooper and Kaplan (1988b) further illustrate the effect of ABC on product costing
and discuss its value from a strategic point of view. Turney (1989, 1991) extends the

concept of ABC to product design and continuous improvement and discusses how ABC

can be used to create behavioral incentives and reduce cost. Cooper and Kaplan (1991)

developed an activity hierarchy, arguing that certain expenses cannot be allocated at the

unit level. They identified four levels of activities: facility-sustaining, product-sustaining,

batch-level and unit-level. Turney (1992a) defines Activity-based Management (ABM) as

using ABC information for continuous improvement and describes how ABC is linked to

strategic choices. Kaplan (1992) describes the connection between ABC and ABM and

Cooper and Kaplan (1992) discuss ways in which ABC information can be used to

increase profits through resource and activity management. Mecimore and Bell (1995)

describe the evolution of ABC from a product-costing focus to a process and business unit








focus and eventually to a company-wide focus. Stratton (1993) argues that ABC should

be extended to financial reporting.

Roth and Borthick (1989) describe an off-line ABC system designed to supplement

the formal accounting system, which is how most companies implement ABC. They

recognized some limitations to ABC, such as the inability to trace certain costs (due to

practical limitations), the arbitrary choice of time periods in measuring product costs and

the omission of costs related to marketing, advertising, R&D, warranties, etc. Hardy and

Hubbard (1992) contrast traditional cost accounting with ABC, discussing the strengths

and weaknesses of both systems, while Bonsack (1991) shows how standard costing and

ABC are compatible.

Needy and Malzahn (1993) use simulation models to identify the conditions under

which strategic decisions and resulting performance differed between traditional cost

accounting and ABC. Babad and Balachandran (1993) provide an optimization model

that balances savings in information processing costs with loss of accuracy. They show

how to determine the number of drivers and identify the representative cost drivers. The

model is formulated as an integer program.


Case Studies and Applications

In recent years numerous case studies have been published describing the

implementation and impact of activity-based costing on organizations: O'Guin (1990),

Harr (1990), Phillips and Collins (1990), Lee (1990), Jones (1991), Haedicke and Feil

(1991), Pederson (1991), Brausch (1992), Plug (1992), Cooper et al. (1992), Rodgers,

Comstock and Pritz (1993), Anderson (1993), McConville (1993), Mays and Sweeney

(1994), Mangan (1995) and Bharara and Lee (1996). Cooper (1991) describes a seven-

step plan for implementing activity-based costing systems and Sharman (1994) suggests a

method to identify activities and drivers for ABC implementation. In 1993, the Institute of









Management Accountants issued a statement that provides an overview of the process of

designing and implementing an ABC system.

Many authors have also written articles describing ABC and how it can be used in

different areas of management: Sharman (1990), Drury (1990), Chaffman and Talbott

(1991), Raffish (1991), Ray and Gupta (1992), Stevenson, Barnes and Stevenson (1993)

and Tippett (1993). Beischel (1990) discusses process value analysis and ABC, while

Yoshikawa, Innes and Mitchell (1994) relate functional analysis to ABC. Steimer (1990),
Beheiry (1991) and Youde (1992) describe how ABC relates to the concept of quality and

Turney (1989) examines the role of ABC in manufacturing excellence. Ochs and Bicheno

(1991) link ABC to manufacturing strategy, while Kaplan (1989) argues that ABC can be

used to better justify flexible manufacturing. Steen and Steensland (1994) suggest ABC

as a tool for on-line profit monitoring in a process plant and Menzano (1991) shows how

it can be used for information systems. Roth and Sims (1991) apply ABC to warehousing

and distribution, Lewis (1991) applies it to marketing and Roehm, Critchfield and

Castellano (1992) apply it to purchasing. Pirrong (1993) describes the use of ABC in

service industries, Lawson (1994) studies the use of ABC in hospitals, Dhavale (1992)

describes the use of ABC in cellular manufacturing systems and Zhuang and Bums (1992)

develop a procedure to implement ABC in non-standard route manufacturing. Recently,

the grocery industry has explored the link between ABC and Efficient Consumer Response

(Haedicke, 1994, Valero, 1994 and Mathews, 1994).


Limitations of ABC

A number of authors have written about the limitations of ABC. For example,

Johnson (1991) argues that although ABC overcomes distortions inherent in traditional

financial cost accounting information, it does not necessarily help companies achieve

continuous improvement. In his book Relevance Regained: From Top-Down Control to









Bottom-Up Empowerment (1992) he explains that activity analysis focuses attention on

changing the amount of activity (or work) a company does for a given amount of revenue,

but it does not focus people's attention on changing how work is done, nor does it link

activity with customer satisfaction. Bakke and Hellberg (1991) feel that while ABC

philosophy constitutes a necessary basis for long-term decisions about product mix, the

information is not satisfactory for making short-term decisions. Tatikonda and Tatikonda

(1991) note that simply allocating cost in a different way does nothing to control those

costs. Roth and Borthick (1991) observe that ABC assumes that costs in each cost pool

are driven by homogeneous activities and are strictly proportional to the activity. If either

of these two assumptions are not met, ABC costs may also distort product costs.

The fact that ABC allocates both fixed and variable costs to activities and products

makes it difficult to make certain economic decisions that depend on marginal costs based

on a fixed production capacity. This shortcoming of ABC has been noted by several

authors. Koehler (1991) argues that firms need direct costing and contribution approaches

as well as ABC. He notes that ABC examples in the literature assume that a company has

limited knowledge of the market price or the elasticity of demand and that ABC is not

very useful for setting the price of a standard product for which there is a competitive

market. Weisman (1991) argues that cost allocation systems, such as ABC, emphasize

cost recovery rather than cost causality and are therefore incapable of providing managers

with the information they need to make good business decisions. He suggests using only

avoidable costs for cost/benefit analysis. Along the same lines, Sharp and Christensen

(1991) claim that activity-based costs suffer a deficiency common to all full cost

approximations: not all resources consumed by a cost object are avoidable in the absence

of the particular object They suggest that for managerial decision-making,activity-based

costs need to incorporate the concept of attributable costs. Scott and Morrow (1991)

make a similar observation, then show how ABC information can be modified to support

make-or-buy decisions.








Woods (1992) notes that while ABC meets the concerns of manufacturing

managers about the relevance of conventional cost data to the actual manufacturing

process by assigning to each product the costs of all activities that are used in its

manufacture, it does not allow for rational economic choices for most organizational levels

because it mixes fixed and variable costs. He suggests that this information can be

provided by an ABC system by giving managers a breakdown of the costs allocated to the

activity and identifying those costs which can be controlled by the activity or department

as variable and those that cannot be controlled as fixed, with the classification of costs as

fixed or variable varying with the level of reporting. Christensen and Sharp (1993) suggest

two refinements to ABC: categorizing activity costs into short-term variable, short-term

fixed and committed fixed costs then determining the allocation rates for both categories

of fixed costs based on the capacity provided through the incurrance of these costs.

Yang and Wu (1993) observe that product unit cost developed under ABC using

historical data is often used to make pricing decisions without considering either the future

price index (for variable cost) or capacity utilization (for fixed costs). Thus products are

underpriced when unit variable cost is underestimated or overpriced when unit fixed cost

is overestimated. They suggest using a "strategic" ABC unit cost, based on the capacity

rate that the company wants the operation to achieve over its useful life or planning

horizon. This enables the user to calculate a close approximation of the true long-term

costs and to make better decisions about product mix, investments and staffing.








Operations Research Models



Economic Order Quantity

Johnson (1988) discusses how companies can use activity-based information to

manage activities, not cost. He introduces the Economic Order Quantity (EOQ) problem

and notes that it takes for granted the activities (setup and storage) whose costs are

optimized by batch size. He explains how Toyota concentrated on reducing setup time

which in turn reduces the EOQ quantity. Instead of managing setup cost, Toyota

managed the cause of the setup cost, time. Hedge and Nagurajan (1992) recognize that

setup cost has both a fixed and a variable component and they model the setup cost per

setup as a = m + Rt, where t is the amount of time it takes for a setup, m is the setup costs

independent of setup time (assumed to be constant from setup to setup) and R is the setup

rate ($/unit time). Note that they still use number of setups as the cost driver, so the cost

allocation ignores the effect of t. They speculate that an ABC analysis might reveal that

setup costs are high, thus motivating the shop floor to reduce the number of setups in

order to reduce costs, a strategy which they label as "short-term". On the other hand, they

observe that the production engineers seek to reduce setup costs in the "long-term" by

reducing setup times. They then combine these two goals in a time-constrained EOQ

model.


Investment Analysis


Reeve (1989) observed that each activity is related to a product by way of a cost

driver. The cost driver is a ratio whose numerator is the cost committed to the activity per

time period and denominator is an estimate of the amount of activity driver used during

the period. An investment can have an impact on an activity though either the numerator

or the denominator. He notes that traditional justification techniques fail to consider the








impact of process improvement efforts on complexity costs and he explains how ABC can

reveal the cost impact of process changes. Ostrenga (1990) suggested that performance

measures should represent a mix of financial and non-financial operating measures. He

noted that performance measures can assist in process management by focusing on the

significant activity levels and measuring the drivers of activities. Improvements in quality,

throughput and other operational benefits may be difficult to quantify, but are real in terms

of competitive posturing and should be included in investment management

Brimson (1989) develops the concept of activity-based investment using an

analysis of the activities that influence cost and quality in a modem manufacturing

environment Traditional investment analysis is based on the cash flow impact of each

investment alternative, a process that does not take into account such important decision

parameters as quality and efficiency. In addition, the traditional view compares investment

alternatives proposed by individual department managers based on the benefits to each

department, without analyzing the effect of the investment on the activities and goals of

the company. He suggests that before comparing investment alternatives a company

needs to identify the activities that support company goals. The investment analysis is

then based on improving the performance of value-added activities and the elimination or

minimization of non-value-added activities. The impact of an investment on the cost of

these activities is determined through ABC analysis, which computes the estimated cost of

each activity under a given investment alternative. Alternatives are also evaluated based

on their impact on performance measures associated with each activity and a portfolio of

investments is established for each key performance measure. The investments that both

improve performance and meet or exceed a target return on investment (ROI) are the

most desirable.

Sawhney (1991) developed a methodology for evaluating manufacturing

investments that are heavily influenced by non-financial considerations. He suggested that

investments should be evaluated in terms of the strategic objectives of the firm (in addition








to the traditional financial analysis) and on their impact on production-related activities.

The objective of the approach is to select investments that provide the greatest

improvement to key activities as measured by critical success factors.


Analytical Hierarchy Process

Partovi (1991) proposes a model for evaluating the appropriateness of adopting

ABC. It is based on the Analytic Hierarchy Process (AHP) developed by Saaty (1980).

The model is in the form of a hierarchy that includes the two stages of ABC. The top half

of the hierarchy corresponds to the first stage of ABC, where total overhead costs are

allocated to the plant's major activities using resource drivers. The second half of the

model allocates the cost of activities to products using activity drivers. The objective of

the model is to allocate overhead costs to products. The author assumes that the values of

the resource drivers are known and management need only determine their ratios for the

AHP model. Pairwise comparisons are used to determining the relative importance of

each activity to other activities with respect to a particular resource driver and the

importance of the activity drivers relative to each activity. Similarly a set of pairwise
comparisons evaluates the different products with respect to the activity drivers. The

result of the model is an estimate of how ABC would allocate costs to products. If the

allocations are significantly different from the values assigned by the current accounting

system, the adoption of an ABC system is recommended.


Break-even Analysis

Metzger (1993) notes that ABC can improve the accuracy and relevance of multi-

product break-even analysis. This is because ABC can more accurately trace cost to each

product line. The traditional model only traces volume-based (variable) costs to each

product, classifying all other costs as fixed. This model further assumes that all products









contribute to fixed costs in proportion to their sales volume. The ABC model does not

make this assumption. Instead, it traces non-volume-based (fixed) costs to each product

line. These are costs that are fixed with respect to individual units, but vary from product

to product. The break-even analysis can then be performed in terms of the variable costs

vs. the traceable fixed costs assigned to each product.

Innes, Mitchell and Yoshikawa (1994, p. 13-15) point out the frailties of

traditional break-even analysis. Costs and revenues rarely follow simple straight-line

relationships and even if such approximations are adequate in the short term, extra

capacity will eventually be required as output grows, causing fixed costs to follow a "step"

pattern. In addition, product costs are influenced by factors such as complexity, flexibility,

quality and service. Omitting these factors from the cost estimation model may lead to

incorrect decisions.


Pricing and Product Mix

The use of ABC to forecast product cost and not just allocate historical costs is

advocated by O'Guin (1992). He argues that ABC must be integrated into the MRP

system in order to obtain valid unit costs for products. Malik and Sullivan (1995) develop

a mixed integer programming model that utilizes activity-based costing information to

determine optimal product mix and product cost in a multi-product manufacturing

environment. They assume that the consumption of overhead resources is either in

periodic steps or involves a one-time occurrence. By modeling indirect costs as step

functions of volume they are able to incorporate the long-term variability of these costs.


Product Design

Emblemsvag and Bras (1994) develop an ABC model for use in the design of new

products. The approach uses ABC methods to obtain reliable estimates of the costs of a








design. The suitability of utilizing ABC in design is explored in the context of design for

product retirement.


The Engineering Perspective

The articles relating ABC to engineering are relatively few. Butler (1994)

discusses ABC and other accounting concepts from an engineering design and

manufacturing perspective. Koons (1992) describes the role of the engineer in the

implementation of an ABC system and Barnes (1991) notes that ABC is important to

industrial engineers because it is closer to the systems IEs use in estimating and project

justifications. The majority of the literature dealing with ABC has been limited to the

accounting field, and, with the exception of the few articles mentioned above, little has

been written about the effect of ABC on operations research models. For this reason, we

feel it is important to explore this subject.













CHAPTER 3
ECONOMIC ORDER QUANTITY


Introduction

In the traditional inventory economic order quantity (EOQ) model, the total

average cost of inventory is modeled as a function of the order quantity and depends on

the cost per unit of the product, inventory carrying cost per unit (based on average

inventory) and a fixed replenishment cost per order. In order to use this model we must

agree on two conditions: first, that the model is a valid representation of the cost behavior

of the inventory policy and second, that the values of the parameters used in the model are

accurate. If we are to accept these conditions we must agree on how cost is to be

measured; hence, we must agree on a cost accounting system. Because the cost

accounting system records and allocates the cost of the inventory policy, the inventory

model must reflect the assumptions made by the cost accounting system.

Consider the first condition. Suppose the accounting system allocates the cost of

carrying inventory based on the amount of space allocated to each item, while the

inventory model assumes that the cost of carrying inventory is based on the average value

of the inventory. In this case, the model assumptions are flawed and the results of the

model will not be validated by actual financial results. As for the second condition,

regarding the accuracy of the cost parameters used in the model, there are several points

to be made. First, the cost accounting system must record costs accurately. This is a

basic requirement of any accounting system, whether traditional or ABC. Second, once

the costs are recorded, they must be allocated to different departments or activities and

eventually to the products, in order to obtain an accurate product cost. Not all accounting









systems allocate costs in the same way and differences in allocation methods will result in

different values for model parameters. The ABC system allocates costs based on the

consumption of activities and allows a much greater variety of activity drivers (allocation

bases) than the traditional cost accounting system, thereby resulting in a more realistic but

more complex cost model.

In this chapter we will discuss the impact of ABC on the inventory economic

order quantity model. In particular, we will look at what happens when an ABC analysis

reveals that the "fixed" cost of placing each order varies with the total number of orders

placed in a given time period. This might be the case, for example, if the accounting

system uses the expenses assigned to the purchasing department to derive the cost per

order used in the inventory model. In this case, the number of clerks in the department

would likely represent the most significant portion of the department's expenses and it

would make more sense to use the number of clerks (rather than a fixed cost per order) to

determine the economic order quantity. Our approach is to incorporate long-term ABC

cost drivers in a manner similar to that of Malik and Sullivan (1995). We model the cost

of placing the order as a step function that depends on the number of clerks in the

purchasing department. We then obtain an optimal solution for both the single-item and

multiple-item cases. Next, we look at a model that combines both a fixed cost per order

and an order cost per clerk. Finally, we examine a model that incorporates inventory cost

as a step function of the number of warehouses, rather than the average cost of inventory.


The Inventory Model

The simplest type of inventory model involves a single item with a known static

demand per period and an infinite planning horizon. There are no shortages allowed and

replenishment is instantaneous. This model assumes that the average cost of the

inventory policy is based on the cost per unit of the product (c), inventory carrying cost








per unit inventory per unit time (h) and a fixed replenishment or setup cost (a). The

average cost per unit of time can be written as


f(Q) = +h-+cD
Q 2


where D is the demand per unit of time and Q is the order quantity or lot size. Thus the
model seeks to find an optimal tradeoff between the number of orders or setups (-) and

the average inventory in stock (Q). The optimal order size is given by:


-2aD
EOQ =F



Looking at this from an ABC perspective, we see that there are two significant
cost drivers: number of setups and average inventory in stock. The number of setups is
the driver used to allocate the cost of the ordering or setup activity and average inventory
in stock is the driver used to allocate the cost of the warehouse or holding activity. If the

accounting system uses these cost drivers, then the cost of ordering or setup would be

allocated to different products based on the number of setups required by each product
line and the warehouse costs would be allocated based on the average inventory level of

each product. This is important to note, as we will see later, because if the accounting
system does not recognize the same cost drivers as the inventory model, the actual costs
seen in the financial records may not support the decision made by the inventory model.
Before discussing the effect of ABC on this model, we must carefully examine the
cost parameters, c, a and h. By definition, a is the fixed cost of placing an order or
performing a setup. Every time we place an order, we will incur a cost a, regardless of the
size, timing or type of order. Of course, this may not always be true. For example, Lee









(1986) examined the case where there is a freight cost associated with the order size in

addition to a fixed cost.

Hedge and Nagurajan (1992) recognize that setup cost has both a fixed and a

variable component and they model the setup cost per setup as A = m + Rt, where t is the

amount of time it takes for a setup, m is the setup costs independent of setup time

(assumed to be constant from setup to setup) and R is the setup rate ($/unit time). They

speculate that an ABC analysis might reveal that setup costs are high, thus motivating the

shop floor to reduce the number of setups in order to reduce costs, a strategy which they

label as "short term". On the other hand, they observe that the production engineers seek

to reduce setup costs in the "long term" by reducing setup times. This apparent conflict is

due to the fact that the authors assume that the ABC cost allocation will continue to be

based on the number of setups, while the engineering analysis implies that setup time and

not number of setups, is the appropriate cost driver for setup costs. This highlights the

importance of coordinating the ABC analysis and implementation with the manufacturing

engineers. If setup time, t, is the significant cost driver and m is small, then the ABC

system should reflect this by using setup time rather than number of setups to allocate

costs. The shop floor will then be motivated to reduce setup time and will not be adversely

impacted by an increase in the number of setups. If, on the other hand, m is large relative

to Rt, then the engineers are working on the wrong cost driver, or two cost drivers should

be used: number of setups for m and setup time for R. In any case, the total setup cost, A,

will still be reduced if t is reduced, so that the increase in the number of setups (based on

the EOQ model) will be offset by the reduced cost per setup and the shop floor will not be

adversely impacted by the reduction in setup time. The bottom line is that the cost

allocation should be based on the most significant cost drivers which should motivate the

shop floor and the manufacturing engineers to reduce these cost drivers. Only if the

engineers choose to ignore the most significant cost drivers will there appear to be a

conflict between the cost system and the engineering analysis.









Porteus (1985) considered the cost of investing in reduced setup cost a. He

assumed that the total setup cost varies with the number of setups as is done in the

traditional EOQ model. He then examined the tradeoff between the investment costs

needed to reduce the setup cost and the operating costs identified in the EOQ model. If
D
we let A = g(x) + a -, where a is the portion that remains constant from setup to setup

and g(x) varies with some other cost driver, for example setup time, as suggested by

Hedge and Nagarajan, then A is no longer a constant from setup to setup as assumed by

Porteus. Instead, we have the following cost function:


Da hQ
f(Q,A) =- +g(x)+ + ikA(a,b,x)
Q 2


where i is the fractional cost of capital and kA(a) is the cost of reducing the setup cost to

level a, given that we start at level a0 (as suggested by Porteus). We now have the

option of reducing the setup cost by either reducing the portion that is fixed from setup to

setup or the portion that varies with some other cost driver g(x). By identifying other cost

drivers, the ABC system can, through cost allocation, help us decide which component to

reduce and what the effect should be in the long run.

Often, h is expressed as ic where i is the fractional per unit time opportunity cost

of capital and c is the cost per unit of inventory. This implies that we are not really

concerned with the actual cost of carrying inventory (such as the warehouse rental or

depreciation, the salary of warehouse personnel, inventory taxes, spoilage, utilities and

insurance), but rather we are focusing on the fact that capital tied up in inventory does not

produce income and is therefore undesirable. In reality, i may be adjusted upward to

account for the actual holding costs as well as the cost of capital, but doing so assumes

that these costs vary with the value of inventory, which may not be true. Alternatively, we

may use h' = ic + h, where ic is the opportunity cost of capital and h represents the actual









(or out-of-pocket) costs associated with carrying inventory. The total inventory holding

costs are expressed as a function of Q.

Any cost accounting system, including ABC, is concerned with allocating the

actual cost of doing business to some cost object, usually a product or service. In a

manufacturing environment, the cost per unit, c, is obtained from the cost accounting

system. The system provides this cost by first accumulating the direct labor and materials

cost for each product produced in the period and then allocating to each product a portion

of the manufacturing overhead. Finally, the total cost allocated to each product is divided

by the number of products produced to obtain c. If we do not manufacture the products,

but rather purchase the inventory from the manufacturer, the accounting system will

accumulate not only the purchase price per unit, but also the costs associated with

obtaining and holding the product. Because the actual costs vary from period to period,

manufacturing firms often establish "standard" costs based on past history and use these

standard costs to value inventory. For example, a standard or average labor rate may be

used instead of the actual labor rate or a standard overhead charge per unit is applied

rather than the actual overhead for the period. Thus the value of c used in the EOQ

model, defined as a per-unit cost, will most likely be a standard cost, which is updated

periodically.

Exactly what is included in c will depend on the overhead allocation method, so we

must be careful when obtaining the value of c from the cost accounting system. For

instance, if the manufacturing overhead allocated to the different products includes

warehouse rental, inventory taxes or insurance, then h is included in the cost per unit and

we must delete these items to obtain c. Similarly, the price per unit may include

components of a, such as freight charges or setup supplies. Finally, the value of a and h

will depend on how the cost system allocates costs to the departments or activities

responsible for placing and receiving orders, performing setups and handling inventory.









Obviously, it is very important that the industrial engineer performing an EOQ analysis

understand the accounting system that is used to derive the cost parameters in the model.

One way to derive a and h is to look at the cost drivers assigned to each activity in

the ABC system. Those activities that can be allocated based on number of setups and

those that vary with the average number of units in inventory can be selected to represent

a and h respectively. But not all activities related to setups, orders or inventory can be

allocated in this manner. For example, the salary of personnel dedicated to performing

setups will be the same (within a range) regardless of the number of setups performed.

Similarly, the warehouse rental does not necessarily vary with the average number of units

in stock. Thus some costs will be excluded from the EOQ analysis if we use this method

for calculating a and h and those costs may be important in the long-term. We can also

develop approximate values for a and h by allocating all the relevant costs based on

number of setups or average inventory in stock, assuming that these are the most

important cost drivers. Alternatively, it may be necessary to revise the EOQ model to

accommodate other cost drivers. An ABC analysis and the resulting cost allocation may

influence how we build this model.


Single Product


For the single-item model, ABC has no effect on the model parameters, as long as

we use number of setups and average inventory as the drivers. Manufacturing costs (both

direct and indirect) are allocated to one product regardless of how many activities may be

involved. Suppose there are two activities for inventory and ordering costs: warehousing

and purchasing. Since only one item will consume the warehouse and purchasing

activities, the total inventory costs and order costs are allocated to one product. Thus h

and a are unaffected by ABC. The single item EOQ model may still need to be revised if









number of setups and average inventory are not the most relevant cost drivers, as we will

see later.


Setup Costs



Number of Clerks as the Cost Driver

As noted earlier, we assume in the EOQ model that a represents the fixed cost of

placing each order and that it is constant regardless of the number of orders placed in a

given time period. In reality this is often not true and the ABC system will reveal this

through the analysis of cost drivers. For example, consider the case where the activity of

placing an order is done by a purchasing clerk and the most significant cost driver in the

purchasing department is the number of clerks. In this case, the total cost would vary not

with the number of orders placed, but with the number of clerks employed. Of course, we

recognize that each clerk has a maximum number of orders that he/she can process in a

given period of time (capacity), so the ABC system would allocate the cost of the

purchasing department to the products based on the usage of this capacity.

Note that this is a long term approach to the problem, as opposed to the short-

term view traditionally taken by the EOQ model. In the short term, the number of clerks

is fixed, so that if there are n clerks and each clerk costs k per period, the total cost is nk

and this term will not affect the order quantity. However, as we will see later, in the long

term, we seek to find not only the optimal order size, but also the optimal number of

clerks, since this is the significant cost driver in the purchasing department. While

conventional economics treats costs as variable only if they change with short term

fluctuations in output, numerous ABC case studies show that many important cost

categories do not vary with short term changes, but with changes over a period of years

(Bakke and Hellberg, 1991). A key assumption underlying activity-based analysis is that









almost all indirect and support costs are variable. Many indirect expenses (such as the

salaries paid to the purchasing clerks) will not vary from month to month with changes in

the volume and mix of monthly production, so they appear to be fixed in the short run.

They become variable, however, each year during the budgeting cycle when the

organization authorizes annual spending levels for each of its support departments. If the

production environment has become more complex because of a greater number of

transactions (setups or orders) then eventually more support people and resources have to

be added to the organization (Kaplan, 1989).

Suppose that a clerk can process m orders per time period and is paid a salary k

during that time period. Then it is reasonable to estimate that a = k/m and this will in fact

be true if the actual number of orders is m. If, however, the number of orders placed

during the time period is less than m, the total cost of the ordering activity will still be k,
D
not a- as the EOQ model assumes. In this case, the EOQ model will underestimate the
Q
D
total costflQ) by the amount of excess capacity: a(m -). The actual total cost for the


period is


f(Q) = k "D +h-+cD
IQmn 2


D D
where is the nearest integer greater than or equal to -. We note that the
IQmI Qm
k
maximum error in the total cost will be k and that the true value of a is --. Suppose we
D/Q

can afford only one clerk. Then the problem can be formulated as


min f(Q) =k+h-+cD
2
D
s.t. m
Q









The solution, Q* = is trivial, since we will seek to minimize Q in order to
m

reduce our inventory costs, given that the total cost of ordering is constant Of course this

results in using our order resource to maximum capacity. A similar analysis can be made
D
for any number of clerks, say nk. In this case we set Q* = in order to minimize the
mn

inventory cost. Comparing this to the traditional model, we note that the constraint in the
D
above equation requires that EOQ > -, thus the traditional model will always result in
mn

the total cost being greater than or equal to the total cost with Q*. The observation that

the order cost is fixed for a certain capacity is highlighted by the ABC system, with its

emphasis on the long-term cost of activities.


Multiple Products


If we allow multiple products, then we have several products consuming the

warehousing and purchasing activities. ABC allows us to recognize the fact that not all

products consume activities at the same rate. By identifying the appropriate activity

drivers, each product i will have cost per unit ci, inventory cost per unit hi and setup cost

ai. Thus we will have for each item



EOQ 1-2aiDi




Because ABC will likely result in different inventory and setup rates for each

product, a multi-product EOQ model is necessary. Such a model is often bound by a set

of constraints, such as space, budget, or number of orders per time period. In this case the

unconstrained optimal lot size for each product may not satisfy the constraints and the

problem may be solved using the Kurush-Kuhn-Tucker (KKT) conditions.








Let us go back to the case where the number of clerks is the cost driver for the
purchasing department. Suppose the clerk can process mi orders of product i in each time
period (for example, a clerk could process 500 orders for product 1 or 250 orders for
product 2 in one year). Thus the capacity of the clerk is given by


Di <




We can formulate this problem as


min f (Q) = k +Xh, + cD,

s.t. i < 1
i Qimi


In general we have the following problem


min f (Q) = k[F Di + hi Qi + ciDi
I Qm, I 2 ,

s.t.. S. I D' SN



where N is an integer representing the maximum number of clerks and we require at least
one clerk (otherwise the orders cannot be placed). Let us relax the integer requirement in
the objective function and solve the problem without the capacity constraint. In this case
we have


g(Q) = k -, + I+cD
i Qii 2 ,








which is a strictly convex function with a unique global minimum at


EOQ, = 2 Dk
himi


Proof:
Since g(Qi) is a function of a single variable, Qi, we need only show that

the second derivative of g(Qi) is strictly positive for all values of Qi to show that it

is strictly convex.

kD. hi
g'(Q) = Q + 2
gQ(iQ= 2

Qi*,


Since Qi, ai, Di, k, mi > 0 (model constraints), then g"(Qi) > 0 for all values of Qi
> 0 and g(Qi) is strictly convex. Thus g(Q) is the sum of strictly convex functions
and is therefore also a strictly convex function with a unique global optimum at
Vg(Q*)=O. QED.


We can also make the following observations (refer to Figure 3-1):


1. g(Q) is a lower bound on fQ), since by definition ID, --.im


2. f(Q) = g(Q) at every integer value of Di


3. flQ) > g(Q) between any two adjacent integer values of I Di
i Qimi








4. fjQ) is linear between any two integer values of X .


5. Since g(Q) has a unique global minimum at EOQi, we know that if
D' = n, thenflQ) will also be minimized at Q = EOQ,.
SEOQm,

6. Since g(Q) is a strictly convex function with a global minimum, its value will
increase as we move away from EOQi in any direction.


Figure 3-1. Cost vs. Order Quantity


Although the EOQi solution is optimal for g(Q), it may not be feasible when we
Di
consider the first constraint, I < N. Since g(Q) is strictly convex and there is only

one constraint, we can use the KKT conditions to obtain the optimal solution. Solving for
Q we obtain:


S2D= ( k + X)
h, m,


cost


f(Q)


g(Q)


Q(n) Q
(+X)


Q(n+ 1) EOQ,
(-1) (X = 0)










were the X is the KKT multiplier given by




N2
substituting this for X into Q, above, we obtain the optimal solution:



1 2D IDh,
N hm, j 2m,



This solution results in using N clerks to maximum capacity, thus reducing the
average inventory size as much as possible.
Since the two terms under radical signs in Q1 (N) are constant for each i we can

write


Qi (N) =
N


where y, = ..

Now suppose we find EOQi but D = x, where x is not an integer. Then
iEOQ,m,

we know from (3) that we can improve the value of f(Q) by simply moving to an integer
on either side ofx. Let xJ = n and Fx] = n +1. If = n, then Qi*(n) > EOQi
i V M,
because n < x and if = n + 1, then Qi* (n+1) < EOQi because n+1 > x.
i Q m,
Furthermore, for any integer q < n < x, Qi*(q) > Qi*(n) > EOQi. Since g(Q) is strictly








increasing from EOQi to infinity, g(q) > g(n) > g(EOQi) and from (2) ftq) > fln) >

fJEOQi). Likewise, for any integerp > n + 1 > x, Qi*(P) < Qi*(n+l) < EOQi. Since
g(Q) is strictly decreasing from zero to EOQi, g(p) > g(n+l) > g(EOQi) and from (2)
ftp) >ftn+l) >f(EOQi). Thus we can conclude the unconstrained optimal solution for
flQ) will be found at either n or n+1 (or possibly both).
In order to determine which is better, n or n + 1, we need to compare the value of
ftQ) at these two points. Letting Q, (n) = we have
n


f (n) = nk + and f(n ) + (n+)k + h I
i 2n 2(n + 1)
1 hit i
f(n+l)-f(n) = k 1 hi
n(n + 1) i 2


1
therefore f (n) < f(n +1) if k 2 hy i h We note that when the above terms are
2n(n + 1)

equal, ftQ) will have two optima, at Q*(n) and Q*(n + 1).

To solve the original problem, we first need to find the optimal number of clerks,
N*. This is because even if I < N and we have met the capacity constraint,
EOQm,
EDO may not be an integer and therefore EOQ, will not yield an optimal solution,
i EOQimi

as shown above. In this case the capacity constraint becomes either XI = n or
i EOQm,
D- = n +1. Note that when Qi* = EOQi we have X= 0 as shown in Figure 3-1.
i EOQimi

When we solve for Qi*(n) X will be positive (since we have reduced the capacity from x to
n) and when we solve for Qi*(n + 1) it will be negative (since we have increased the
capacity from x to n + 1). Thus X is no longer the traditional KKT multiplier, but is
D.
simply being used to adjust the value of Q1* to obtain an integer value for I *
i Q1 im,








To obtain the optimal order quantity, we first look at the number of clerks required
to process the EOQi amounts, D then compare this amount to N and solve for
EOQm,

Qi*. We have three cases:


Cas 1: D < N and not an integer.
S EOQmi

Let C Di = x, Y = 2D D'hi
Le EOQm = 4Y-X" LxJ=nandx-l=n+l
SEOQmn, h,m, t 2m, Z
If k2 + )hiy, then N* = n, otherwise, N* = n+1
2n(n + 1) i

N* hm n 2m,


Cse : < N and an integer n.
EOQm,
Then N* = n and Qi* = EOQ,


Case3: D' > N
EO Q. m,

then N* =N and Qi (x) =, -
N h,m, j 2mw


Note that the third case implies that an increase in the number of clerks could lead
to a better solution. To find that solution, we would treat case 3 in a manner similar to
case 1: let [x]= n and rx= n+1, where ~ D' = x, then compare Q*(n) to
EOQ m,
Q*(n + 1) to find the optimal solution and the optimal number of clerks, N*. Again, this
would involve both a positive X (for n) and a negative X (for n + 1).








Fixed and Variable Setup Costs

In reality, there are both fixed and variable components in the total setup costs:

A = k+ ax


where x is some cost driver (for example, D), a is the cost per unit of driver x and k is the

component that does not vary with x and is therefore a "fixed" cost. Traditionally, the
EOQ model has chosen to use the number of setups as the cost driver so that x = and

k = 0 in the equation above. This may be appropriate if the number of setups is indeed the
primary cost driver for the setup activity. An ABC analysis of the manufacturing process

would confirm this, or it may reveal that other costs (k) are also significant and should not
be allocated based on number of setups, or that another cost driver may be more

appropriate. The point is that we must choose x carefully, so that k is small relative to ax
in order to minimize the distortion, or we may decide to use more than one cost driver.
For example, we can revise the traditional EOQ model to recognize that a portion of the
total setup cost varies with the number of purchasing personnel, while a portion is

constant from order to order. Again we assume one person costs a fixed amount k and

can process a maximum of mi orders of product i in each time period:


min f (Q) = k D- +[a R + h +cD,
Qi m, i Q, 2
s.t. I < N


We can relax the integer requirement and solve without the first constraint:


ming(Q)=k Di + aD + h +ciD,
i im, Q 2










Since g(Q) is a strictly convex function, it has a global optimum at Vg(Q*)= 0.

Proof:

Since g(Qi) is a function of a single variable, Qi, we need only show that the

second derivative of g(Qi) is strictly positive for all values of Qi to show that it is

strictly convex.


kD, a,D, hi
g'(Q,)= W -- +-
Qm, i Q, 2
2kDi 2aD,
g"(Q.) '+



Since Q, ai, Di, k, mi > 0 (model constraints), then g"(Qi) > 0 for all values of Qi
> 0 and g(Qi) is strictly convex. Thus g(Q) is the sum of strictly convex functions
and is therefore also a strictly convex function with a unique global optimum at
Vg(Q*)=0. QED.

Solving for Qi*, we obtain EOQi


EOQ, = (k + am,)

D.
We can now check to see if this solution satisfies the first constraint, Y i < N. If it
i Q ii
does not, then the constraint is binding and we use the KKT conditions to obtain the

following equations:


2D.
Qi =1 (k + aim, + ) (1)
Shmi









and ( ,mi = N (2)
(k ++ai ) +)



Unfortunately, we cannot solve for X directly, since aimi is not constant for all i.
DI
EOQm; D. 1 D
Let = EO and Qi =Y EOQi, then -D =I N.
N i Q^m, yi EOQm,
This satisfies equation (2), but with a different ki for each Qi which we obtain by setting

Q- = Q, in equation (1):

ki = (k + a,mi )( 2 1


Because equation (2) is a strictly decreasing function of X, it can be shown that
min{Xi) < X* < max Xi) (Ventura and Klein, 1988) and we can find X* using a bi-section
search.
Note that we can make the same observations onflQ) and g(Q) as we did earlier:

1. g(Q) is a lower bound on f(Q).

2. flQ) =g(Q) at every integer value of I D
i Qimi

3. flQ) > g(Q) between any two adjacent integer values of I Di
i Qimi

4. flQ) is linear between any two integer values of I D,
i Qm,

5. Since g(Q) has a unique global minimum at EOQi, we know that if
EOQm = n, thenfiQ) will also be minimized at Qi* = EOQi.
iEOQimi








6. Since g(Q) is a strictly convex function with a global minimum at EOQi, its
value will increase as we move away from EOQi in any direction.


We can also show, as we did earlier, that the optimal solution forflQ) will be

found at either n or n+ 1 (or possibly both). Returning to our original problem f(Q), the

optimal solution will be based on the optimal number of clerks (an integer, as shown

above). There are three possible cases:


Case : D' < N and not an integer.
SEOQm,

Set LxJ =n and x] = n+1 where D-- = x
i EOQm,

Find X*(n) and ,*(n+l)
f2D.
Compute Qi*(n) and Qi*(n+l) where Qi (n) = [k + aimi + (n)]
ihm,

Compare fQi*(n)] tof[Qi*(n+1)] and select the lower cost. Note that N* will be

either n or n+1 (or possibly both) based on this comparison.


Ca 2: '- D < N and an integer n.
EO Qm,

then N* = n and Qi* = EOQi


Ce 3: 1 D >N.
7EOQ.mi

Set D: = N and solve for ,*. Note that N* = N.
SEOQmi

Q i(k + am, + ,*)


Di
Since the optimal solution is an integer value of the first case involves
f EOQm,

finding the optimal number of clerks as well as the optimal order quantity, because we are









adjusting the capacity constraint from x to either n or n + 1. Also, case 3 could be used to

justify an increase in the number of clerks, as shown in the previous section.


Inventory Costs


In the simple EOQ model the total inventory cost is a function of volume, Q. This
assumes that the cost driver is average inventory in stock (9). In reality, inventory cost

may be more dependent on other drivers, such as the size of the product or the amount of

handling required, or even the total number of items handled D. If the allocation of the

warehouse cost is made at the product level then it will not vary with the average number

of units in stock.

For example, suppose warehouse costs are to be allocated to two products: X is a

small, easy to handle product, while Y is a large, cumbersome product requiring special

machinery. If costs are allocated based on size, we might allocate 25% of the warehouse

costs to product X and 75% of the costs to product Y. The 75% is then allocated to the
individual units of Y based on average volume in stock (L) to determine hy. Thus we

see that the higher the lot size, the smaller hywill be. This is because regardless of

volume, product Y must absorb 75% of the costs. Of course, this is an oversimplification.

In reality we would probably have two cost drivers for warehousing, one for fixed costs

(such as machinery) and another for variable costs (such as insurance), so that the total

warehouse cost is


H = k + hy


where hy is the portion that varies with the average level of stock and k is the portion that

is fixed. If h is the dominant term, then we may use H = h as is the case in the traditional

EOQ model. If, however, k is the dominant term, then H no longer varies with the








average number of units in stock, as shown above. To incorporate both terms we must

revise the EOQ cost function as follows:


aD hQ
f,,,(Q) =-+g(x)+ +h(y)+cD
Q 2


where g(x) represents the portion of the setup activity that is fixed or may vary with a cost
driver other than number of setups and h(y) is the portion of the warehousing activity that

is fixed or varies with a cost driver other than average volume.


Number of Warehouses as Cost Driver

Suppose, for example, that the warehouse rental is k for a given size of warehouse.
Each warehouse can accommodate up to mi units of product i. We now have a situation
similar to the step function for setup costs. If the stock level exceeds the capacity of the

warehouse, the company must rent another warehouse. Thus we have the following
model



min f (Q)=k +1 [a D' +hi -L+ciD
I m, Q, 2
s.t. 2 im,


where N is the maximum number of warehouses available.

A procedure similar to the one used for the order step function can be used to
solve for this model. We first solve the problem without the integer requirement and the

warehouse constraint:


min g(Q)= k + aL, + e h L+ci
Sm, m 2









it can be shown that this is a strictly convex function with a global minimum at Vg(Q*) =

0 and that minimum is


S2a.iDimi
EOQ. = 2a DEm+
2k + h,m,


When we include the warehouse constraint, i < N we first check to see if the
Smi

EOQi quantities satisfy the constraint. If not, we use the KKT conditions to obtain


Q = -2a,D,m,
S 2(k+X)+hmi



Again, we cannot solve for X* directly, since himi is not constant from product to

product, but we can use a bi-section search between min{Xi*} and max{(i*} to find the

optimum X, where

2k + himi EOQ k him
N2 mi 2


We have three possible cases:

Case 1: EOL < N and not an integer
M m,
Set xJ = n and Fx]= n + where EOQ' = x
i m,
Find X*(n) and X*(n+l)
2 2aiDim,
Compute Qi*(n) and Qi*(n+l) where Qi (n) = 2a(D*),m
2(k + A*) + hm;








Compare f[Qi*(n)] tof[Qi*(n+])] and select the lower cost. Note that N*
will be either n or n+1 (or possibly both) based on this comparison.


EOQ,.
Case2:
then N* = n and Qi* = EOQi


Ce 3:^ _EOQ.


Set -EOQ = N and solve for X*. Note that N* = N.
i mi
= 2aDim,
2(k +X *) + h,m



Conclusion

We see that ABC seeks to reveal a more accurate picture of the product cost and
allocates fixed as well as variable manufacturing overhead to the products. If, for the sake
of simplicity we choose to ignore the fixed costs and base our EOQ analysis on variable

costs (which vary with Q), then our results may be distorted. In this chapter we examined

cases where other cost drivers, such as the number of clerks or the number of warehouses

are significant cost drivers. By relating these drivers to the order quantity (as a step

function of Q), we were able to show how they can impact the optimal order quantity. Of

course, if there is no relation between a cost driver and Q (this would be the case if the

cost in question is fixed for all levels of Q), then the optimal order quantity would not be
impacted by that cost driver. The total cost, however, would still be impacted and

minimizing total cost would involve finding not only the optimal Q, but also optimizing

other cost drivers.








The key point here is that the ABC analysis will not only change the values of c, a

and h in the EOQ model (which might change the value of the optimal lot size, Q*), but it

might also affect the validity of the assumptions in that model. If this is the case, the ABC

cost allocation will provide incentive to the manufacturing department to change the EOQ

model. The incentive will come from the allocation of costs which the manufacturing

department is trying to control. In order to control costs, the industrial engineers in the

manufacturing department will have to make the same assumptions (about cost drivers and

cost behavior) that the ABC model is making. Otherwise, they will be frustrated in their
efforts and will erroneously assume that the cost system is irrelevant.













CHAPTER 4
INVESTMENT ANALYSIS


Activity-based Investment

Management must be able to go beyond cost when choosing between investment

alternatives. To remain competitive, firms must incorporate strategic goals into their

investment decisions and these goals often involve non-financial benefits, such as quality,

efficiency, flexibility and customer satisfaction, to name a few. The inadequacy of

traditional investment analysis in evaluating non-financial benefits is well known and has

resulted in the use of multi-attribute decision techniques, like AHP, to account for such

factors (Canada and Sullivan, 1989). These techniques, while taking into account the non-

financial benefits, fail to consider the impact of investment alternatives on activities.

Rather, they simply consider cost (usually net cost savings) as one of the decision

attributes within the model. By ignoring the impact on activities, the models fail to

prioritize investments based on how they will affect the business process. The result is

that the model often favors an investment that has significant benefits to a single

department or activity, without considering the relative importance of that activity to the

overall business process and the strategic goals (Brimson, 1989).

The natural extension to ABC and ABM is activity-based investment management

Brimson (1989) provides a framework for this based on an analysis of the activities that

influence cost and quality in a modern manufacturing environment. Traditional investment

analysis (using discounted cash flow techniques) is based on the cash flow impact of each

investment alternative, a process that does not take into account important non-monetary

decision parameters such as quality and efficiency. Scoring techniques, such as the multi-









attribute decision model, integrate non-monetary factors into the decision process, but do

not account for the impact of the cash flow on the business process.

In addition, the traditional view compares investment alternatives proposed by

individual department managers based on the benefits to each department without

analyzing the effect of the investment on the activities and goals of the company. This can

result in short-term solutions that treat the symptoms of a problem. Getting to the root

cause of the problem requires an understanding of the cost drivers. An effective

investment management system identifies those cost drivers with the greatest impact on

activities and those activities with the greatest impact on the success of the organization.

By allocating the investment cash flow to the activities, management can understand the

effect of the investment on cost drivers and activities.

While traditional investment strategies seek to control costs, activity-based

investment seeks to control the costs of the activities themselves. This approach can help

lower costs by identifying cost drivers and allocating scarce resources to critical activities.

Brimson suggests that before comparing investment alternatives a company needs to

identify the activities that support company goals. Activities provide a consistent basis for

analyzing investments and monitoring the actual results through an ABC accounting

system. The investment analysis is then based on improving the performance of value-

added activities and the elimination or minimization of non-value-added activities. The

impact of an investment on the cost of these activities is determined through ABC

analysis, which computes the estimated cost of each activity under a given investment

alternative. Alternatives are also evaluated based on their impact on performance

measures associated with each activity and a portfolio of investments is established for

each key performance measure. The investments that both improve performance and meet

or exceed a target ROI are the most desirable.









Non-financial Considerations

Sawhney (1991) has developed a methodology for evaluating manufacturing

investments that are heavily influenced by non-financial considerations. Like Brimson,

Sawhney suggests that investments should be evaluated in terms of the strategic objectives

of the firm (in addition to the traditional financial analysis) and on their impact on

production-related activities. The objective of the approach is to select investments that

provide the greatest improvement to key activities as measured by critical success factors.

Sawhney assumes that key manufacturing activities have been identified by management

prior to the analysis (this is in fact true if an ABC system has been implemented by the

firm).

Sawhney uses simulation models to evaluate the performance of various activities
within the manufacturing system under different investment alternatives. The results of

the simulation are performance measures such as lead time, operational output, average

inventory level and equipment utilization. In addition, management provides a subjective

evaluation of the importance of each activity relative to the performance measures used to

analyze the investments. The effects of each investment on specific manufacturing goals

are then evaluated based on target levels. The investments are ranked using subjective

weights for the contribution of each manufacturing goal to the overall strategy. Finally, a

normalized importance weight is assigned to the results of the performance analysis as

well as to other critical attributes (such as net present value, riskiness and price) and the

investment selection is made based on the highest overall score.

We propose to formalize the definition of the relationships between manufacturing
goals, activities and the investment decision by using AHP. This method provides a more

consistent weighting scheme than other scoring techniques (see Chan and Lynn, 1993) for

a comparison of discounted cash flow analysis, the multiple-attribute decision model and









AHP). We will then use ABC to develop the cost relationships among investment

alternatives and activities and AHP to define the link between investment alternatives,

performance measures and activities. Once these relationships have been established we

will incorporate them into two separate decision models: a cost impact model and a

performance impact model.

The advantage of AHP is that it provides a framework for prioritizing goals,

objectives and alternatives. In our decision model, discussed in the next section, AHP

ensures that strategic goals (or manufacturing goals based on strategic goals) are used as a

basis for making investment decisions. It is used to determine how performance measures

are related to goals and how activities contribute to performance measures.


Decision Model

Investments affect activities in two ways: by altering the way they are performed

(in some cases eliminating them) and by changing the cost of the resources consumed by

the activity. The first effect can be seen through changes in performance measures. The

second effect can be seen through changes in the cost of the activities. The two changes

are combined to produce a new cost allocation rate for each activity, which in turn will

affect the cost and profitability of products and services using the activities (see Figure 4-

1). We propose to evaluate the performance and cost impact using two separate models:

a cost impact model and a performance impact model.

The methodology consists of the following steps:

Step 1: Define the relationship between activities and strategic goals by
using AHP techniques to rank activities in terms of strategic goals. This step
will also define the relative importance of the strategic goals.

Step 2: For each investment alternative, determine the net dollar effect on
resources, including capital investment. Distribute this net effect from
resources to activities using ABC techniques.








Step 3: Define the relationship between activities and performance measures
by using AHP techniques to rank activities in terms of performance
measures.

Step 4: Combine steps 1 and 2 into a cost impact model to determine the
cost score for each investment alternative.

Step 5: Combine steps 1 and 3 into a performance impact model to
determine the performance score for each investment alternative.

Step 6: Plot the cost and performance scores of each alternative on a cost
vs. performance graph to select the best investment alternativess.


We will discuss the cost impact model first and illustrate it with an example. Then

we will discuss and illustrate the performance impact model. Finally we will illustrate the

use of the cost vs. performance graph to select the best investment alternative in our

example.



ABC Cost
Flow

I
CostResources
Resource
Drivers

Investments- Performance --Activities Goals
Measures

Cost
Drivers

Products

Figure 4-1. Cost and Performance Impact of Investments










Cost Impact

By analyzing the resources consumed as a company performs its activities and

measures its performance, management can identify areas where change may achieve

significant cost reductions. We can accomplish this by allocating the cost impact of

investments to critical activities using ABC drivers, in essence performing a "what-if"

analysis of the investment. This provides an objective assessment of the cost effect of

each investment, not only in terms of net present value but also in terms of the business

process. Failure to allocate the cost impact of investments to critical activities would limit

management's ability to control and improve the performance of these activities through

capital investment In addition, the evaluation of investments in terms of activities allows

the analyst to account for various operational interdependencies that are not captured by

traditional stand-alone analysis of capital investments. Detecting the impact of an

investment on activities allows for a more realistic evaluation of alternatives which

improves the selection process (Sawhney, 1991).

When the cost savings are determined for each investment, the effect on cost

drivers (e.g., quality, cycle time, productivity) must be considered. This involves a

thorough examination of how the investment will change the performance of each activity

and therefore the consumption of resources. Although the cost drivers are not considered

individually, the overall impact of each investment on the cost drivers is imbedded in this

analysis. For instance, we may note that a particular machine reduces raw material waste.

This savings results from changes to cost drivers such as quality and productivity. Rather








than trying to determine how much of this savings is attributable to each cost driver, we

consider the aggregate effect on resource consumption.

The cost allocation does not, however, provide information on the relative merit of

the cost effects. Our methodology provides this crucial step by linking the activities to the

strategic goals using AHP. Without this step, management must intuitively determine if,

for example, cost savings in one activity are more important than cost savings in another

activity. As Brimson notes, a common complaint among manufacturing executives is that

traditional investment analysis methods often fail to justify advanced manufacturing

technologies, even though managers believe the company should make the investment to

remain competitive. Our cost impact model seeks to quantify this intuition and provide

managers with an alternative assessment of the cost impact of investments.

Let us assume that manufacturing costs are allocated using ABC. Specifically,

actual expenses for labor, materials and overhead are accumulated in resource cost pools

and allocated to activities using resource drivers. This is the first stage of ABC. Each

investment will have a measurable effect on the cost of resources and thus on the total

labor, materials and overhead accumulated in the cost pools. Using traditional forecasting

methods, we can estimate the periodic operating costs, as well as the resource driver

usage, of each investment alternative. Both these estimates are then incorporated into the

ABC model to allocate the cost effects of the investment to the activities. We will allocate

the net cost savings (or cost increase) in each resource pool to the activities, using the

estimated driver quantities. This procedure is done separately for each investment

alternative.








In addition to the operating costs, we also compute the periodic annuity that is

equivalent to the initial cost of the investment (purchase price plus installation and startup

costs less salvage). We add this to the ABC model as a resource pool and allocate it to

the activities based on machine hours. This allows us to include the initial capital outlay in

our cost analysis (see Figure 4-2). Note that in order to compare investment alternatives

with different lives, we can either discount both alternatives using a limited planning

horizon (coterminated assumption) or we can use the lowest common multiple of the lives

of the alternatives (repeatability assumption). Alternatively, if cash flows from the

shorter-lived project can be assumed to be reinvested at a relevant rate, we can

incorporate this into our calculations (see Clark, Hindelang and Pritchard, 1979 for a

discussion of projects with unequal useful lives).




Net change in cost capa
of Resources $ annuity


Estimated Resource
Drivers


Activities

Figure 4-2. Allocation of Cost Impact to Activities


Once we have allocated the cost impact of each investment to the activities, we

have a net change in cost for each activity under each investment scenario. We can use

these dollar figures to connect the activities to our investment alternatives in our cost

impact model. The rest of the model (above the activities) is based on AHP, as shown in

Figure 4-4.








Our cost impact model is basically an AHP model modified at one level to

incorporate ABC. Our overall objective is to choose among several investment

alternatives. In AHP terms, the strategic goals are attributes and the activities are sub-

attributes. The priority weights for the strategic goals and activities are determined using

pairwise comparisons. The priority weights linking the investment alternatives to the

activities are derived from the allocation of resource dollars in the first stage of the ABC

model Once all the priority weights have been determined, we multiply the weights along

each path leading to an alternative and add them to arrive at a score for that alternative.

Assigning priority weights to the investment alternatives based on the ABC model

(instead of pairwise comparison) results in several important differences between our cost

impact model and the traditional AHP model. First, because we are allocating net cost

savings, it is possible that some of the priority weights will be negative. This would be the

case when the net effect of an investment on a particular activity is to increase the cost of

that activity (negative cost savings). Second, we will not normalize the priority weights

derived from our ABC model, because we would lose the true cost impact by doing so.

For example, suppose activity 1 has a net cost savings of $4,000 under investment A and

$1,000 under investment B, while activity 2 has a net cost savings of $10 under investment

A and $40 under investment B. Assume both activities are equally important If we

normalize the cost savings for each activity, we would assign a priority of 0.8 to A and 0.2

to B for activity 1 and 0.2 to A and 0.8 to B for activity 2. Thus, the activities would have

equal impact on the final decision, even though common sense tells us that a $4,000

savings is much more significant than a $40 savings. To avoid this problem, we preserve








the magnitude of the cost savings by not normalizing the priority weights of the

investment alternatives.

Example. Suppose management is interested in improving capacity, quality and

productivity. They wish to evaluate two new machines for this purpose. Machine A uses

a new technology that results in less raw material waste and uses less fuel, but because of

its complexity, will require more maintenance and some additional management effort.

Machine B does not reduce the amount of raw material usage, but because it uses a

different process, the company can purchase cheaper raw material. This, however, will

result in additional management effort, since it must be purchased from several different

vendors. Machine B also uses more fuel but requires less maintenance than the existing

machine. The purchase of these machines will not affect the amount or cost of direct

labor.

Management has computed the equivalent annuity (on a monthly basis) for the cost

of machines A and B to be $10,000 and $8,000 respectively. There are four resource cost

pools in the ABC model and management estimates the following monthly cost savings

(including capital investment):


Table 4-1. Cost Savings
Capital
Raw Material Fuel Management Maintenance
Investment

Machine A $20,000 $30,000 -$5,000 -$15,000 -$10,000

Machine B $50,000 -$10,000 -$20,000 $10,000 -$8,000








Note that if management used traditional investment analysis, they would use the

information in Table 4-1 to conclude that the net monthly cost saving of machine A

($20,000) is lower than that of machine B ($22,000) and thus would choose machine B.

Using AHP techniques, management has developed the following priority weights

for strategic goals and activities:




Investment
Decision


Capacity Quality Productivity

.4 .6 .5 .4

RawMat Rough Finish Purch/ Inspect
Prep Cut Work Sched
.14 .17 .40 .20 .09

Figure 4-3. AHP Priority Weights for Goals and Activities


The numbers underneath each activity in Figure 4-3 indicate the relative

importance to the investment decision of each activity and will be used in both the cost

and performance impact models. This represents the first step in our investment analysis.

Management has identified five critical activities and estimates resource driver usage under

each alternative will be as follows:








Table 4-2. Resource Driver Usage
Raw Material Rough Finish Purchasing/
Invest A/Invest B Preparation Cut Work Scheduling Inspection

Raw Material (tons) 100/120

Fuel (gallons) 0/40 250/250 250/250

Management (hours) 10/15 5/5 5/5 30/40 10/10

Maintenance (hours) 20/5 15/5

Cap Inv (machine hrs) 0/74 500/463 500/463



We can then distribute the cost impact of the resources to the activities as shown

in Tables 4-3 and 4-4:


Table 4-3. ABC Cost Allocation for Machine A
Invest A Raw Material Purchasing/
($1,000) Preparation Rough Cut Finish Work Scheduling Inspection
Raw Mat 20 x (100/100)

Fuel 30 x (250/500) 30 x (250/500)

Mgt -5 x (10/60) -5 x (5/60) -5 x (5/60) -5 x (30/60) -5 x (10/60)

Maint -15 x (20/35) -15 x (15/35)

Cap Inv -10 x (500/1000) -10 x (500/1000)

Total 19.17 1.01 3.15 -2.5 -0.83








Table 4-4. ABC Cost Allocation for Machine B
Invest B Raw Material Purchasing/
($1,000) Preparation Rough Cut Finish Work Scheduling Inspection
Raw Mat 50 x (120/120)

Fuel -10 x (40/540) -10 x (250/540) -10 x (250/540)

Mgt -20 x (15/75) -20 x (5/75) -20 x (5/75) -20 x (40/75) -20 x (10/75)

Maint 10 x (5/10) 10 x (5/10)

Cap Inv -8 x (74/1000) -8 x (463/1000) -8 x (463/1000)

Total 44.67 -4.67 -4.67 -10.67 -2.66



The calculations in Tables 4-3 and 4-4 are based on cost savings (Table 4-1) and

driver usage (Table 4-2). For example, for investment A, we know from Table 4-1 that

the estimated cost savings in fuel will be $30,000. To allocate these savings to the

activities, we use the information in Table 4-2. It shows, for example, that Rough Cut

uses 250 out of a total of 500 gallons. Therefore, we will allocate half of the fuel savings

to Rough Cut (30,000 x 250/500). We follow the same procedure for all the activities

until all the cost savings have been allocated.


We now have the priority weights that we will use to link each investment to the

activities in our cost impact model. This is the second step in our investment analysis. We

can use the results of the first two steps to create our cost impact model (shown in Figure

4-4). The numbers underneath each alternative in Figure 4-4 represent that alternative's

score. The score is obtained by first multiplying the relative importance of each activity

(obtained from Figure 4-3 and shown in parentheses) by the ABC cost allocation for each

alternative (obtained from Tables 4-3 and 4-4), then summing the results for each

alternative. For example, the score for alternative A is calculated as follows:









(0.14 x 19.17) + (0.17 x 1.01) + (0.40 x 3.15) + (0.20 x -2.5) + (0.09 x -.83) = 3.54.

Note that the final result favors machine A even though the net cost savings were higher

for machine B.


3.54 1.22

Figure 4-4. Cost Impact for Example


Performance Impact

One of the key features of an activity-based investment analysis is the evaluation of

the performance of an activity rather than narrowly focusing on cost. Activity-based

investment management links the strategic plan to the activities through quantitative

performance measures. It decomposes each of the performance measures into the specific








activities pertaining to it The total impact of changing activities can then be measured in

terms of tangible performance measures (Brimson, 1989).

The link from performance measure to activity is a natural result of implementing

ABM. Management establishes performance measures based on the information they need

to control and improve activities. Performance measures allow management to influence

activities that are critical to strategic goals. Thus activities provide a tangible link between

operating indices (performance measures) and long-term objectives (strategic goals).

Without this link, management is left with "intangible" benefits from long-term goals

which they perceive as important but unmeasurable. By analyzing the business process,

management can link each performance measure to one or more activities. Our model

then relates the investment alternatives to the strategic goals through the activities.

Evaluating investments based on their impact on performance measures allows

management to quantify "intangible" benefits and make better investment decisions.

The performance impact model links investments to activities through performance

measures rather than resources. Strategic goals are still attributes, but our sub-attributes

are now activities and performance measures. All the priority weights in this model are

derived from pairwise comparisons using AHP techniques. Note that the first two levels

of the model were developed earlier in step 1. The development of priority weights

linking performance measures to activities and investment alternatives represents the third

step in our investment analysis.


Example. Assume management has chosen the following performance measures
(shown with the activities they relate to):








Table 4-5. Performance Measures
# customer
% waste fuel/machiner % defective units/mach hr lead time complaints
Raw Mat Prep Rough Cut Rough Cut Rough Cut Purch/Sched Inspection

Rough Cut Finish Work Finish Work Finish Work



The relative importance of each performance measure to each activity can be

determined by management using AHP techniques (step 3). We will use the same relative

weights for activities and goals that we used in the cost impact model (from step 1). We

can now use the results of steps 1 and 3 to create the performance impact model for our

example, as shown in Figure 4-5. Note that machine A is slightly favored based on

performance impact, but is by no means a clear favorite.



Choosing Investment Alternatives

We can now combine the results of our cost and performance models to select the

best investment Note that our models assign a "score" or weighted evaluation to each

investment alternative, one for cost and one for performance (a high score in the cost

model indicates favorable cost savings). We can use a cost vs. performance graph to help

us select the best alternative (see Figure 4-6). On this graph, those investments falling in

quadrant II are the most desirable, while those falling in quadrant II would be the least

desirable. Note that the cost "scores" must be normalized before imputing them into this

graph. For our example, we first normalize the cost scores to .74 for machine A and .26

for machine B. The scores are then plotted on Figure 4-6 and we see that machine A is

the better investment, mostly as a result of its cost impact.






65






Investment
Decision

2 .5

Strategic AHP
capadty quaJly poduct(iv1)
Goals (step 1)
4 .6 .5 A
.5
ROw Mat Rough Finish Purch/
Activities Cut Work Sched Inspect
21 .5 2 .4 .


Performance fuev | i units/ I d l customer
Measures was mach hrs mach hrs time complaints

.8 .5 AHP

(step 3)


Investment A
Alternatives
.52 .48

Figure 4-5. Performance Impact for Example


Cost Savings

High I III

.A


.5 ............. ..... ... ....................


B.


II IV

Low High

Performance

Figure 4-6. Cost vs. Performance








Conclusion

Although the performance impact model uses AHP, a well-established decision

technique, it focuses on strategic goals, activities and performance measures. A key to

the success of this approach lies in making sure that performance measures do indeed tie

into strategic goals. If this is not the case, there is a disconnect between company goals

and departmental goals, particularly if performance measures are used to evaluate division

performance. As a result, department heads will not be focusing on activities that support

company goals and investment options will be selected on the wrong basis.

The example used in this chapter compares two investment alternatives. The

underlying assumption is that management has decided to make a capital investment and

that each of the alternatives is within management's budget. The model then provides a

framework for ranking the alternatives. Note that the model could just as easily

accommodate more than two alternatives, as long as each alternative is within the budget.

If the budget can accommodate more than one alternative, then management can use the

ranking results to choose the best mix of investments.

In developing the cost impact model, we did not directly include the effect of

depreciation on overhead. Instead, we used the equivalent annual cost of the initial

investment As long as we are comparing two new investment opportunities, this method

works well, since it considers the time value of money. However, if we wish to compare

an existing technology with a new technology, we could use depreciation to account for

the effect of the initial investment. Of course, the cost impact model will tend to favor the

old (existing) technology (as is the case in traditional investment analysis) since older

technology will probably have a lower (or zero) depreciation charge. On the other hand,

the new technology will most likely be favored in the performance impact model, thus

allowing the decision maker to consider the relative merits of non-financial as well as

financial criteria.








Although it was not illustrated in our example, it is possible that the cost impact

model will assign a negative score to one or more investment alternatives. This would

occur when the investment alternative has a negative impact on the most important

activities that is not offset by the positive impact on less important activities (even if the

net cost impact prior to distribution is positive). When this happens, we can still

normalize the scores, retaining the sign of each score, but we must expand our cost vs.

performance graph to include negative numbers. Since we are not allowing negative

performance scores, only the cost axis would be affected. The result would be to expand

regions II and IV into the negative range, without changing the relative desirability of each

region (III would remain the most desirable, while I would remain the least desirable).

In order to remain competitive in the future, firms must make investment decisions

based on strategic goals. Contrary to traditional investment analysis, the investments that

best support these goals may not always be those with the highest financial return. By

incorporating activities and strategic goals into investment analysis, management can look

into the future, rather than making a decision based primarily on past performance.

Traditional financial analysis ranks investments based on net cost savings (or some related

measure, such as payback period). Our cost impact model goes beyond this step, by

looking at how the net cost savings are distributed among activities. It then ranks the

investments according to how they benefit the most important activities (based on

strategic goals). As demonstrated in our example, an investment that is superior based on

net cost savings may not be the best choice when evaluated on activities and strategic

goals. Thus, failure to consider the cost impact on activities and strategic goals may lead

to incorrect decisions.













CHAPTER 5
DETERMINISTIC SCHEDULING


Cost Considerations

Scheduling plays an important role in manufacturing as well as in service

industries. In the current competitive environment, effective scheduling can be critical for

survival in the marketplace. Companies have to meet shipping deadlines to supply Just-in-

Time customers, scarce resources have to be used in the most efficient manner and

activities have to be organized to insure optimal performance. Activity-based costing can

affect scheduling models in several ways. First and most obviously, ABC information can

change the value of cost parameters in a scheduling problem. Secondly, ABC can identify

schedule-dependent cost drivers that can be optimized using scheduling techniques.

Finally, as part of an ABC analysis we can recognize opportunities for cost improvements

by focusing on activities that may be improved by better scheduling or using scheduling to

minimize the cost of a process.

Before discussing these effects, we offer a word of caution about terminology.

Scheduling is commonly described as the optimal allocation or assignment of resources,

over time, to a set of tasks or activities. The resources may be machines, people or space

and the activities could be steps in a production process, stages in a construction project

or tasks at an airport. Activity-based costing measures the cost of resources as they are

consumed by activities and cost objects. This common use of terms (resources and

activities) can lead to some confusion if we are not careful.

For example, the number of machines is typically used to define the processing

environment of a scheduling problem (single machine, parallel machines, machines in









series, etc.). The scheduling problem also specifies how jobs are processed on the

machines (job characteristics). If the machines represent steps in a production process,

they would be defined as activities in ABC. On the other hand, if they represent space to

be allocated for different activities, they would be considered resources in ABC.

Likewise, a job in a scheduling problem can be either a cost object or an activity. If the

job represents a product undergoing various steps in a production process, then it would

be a cost object from an ABC perspective. If instead we are assigning several tasks to

different people in a shop, each task would represent an activity in ABC. Although these

differences may not present any difficulty when formulating an abstract scheduling model,

they must be carefully considered if we wish to apply the results of the model to a real

world problem.


Cost Parameters

Scheduling problems seek to minimize some performance parameter based on

given process times (pj), setup times (si) and due dates (dj). For example, we can minimize

makespan, defined as max (C, .... C}, where Cj is the completion time of job j, or we
can minimize the sum of the completion times, I C, known as the flowtime. If we wish

to incorporate a cost parameter, we would minimize the weighted sum of the completion
times, Y w C, or the weighted flowtime. In the first two cases the performance

parameters are unweighted (wj = 1), while the third case uses a weighted parameter.

Using an unweighted performance parameter implies that all tasks or jobs are equally

important. It does not imply that there is no penalty cost associated with suboptimal

performance, but rather that the penalty function is the same for all jobs.

Consider a common penalty function, lateness. The lateness of jobj is defined as

Lj = Cj dj and the associated penalty function is shown in Figure 5-1 (wj = 1). If we

choose to use the weighted lateness as our performance parameter, then the slope of the









penalty function is defined by wj and the greater the weight, the higher the penalty (see

Figure 5-1). By assigning different weights to different jobs, we incorporate the relative

cost of lateness and we acknowledge that some jobs are more expensive than others.




Li wi =l
wi=1

/ w' = .5
4 .5


dj Ci


Figure 5-1. Lateness Penalty Function



Because activity-based costing is concerned primarily with the allocation of costs,

it will not directly affect those scheduling models whose performance parameter is

unweighted. However, even for those models where we are concerned with optimizing

performance rather than cost, there is an underlying assumption that optimal performance

results in cost savings. For example, if the objective function is to minimize idle time, we

are assuming that idle time is a waste of resources (capital), but no attempt is made to

assign a dollar value to the wasted resources. If we seek to minimize the number of tardy

jobs, we are implicitly minimizing some cost penalty associated with tardy jobs, but again,

we are not concerned with the dollar loss associated with tardiness. Although there is in

fact a penalty function associated with each of the performance measures, the dollar value

of the penalty is not explicitly included in the scheduling model, but is instead used to

justify the objective of the model.

Weighted scheduling problems explicitly include cost in the scheduling model

through the use of weights. Each job j is penalized an amount wj relative to a








performance measure, such as completion time Cj. The value of the penalty weight can be

assigned based on some subjectively determined relative importance of the jobs, which

may not be based on actual costs, or it can be assigned based on the expected dollar loss

that will result from substandard performance. It is the later weighting assignment that is

of interest to us, because ABC is particularly well suited to providing these weights.

To see how ABC is better suited to providing the cost weights in a scheduling
model, we need only observe that such costs are generally considered indirect costs. For
example, the weighted completion time gives an indication of the holding or inventory

costs associated with the schedule (Pinedo, 1995, 13). A traditional accounting system

would allocate holding costs based on volume, so that each job received an equal amount,

w. An ABC system, on the other hand, could assign holding costs using non-volume

drivers such as square footage or dollar value. This would result in different costs (wj) for

different jobs based on their usage of the holding activity. Weighted tardiness provides

another example. Here the weight is the penalty associated with a late delivery. The cost
of that penalty will likely vary from job to job, but that fact will not be captured by a
traditional accounting system. An ABC system, however, could provide this information

by identifying those activities and costs associated with late delivery and assigning the cost
of those activities to each job based on an appropriate cost driver.

Although scheduling models have always recognized that penalty costs may be
different from job to job, the values of the weights are usually determined subjectively, for

instance, by assessing the relative "importance" of a job. This was necessary because

traditional cost accounting systems offered no help in this matter, since overhead
allocation was based on volume and did not discriminate between job types. With ABC it

may be possible to extract the information from the cost system, thus providing a less
arbitrary assignment of weights and a more accurate scheduling model









Schedule Dependent Cost Drivers

Even if a scheduling model does not explicitly consider cost through the use of
weights, it may still be influenced by ABC. Such is the case when the cost driver used to

allocate resource or activity consumption can be improved through better scheduling. In

other words, if the cost driver used by the ABC system to allocate cost is schedule-

dependent, then we may use a scheduling model to improve the performance of the

process. Likewise, the ABC analysis may show that a schedule-dependent driver should

be used to allocate activity costs, highlighting an activity that could benefit from

scheduling optimization.

Note that if the cost driver used by the ABC system is not schedule-dependent,
then improvements gained through schedule optimization may not be reflected in the

accounting system. Hedge and Nagurajan (1992) looked at this problem as it relates to

setup time. They suggested that an ABC analysis might reveal that setup costs are high,

thus motivating the shop floor to reduce the number of setups in order to reduce costs.

On the other hand, the production engineers seek to reduce setup costs by reducing setup

times. This apparent conflict is due to the fact that cost allocation is based on the number

of setups, while the engineering analysis implies that setup time and not number of setups,

is the appropriate cost driver for setup costs. If setup time is the significant cost driver,

then the ABC system should reflect this by using setup time rather than number of setups

to allocate costs. The shop floor will then be motivated to reduce setup time and will not

be adversely impacted by an increase in the number of setups. In reality, both cost drivers

may be appropriate and should be incorporated into the cost accounting system.










Setup Time

As an example, consider the well known scheduling problem of minimizing

sequence dependent setup times. As noted above, setup time may be used to allocate the

costs of the setup activity to the products. Given this allocation, the plant manager would

seek to improve the process by reducing setup time. If the setup times are sequence-

dependent, we wish to minimize the total setup time and we have the following problem:


MinY s,


where sij is the time required to setup from job i to jobj. This problem has been well

studied and is equivalent to the traveling salesman problem, which is NP-complete, but

can be solved with heuristic methods (see, for example, Johnson and Montgomery, 1974,

p. 339).
This is a case where ABC did not directly affect the scheduling problem, but it did

provide an incentive for the type of scheduling model to be used. Where a traditional cost

system would not even recognize setup time as a cost driver, the ABC system would,

provided of course that setup costs are indeed dependent on setup time. By using setup

time in the cost accounting system two things are accomplished. First, as a result of the

cost being tied to setup time, an incentive is created to minimize setup time. Secondly, the

savings achieved by scheduling techniques will be reflected in the financial records and can

be measured in dollars and cents. This will validate the benefits of efficient scheduling.


Number of Setups

Another cost driver for the setup activity might be the number of setups required

by a product (a batch-level activity). This might be the case if each setup had the same








cost regardless of the type of product. In this case the process would be improved by

minimizing the number of setups subject to some other performance requirement such as

due date or flowtime. For example, if we are concerned with due dates we would have the
following problem:

Min x.
s.t. c,

were xj is the number of setups required to process all the jobs of type j, ci is the

completion time of job i and di is the due date of job i. We assume that there are several

similar jobs (all typej) which could be processed as a batch, with only one setup required

per batch. This of course would minimize the number of setups provided we had no other
constraints. In our example, however, we make the more realistic assumption that the due

date is also important, which may affect the order in which we process the batches, or
even which jobs we can include in a batch and consequently the number of batches and

setups. Again, this is an example where the motivation for the scheduling problem arises

from the cost driver identified in the ABC system.


Cost Improvements

Optimizing the sequence of activities in a manufacturing process is a classical

scheduling problem. While ABC may not change the objective of this problem, an ABC

analysis can help identify activities and define the process. This information can then be

used to build a scheduling model and optimize performance. Even the performance of an

individual activity may be optimized through scheduling techniques and this fact may be

recognized in the ABC analysis. This is the essence of activity-based management. Once

we have identified the activities, we seek to improve the activities and the process rather









than simply trying to manage the costs. In some cases, we can also improve the cost of a

process through better scheduling.


Cost Minimization

ABC traces the cost of resources to activities and focuses attention on the cost of

activities. This suggests the possibility of minimizing the total cost of activities (the

process cost) as a scheduling objective. For example, consider the case where a

production line has two machines that accomplish the same task (activity). Machine A is

completely automatic and only requires periodic checking. Machine B is older and

requires a full-time operator. The ABC system could provide the cost per item of each

machine, say WA and wB. Our objective is to minimize the total cost of production and we

can do this by optimizing the scheduling of products (jobs) through the two machines:

Min Ywjx,


where xj is the total number of jobs assigned to machine. A similar situation would arise

if we had several subcontractors available to perform a variety of tasks and each

subcontractor has a different cost per task.

Without any constraints, the trivial solution would be to process all the jobs on the

machine with the lowest per unit cost (wj). But in reality we have the typical constraints,

such as due date, completion time and lateness. If we are concerned with due dates for

example, we would have the following problem:

Min ,wxj
s.t. c, d,


where c, is the completion time of job i on machine and di is the due date of job i. Note

that the problem could be modified for different cost drivers. For example, if time is the

critical cost driver, w, could be the cost per hour of machine j and xj could be the total









number of hours spent on machine j. This might be the case if the ABC system uses

machine hours as the cost driver. Letting ty be the number of hours job i takes on machine

j, we can formulate the problem as

fMin Yw;t/
s.L c, < d,

where tj = i t, is the total time spent on machine j. Our goal is to find a schedule that

meets our due date constraint while minimizing cost.


Conclusion

The benefits of optimal scheduling are widely accepted but poorly defined. In

most cases benefits and costs are couched in subjective terms such as "goodwill" or
"penalty" that offer no measurable results. By incorporating scheduling parameters in the

cost accounting system, ABC can allow us to objectively measure the benefits of better

scheduling. If the cost drivers used by the ABC system to allocate resources to activities

and activities to products are schedule-dependent, then the benefits of an optimal schedule

will be reflected in the cost system. This will in turn provide a tangible, verifiable

incentive for the manufacturing managers to optimize scheduling. In addition, the

increased detail provided by ABC offers the opportunity to incorporate real cost

parameters in scheduling models, thus creating a more realistic model.













CHAPTER 6
COST/SCHEDULE ANALYSIS


Traditional Model

Cost/Schedule analysis is based on the relationship between cost and time for a
project. Given the normal duration of each activity and the precedence relationships

between the activities, we can construct a feasible schedule. Typically we start with a

project network showing the activity precedence, with directed arcs representing the

activities and nodes representing the beginning and end of activities. The network starts

with one unpreceded node and ends with one unsucceeded node. It is labeled so that for

every arc (i,j), i < j. We represent an activity by (i,j), denote its duration time as t, and its

start time as Ti. We can use the network to calculate the total duration of the project,

which is determined by the length of the longest path of activities, referred to as the

critical path. If any activities on the critical path are delayed, the duration of the entire

project will be delayed.

The traditional cost/schedule model assumes that activity duration can be

shortened as some nondecreasing function of cost. In other words, the longer the activity

duration, the less expensive the cost of the activity. Thus, if we wish to compress the total

duration of the project, the model assumes that total direct costs will increase. For

example, we can complete the project earlier, but we may have higher labor costs as a
result of subcontracting the work or paying overtime. On the other hand, the model

assumes that total indirect costs, such as rent and utilities, will increase with time, so the

longer the project lasts, the greater our total indirect costs. Thus, we seek the optimal

project duration so that the sum of direct and indirect costs is minimized.








The initial problem deals only with direct costs and consists of finding the least

cost way of reducing activity duration times in order to meet a fixed project duration, X.

The simplest model assumes a linear cost-time relationship (ay bytu) where ay is the

maximum direct cost of performing the activity in the shortest possible time and by is the

cost per unit of time reduction. For each activity we specify an upper bound, f1 (known

as the normal time) and a lower bound, tf (known as the crash time). The minimum total

direct cost of a project of duration can be formulated as follows:

Min I (a -bQt) D(X)
(i,j)EA
s. t. T~+t T,<0 V(i,j) e A
T, T, I t < t, < tn V(i,j)e A

where Ty is the realization time of event i,

ti is the duration of activity (i,j),

X is the project duration (completion time),

f1 is the crash duration of the activity and

ft is the normal duration of the activity


The purpose of this linear program is to find the optimal realization times and

duration times for each of the activities given the project duration, X. We can use D(X) to

find the minimum direct cost for each X between T, (min) based on crash times and

T, (max) based on normal times. This will allow us to construct the direct cost vs.

duration curve for the project which will be a nonincreasing convex function of time. We

will call this the activity cost curve, since it is based on the cost of the activities. Indirect

costs (assumed to be a nondecreasing convex function of time) must be added to this

activity cost curve to obtain the total cost curve. The total cost curve for the project will

be convex and will have a minimum at X*. This will be the project duration that will result

in the least total cost.








ABC Model

Direct project costs include labor, supplies and equipment, while indirect costs

(also referred to as overhead) include such items as rent, interest, utilities and other costs

that normally increase with the length of the project but are not assigned to activities.

Activity-based costing suggests that we should allocate indirect costs at the activity level

and not necessarily as a function of time. For cost/schedule analysis, only those indirect

costs that vary with time will affect the optimal schedule since we are seeking to optimize

cost as a function of time. Costs that are fixed with respect to time will increase the total

cost of an activity, but not the cost of compression. Nevertheless, ABC will identify other

cost drivers that could be optimized. Optimizing these other drivers would change not

only the total cost of the project, but it might also change the cost of compression for one

or more activities, which would result in a different cost vs. time function.

Because time is the cost driver of interest in the cost/schedule model, we will

assume that there are direct costs that can be allocated based on time, just as the
traditional model does. The difference lies not in the allocation basis, but in the

consumption of indirect costs by activities. Using ABC, we will be able to allocate some

(or all) of the indirect costs to those activities that consume the overhead resources using

a variety of cost drivers, not just time. As mentioned previously, overhead will consist of

a fixed portion that does not vary with time, which we will denote as cy and a variable

portion, d#, which represents the cost per unit time of indirect resources. For simplicity,

we will assume a linear relationship (c + dyti) for the indirect costs assigned to each

activity, as is normally done in ABC systems.

Having allocated indirect costs to each activity, we must consider how the indirect

costs will affect the cost vs. time function. We will assume, as we did originally, that the

direct cost vs. duration relationship for each activity is linear and decreasing. We will also









assume that the indirect cost vs. duration relationship for each activity is linear and

increasing. Thus our new objective function will be

Min I (a, -byt)+(c, +dt,)
(i,j)EA


For each activity, if by > dy, the cost vs. duration relationship will be linear and

decreasing, as it is in the original model, but the cost per time unit of compression will be

decreased. However, if by < dv, the cost vs. duration relationship will be linear and

increasing and if by = dy, the cost of activity (i,j) will be fixed over the length of the

project. Thus we see that ABC can radically change the basic assumption of the

traditional cost vs. schedule model that compression of activity duration always increases

cost.

Although compressing the duration of an activity may indeed increase direct costs,

allocating indirect costs to the activity may reverse the total cost vs. time relationship, so

that for some activities, compression of duration can lower total cost. Thus, there may be

activities that we wish to make as short as possible, which is never the case in the

traditional model. Even for those activities where the cost vs. time relationship remains

decreasing, the compression cost per unit time is decreased. By tracing the indirect costs

to those activities that require them, we can get a more accurate picture of the cost

behavior of the activities with respect to time, which leads to better project scheduling

decisions.

The objective is to minimize total cost. The traditional model only minimizes

direct costs by compressing those activities that have the lowest direct cost per unit of

time reduction (by). It completely ignores the link between activities and indirect costs.

The ABC model on the other hand, captures the relation between activities and indirect

costs and minimizes total cost, not just direct cost. Some activities that appear to have a

high cost per unit time of reduction in the traditional model, may in fact have a low total





81



cost per unit time of reduction in the ABC model. Even two activities that have the same

cost per unit time of reduction in the traditional model may end up with completely

opposite cost vs. time functions in the ABC model. This is because one activity may

consume very few indirect resources (by > dy), so that its cost vs. time function remains

decreasing (Figure 7-1), while the other may consume large amounts of indirect resources

(by < d0), so that its cost vs. time function becomes increasing (Figure 7-2). This is

possible because ABC does not distribute the indirect costs evenly across all activities as is

implicitly assumed in the traditional model.


cost




a .. total


cl .....** direct

f t time

Figure 7-1. Activity Cost When by > dy









cost

total

,* indirect











Figure 7-2. Activity Cost When by < dy



There may still be some indirect costs which cannot be reasonably traced to

activities, such as interest on borrowed money. These project level costs would be treated

in the same manner as all indirect costs are treated in the traditional model They must be

added to the activity cost curve in the final step of the analysis in order to find the

optimum project duration, X*. But even if some indirect costs are not traced to activities,

the ABC model still provides a more accurate picture of cost behavior. By using ABC to

rationally allocate indirect costs to each activity in the project, we are able to make a

better informed decision about the cost of reducing the project completion time.


Conclusion


The cost vs. schedule model provides a classical example of how a model has been

created to fit the available accounting data. With traditional cost accounting lacking the

appropriate details to properly allocate indirect costs, the decision makers were forced to

use a primitive model. Although ABC does not radically change the mathematical

formulation of the cost/scheduling model, the impact can be significant Including the

traceable indirect costs for each activity can dramatically alter the cost vs. time function





83


and thereby change the critical path of the project, which will in turn change the order in

which activities are crashed. Thus the results of the ABC decision may differ from the

traditional model.














CHAPTER 7
PRODUCT MIX


Traditional Model


One of the most commonly used operations research models is the product mix

model. This model is usually formulated as a linear program with the objective of

maximizing profit for a given set of products and resource constraints and is typically used

to illustrate the application of linear programming. The decision variables, x,, represent

the amount of product i to be produced under a given set of resource constraints.

Traditionally the objective function considers one of two cases: the short-term

contribution margin (which excludes fixed overhead costs) and the long-term full-

absorption margin (which includes fixed overhead as a percentage of the volume). The

short-term case can be formulated as follows:

Max X pixi (m, + ,)xi

i
s.t. 'Zm,x, < M

,lixi <- L



where pi is the sales price, mi is the direct material cost and li is the direct labor cost. The

long-term case is formulated as:

Max Yp,x, (mf + 1, + f)x,

s.t. L Cxi !< M

i









where fi is the overhead rate per unit. The model suffers from several shortcomings.

First, in the case of marginal cost, the assumption is that the indirect cost are fixed and

unaffected by the decision parameter. Second, in the case of full-absorption costing, all

indirect costs are assumed to be proportional to production volume (xi). Clearly, neither

of these two choices is entirely valid and the truth is that while some overhead does vary

with production volume and cannot be ignored (even in the short-run) other indirect costs

vary with complexity, a parameter captured by an ABC system, but ignored in a traditional

cost system. This leads us to the third shortcoming of the model, the fact that it does not

accommodate details that may be available from an ABC system. This is an excellent

example of how the cost accounting system can influence a decision model. Since the
traditional cost accounting system did not provide the variety of cost drivers that can be

found in an ABC system, the operations research model was limited as well.


Volume-Related Fixed Costs

ABC recognizes that not all "fixed" cost is really fixed, but may in fact vary in the
long term or with other cost drivers besides volume. Malik and Sullivan (1995) try to

capture the long-term aspect by modeling fixed costs as step functions of volume. Their

model assumes that each resource has a maximum volume of product i that can be

produced and that the cost to increase this capacity is kf. They formulate the problem as

follows:'










SWe have revised some of the notation used by Malik and Sullivan to be consistent with
the notation we use in the rest of this paper.









Max pix, -(m, +I,)x, k ji[xi
s.t. Xm,x, < M
l, x, < L
i




where nii is the capacity (in units) of resource for product i and Oj is the limiting
constraint for resource. While this model is a definite improvement over the traditional
model, it too has some problems.
First, the notation used by Malik and Sullivan is confusing, because they refer to
resources being consumed by products, which is the traditional view of cost allocation. If
the model is based on ABC information, they should refer to activity (rather than
resource j). Second, the model only considers those indirect costs that can be allocated
with volume-related cost drivers. It ignores the indirect costs that vary with non-volume-
related cost drivers (those that vary with complexity rather than some function of volume).
Finally, by summing the incremental activity (resource) step costs for each product
separately, the model assumes that the capacity of each activity (resource) is divided into

product capacities which are mutually exclusive. This might lead to incorrect results.

For example, consider a case similar to the one suggested by the authors (p. 172):
a certain shop floor area can accommodate six machines for product 1, so kji would be
one sixth of the total rent/cost (kj) for the area, or kji = k/6. The same area can only
accommodate three machines for product 2, so kj = k/3. Product 1 machines can
produce a maximum of 100 units per period, while product 2 machines can produce up to
300 units per period, so nil = 100 and n.7 =300. Now suppose we produce 80 units of
product 1 and 500 units of product two, so we need one machine for product 1 and two
machines for product 2. Clearly, we do not need to increase the shop floor area to








accommodate these three machines, so the total cost of the shop floor resource will be ks.
However, the proposed model would calculate the shop floor cost as follows:

k/ 80 k/s 500o 5k,
/6 100 + 3001 6


A better way to model the shop floor cost would be the following:





where a# is the number of product i machines used on the shop floor (activity j) and mf is
the capacity of the shop floor in terms of machine i. The number machines used is a step
function of quantity:


a, = -


Thus the total cost of the shop floor becomes


6 3+6 3


which is the actual cost of the shop floor, as shown earlier.


ABC Model

In order to capture both the volume-related indirect costs and non-volume-related
indirect costs allocated by an ABC system, we must use a more general model for indirect
costs:


k[ l a (1)








where aip is the amount of activity j driver consumed by product i and myj is the capacity of
activity for product i. We can now consider three cases: the cost driver is volume (aji =
xi), the cost driver is volume-related [aji = fj(xi)] and the cost driver is not volume-related
(aji is not a function of xi).

Cost driver is volume. In this case af = x# (the volume of product i using
activity) and mip = nfj. This gives us the long-term step function cost of each activity.
Note that if product i does not use activity we simply let xji = 0. With volume as the cost
driver model (1) becomes


k x (2)


Cost driver is volume-related. In this case af = ffxi). For example, if the cost
driver is the number of setups, we can easily relate it to the volume through batch size:

Let a,# = number of setups on machine for product i
si = batch size of product i on machine
then a,; = andf,(x,)= x
Sji Sji

Also nm = maximum number of batches of product i on machine j, so
nj, = mi x sj, = maximum volume of product i on machine

So model (1) can be put in the same form as (2)

k [ I(s ,)(a = k) x
i (sji)(mi) I n


Cost driver is not volume-related. If the cost driver is related to complexity
instead of volume, then it is "fixed" over all ranges of volume. This implies thatfj/x,) = 0
or that ni is so large that xj/n1, is always less than one. In this case model (2) is of little
use, but model (1) still works. For example, suppose the cost driver is the number of
engineering change orders or maybe the scheduling hours spent on each product In both









cases the volume of a particular product does not effect the total indirect cost, but it still

varies from product to product based on non-volume cost drivers.
In order to capture the information provided by all the ABC cost drivers we must

use the following product mix model:


Max P ixi-[kj i m1Ai | aJ1 ]z}j

s.t. ,m'ixi, M
i
,lixi < L
Xl*,x, L




where vi = variable costs of product (cost driver is volume)
a, = ai- = total amount of driver consumed for the period

(1 if product i is produced
0 = otherwise

this allows us to incorporate not only the volume-related ABC drivers, but the non-
volume-related ones as well. Note that the last term of the objective function represents

the portion of "fixed" or indirect cost assigned to product i (F,). Of course, the portion of

F, that is not volume-dependent is only an approximation based on the expected cost of

activities and estimated driver usage (which can be derived from the ABC system), but it

still provides a more realistic estimate of the total effect of including product i in the
product mix. The problem can be solved as a mixed integer program similar to the

example given by Malik and Sullivan.


Conclusion

By considering all the information provided by an ABC model we can improve the

traditional product mix model in several ways. First, we can obtain better information









about the product costs. This alone improves the accuracy of the model, but does not

address the problem of how to handle "fixed" costs. A second improvement can be

achieved by incorporating the long-term variability of "fixed" costs using a step function

of volume. This creates a more useful model, that can be applied to both short-term and

long-term decisions, but fails to include those indirect costs that do not vary with volume.

Finally, we can create a more general model that includes non-volume-related cost drivers

that are fixed over volume but vary from product to product. This general approach

allows us to take full advantage of the information provided by the ABC system,

incorporating one of the key aspects of ABC, the accurate tracing of indirect costs.

The ABC model presented in this chapter highlights the advantage of ABC over

traditional cost accounting systems. By tracing indirect costs to activities, we are able to

understand the true nature of the business process and use the most appropriate drivers to

allocate costs to products. The activities become the focus of the cost analysis and this is

reflected in the product mix model through the use of driver capacity, rather than volume

capacity, to measure the impact of products on fixed costs. The result is a more accurate

and realistic model.




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