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 Front Cover
 Abstract
 Title Page
 Center information
 Table of Contents
 Acknowledgement
 Summary
 Main
 Appendix
 Reference














Title: Determining dairy delivery case life using a practical sampling procedure
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Permanent Link: http://ufdc.ufl.edu/UF00027840/00001
 Material Information
Title: Determining dairy delivery case life using a practical sampling procedure
Alternate Title: Florida Agricultural Market Research Center Industry Report - University of Florida ; 81-12
Physical Description: Book
Language: English
Creator: Degner, Robert L.
Shonkwiler, Scott
Publisher: Florida Agricultural Market Research Center, Food and Resource Economics Dept., Institute of Food and Agricultural Sciences, University of Florida
Publication Date: 1981
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Spatial Coverage: North America -- United States -- Florida
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Bibliographic ID: UF00027840
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Front Cover
        Front Cover
    Abstract
        Abstract
    Title Page
        Page i
    Center information
        Page ii
    Table of Contents
        Page iii
        Page iv
    Acknowledgement
        Page v
    Summary
        Page vi
        Page vii
    Main
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
    Appendix
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Reference
        Page 18
Full Text




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ABSTRACT *


Loss of dairy delivery cases continues to plague Florida dairy

processors despite control measures adopted by many firms in recent

years. Losses to Florida processors in 1981 may exceed $2,000,000.

This study provides managers of dairy processing firms with a

management tool which will help to (1) determine the rate of loss for

different types of cases and (2) determine loss rates by age of case.


Key words: dairy delivery cases, dairy processing, dairy delivery

case loss rates















Determining Dairy Delivery Case Life Using
a Practical Sampling Procedure










Robert L. Degner and J. Scott Shonkwiler

















September 1981

The Florida Agricultural Market Research Center
a part of
The Food and Resource Economics Department
Institute of Food and Agricultural Sciences
University of Florida, Gainesville, Florida















The Florida Agricultural Mrket Research Center

A Service of
The Food and Resource Economics Department
Institute of Food and Agricultural Sciences

The purpose of this Center is to provide timely, applied research

on current and emerging marketing problems affecting Florida's Agri-

cultural and marine industries. The Center seeks to provide research

and information to production, marketing, and processing firms, groups
and organizations concerned with improving and expanding markets for Florida
agricultural and marine products.

The Center is staffed by a basic group of economists trained in

agriculture and marketing. In addition, cooperating personnel from IFAS

units provide a wide range of expertise which can be applied as determined
by the requirements of individual projects.















TABLE OF CONTENTS '

Page

LIST OF TABLES............................ ................ ..... iv

LIST OF APPENDIX TABLE....... ..... .............. ..... ............. iv

LIST OF FIGURES.................................................. iv

LIST OF APPENDIX FIGURE............ .....................,....... iv

ACKNOWLEDGEMENTS.................................................. v

SUMMARY................ .. .. .............. ............. ..... .... .. vi

OBJECTIVES............................................. ..... .... 2

RESEARCH PROCEDURE............... ................................... 2

Determining Case Life Through Sampling ........................ 3

Obtaining the Sample................................ ... ... 6

Analyzing the Sample: An Example.............................. 8

CONCLUSIONS....................................................... 12

APPENDIX................................ .......................... 13

REFERENCES................................... .... ................. 18

















iii














LIST OF TABLES


Table

1 Sampling rates for various types of cases or types of dates.....

2 An example of data and calculations required to determine case
life..................................... ........................


Page

4


9


LIST OF APPENDIX TABLE


Page


Table

1 An example of data and calculations required to determine
case life using a statistical procedure........................


LIST OF FIGURES


Figure

1 Typical date codes found on dairy delivery cases. Both
indicate a case manufactured in March of 1981.................

2 Percent of cases remaining in a distribution system over time
(from Table 2, Column 6) ....................................


Page


LIST OF APPENDIX FIGURE


Figure

1 Percent of cases remaining in a distribution system over time...


Page

17















ACKNOWLEDGEMENTS


This research was funded in part by a grant from the Florida Dairy

Products Association. Mr. R. Gene Smith, Chairman of the Board, and

Mr. Joseph R. Antink, President, gave leadership to the Association in

supporting this project.

Our appreciation is expressed to executives and employees of Borden,

Inc., Orlando and Tallahassee, T. G. Lee Foods, Orlando, and Pet, Inc.,

St. Petersburg, for their excellent cooperation in providing data and

access to their plants for developing and testing the case sampling

procedure.

Thanks are also due Ms. Patricia Beville and Mrs. Lois Schoen for

typing the manuscript and Mrs. Susan Howard for preparing the graphs,
and to Mtss Judy King for data processing.














SUMMARY


* Loss of dairy delivery cases continues to plague Florida dairy
processors despite control measures adopted by many firms in recent
years. Losses to Florida processors in 1981 may exceed $2,000,000.
* This study provides managers of dairy processing firms with a
management tool which will help to (1) determine the rate of loss
for different types of cases and (2) determine loss rates by age
of case.

* A statistical sampling technique and analytical method has been
developed which is simple and inexpensive to administer.

* The technique requires that each batch of cases be uniquely identifi-
able; the most practical way of doing this is to have the manufacturer
imprint each lot of cases with a manufacture date.
* The dates of service for each batch of cases must also be ascertain-
able from company records.

* Large, legible manufacture dates facilitate the sampling procedure.
The "easiest to read" dates can be sampled at the rate of 1,400-1,500
per hour compared with only 200-300 per hour for difficult to read
date codes.
* The recommended sample size is 2,000 cases.

* Sampling may be done at any time after the most recent batch of cases
has been thoroughly distributed throughout the system, usually about
one month after introduction.

* Sampling may be done at any convenient location in the case storage
area or on-line. If done on-line, an acceptable procedure would
be to select every "nth" case as it passes by.
* Avoid bias in drawing the sample. Take care to include every case
selected, regardless of type or legibility of date. Every effort
must be made to determine dates of all cases selected.

* Tabulate the number of cases observed for each manufacture date. Then
determine the proportion of each date to the original number purchased
and placed into service. This proportion or ratio is the "sample
ratio".









* The sample ratio for the most recent batch of cases in the system
serves as a base. If it is assumed that none of the newest cases is
missing, the sample ratio for the most recent batch is one, or
equivalent to 100 percent (the percent of cases still in the system).
The sample ratios for the other case dates expressed as a ratio to
the sample ratio base reflects the proportion of each date left in
the system.

* Comparison of results for different company locations, case types,
or management practices can help identify ways to reduce case costs.














Determining Dairy Delivery Case Life Using a
Sampling Procedu're


Robert L. Degner and J. Scott Shonkwiler


Studies conducted by the Florida Agricultural Market Research

Center (FAMRC) in 1977 and 1979 placed dairy delivery case losses for

Florida dairy processors during 1976 and 1978 at $1.3 and $1.5 million,

respectively (Mathis and Degner, 1977, 1979). Case losses cost pro-

cessors 0.53 and 0.56 cents per gallon of fluid product for the re-

spective study years.
Although most Florida dairy processing firms have adopted measures

to ameliorate the case loss problem, many plant managers feel that

losses are greater than ever. If the 1978 costs are simply adjusted for

inflation, the current annual losses exceed $2 million. This continuing
problem and the associated escalating costs make it imperative that

processing plant managers be able to accurately monitor their case

inventories and estimate the rate at which cases disappear from their

distribution systems. Knowing the disappearance rate for cases of

different materials or design, different case management policies, or
for individual plants, would provide a management tool which could

reduce future case losses. Further, accurate information on loss rates

may be used to modify depreciation schedules, possibly resulting in tax

savings.









OBJECTIVES


The primary objective of this study was to develop a technique for

determining the rate of loss of dairy delivery cases for individual

firms. Specific objectives were to:

1. Determine the relative loss rates for cases made of wire and

plastic.

2. Determine case loss rates by age of case.

3. Provide processors with a sampling method to meet the above

objectives which is relatively simple and inexpensive to
administer.

RESEARCH PROCEDURE


The theoretical basis for the study rests on the ability to compare

an observed (sample) distribution of dairy cases remaining in a system

with a known distribution (over time) of case acquisitions. This com-

parison requires 1) the ability to determine the actual numbers of dairy

delivery cases placed in service by a given processing plant at specific

points in time (from processing plant records) and 2) the ability to
identify individual cases as to the date placed into service (from manu-

facture dates or codes stamped on cases).
Four major processing plants cooperated in the study. All provided

case purchase records for a minimum of two years and all allowed access

to case handling areas so that researchers could observe case flow rates
and record case manufacture dates from a sample of cases. All plants

were visited by FAMRC personnel one or more times in early 1981.










Unfortunately, none of the cooperating plants maintained the numbers

of cases of a given manufacture date put into service on specific dates.

Several plants had also received shipments of cases which had no manu-

facture date, thereby precluding the use oi their case data. However,

it was possible to examine records of case purchases and relate these to
manufacture dates found on cases in several plants so as to obtain

sufficient data to develop the basic procedure. Further, information on

time requirements and other practical aspects of sampling was obtained

at all cooperating plants. Several techniques were developed and evaluat-

ed, but the one described in the following section was judged to be the

simplest and most practical to use, and yet very effective.

Determining Case Life Through Sampling


In order to use the case sampling procedure described below, a pro-

cessing plant must have 1) cases which have manufacture dates or codes

imprinted on them and 2) accurate records which indicate when cases of a

particular manufacture date were put into service.

The case manufacture date or code is extremely important because it

uniquely identifies a given batch of cases. Most case manufacturers

routinely imprint or emboss numbers representing the month and year on

their cases. On plastic cases the numerals are usually found imprinted

on two opposing side panels. On wire cases, they are usually stamped or

embossed on several of the sheet metal corner supports.
Some cases, particularly those made of plastic, will have a date

code rather than a numeric month and year date. Typically, such codes

will consist of a grid or "clock" which will contain one dot for January,

two for February, etc. The year of manufacture will usually be found in








the center of the grid or circle (Figure 1). On some cases the code is

found on a side panel, and on others, the bottom. Obviously, the size

and location of the manufacture date greatly affects legibility, which

in turn affects the time required to record dates from a sample of

cases. Plastic cases with relatively large ( inch to 1 inch) numerals
in contrasting colors on side panels could be sampled at the rate of

1,400 to 1,500 per hour. Metal cases with numerals about the same size

were sampled at 400 to 500 per hour, and only 200 to 300 plastic cases

with date codes could be sampled per hour (Table 1).

Table 1.--Sampling rates for various types of cases or types of dates.


Type of case, date Sampling rate

(Cases per hour)

Plastic, large contrasting numerals 1400 1500

Metal, large embossed numerals 400 500

Plastic, coded dates 200 300



Obviously, the sampling rate depends on the skill and experience of

the sampler, the location in the plant where sampling is done, and the

method used to record the datj. FAMRC researchers found that dictating

dates into a portable tape re order saved considerable time compared

with writing them down. If it is anticipated that the dates will be
used for sampling purposes, every effort should be made to get the

manufacturer to put large numeric dates on the side panels or the corner

supports. Codes should be avoided, as they require considerable more
time to decipher and record.


















0 00



81


Note: actual size
is approximately
one inch.


Figure 1. Typical date codes found on dairy delivery
cases. Both indicate a case manufactured
in March of 1981.









Most plants visited had an assortment of different case types, with

different types of dates or codes. When sampling from such an assortment,
it is important to read every date on cases included in the sample, not

just those that are most legible. This will reduce sample bias, which
is discussed in greater detail in the next section. If the above con-
ditions have been met, i.e., dated cases and accurate records indicating

when cases of a particular manufacture date were put into service, this

procedure can be used. The next step is to record manufacture dates
from a random sample of cases.

Obtaining the Sample


The optimum time for sampling cases is as soon as possible after

the most recent batch of cases has been absorbed by the system and has
become randomly distributed. While the exact time is difficult to

specify, it is estimated to be about one month after introduction of new

cases to the system for most plants. If sampling is done too soon, the

majority of the newest cases might remain together, and could be under-
sampled if they are all at customers or away from the plant at once.
Similarly, they could be oversampled if large numbers are back at the

plant simultaneously. On the other hand, if too much time elapses after
introduction of a batch of cases into the system, substantial numbers
could already have been lost and estimates of case losses based on the
technique described in the next section may be too low.

A sample of approximately 2,000 cases is sufficient for most plants

to insure reasonable accuracy. Every effort must be made to insure that

a random sample of dates will be recorded. In most plants, cases of all
ages and types will be uniformly or randomly distributed through the

distribution system. However, if cases tend to be sorted for some










reason, i.e., because of driver preference for a particular type of case

or because some cases pose handling problems in certain lines, care must

be exercised or a biased sample may result.
At the four cooperating plants, samples were obtained in various
locations such as filling lines, case storage areas, unloading docks,

and the case washing line. The sample dates should be obtained wherever

dates can be easily read, without introducing bias into the sampling
procedure.
Bias can be introduced whenever the sampler cannot read the date on

every case that passes by or if he cannot keep up when sampling every
"nth" (every 3rd, 4th, etc.) case that passes by when sampling in a
line. Bias would be introduced because the sampler would tend to read
highly legible cases, but undersample cases with less legible dates.
Similarly, bias can be introduced in sampling from stacked cases if

the sampler is less than diligent about recording dates that are

difficult to read.
FAMRC researchers found that the line emerging from the case washer
was the best place to obtain a sample in most plants. As the cases
emerge from the washer, they are usually stacked five or six cases high.
A sampler can easily record dates from every case in a given stack.
If more time is required to examine a hard to read date, the case can
be removed from the line for closer inspection and another substituted.
Similarly, a whole stack maybe removed from the line for closer scrutiny.

Any number of stacks of cases can be ignored, but every case in a given
stack must be read to minimize bias.









The only type of case that should be ignored is a foreign case.

Foreign cases constituted an extremely small proportion of the cases

observed in cooperating firms' plants, but even so, foreign cases cannot

be analyzed because of the obvious lack of'acquisition data.

Analyzing the Sample: An Example

The case data shown in Table 2.is based on actual case acquisition
records and a sample of case manufacture dates observed at one of the

cooperating plants. The actual numbers of cases purchased have been

scaled (adjusted by a constant value) to maintain confidentiality, how-
ever. Data in columns (1), (2), and (3) were obtained from plant records.
The plant was visited in early February and case manufacture dates

were recorded from a sample of 2,173 cases. Early February was chosen

as the time to draw a sample because the plant had acquired a shipment

of cases in early January; about a month had elapsed since the last

batch of cases had been acquired. A month was judged to be sufficient
to allow the newest cases to be thoroughly dispersed in the system.

Fortunately, case manufacture dates corresponded very closely with

the dates when cases were put into service. The numbers of cases observ-
ed of each manufacture date were tabulated; the results are shown in
column (4) of Table 2. For example, in our sample of 2,173 cases, 145

were observed out of the shipment acquired with the date 1-81. Because

tabulation only requires counting, it is easily done by hand, but clerical

time can be saved by using a small computer if available.

After tabulating column (4), column (5) is calculated by dividing

the number of cases observed of a specific age by the number of cases







Table 2.--An example of data and calculations required to determine case life.


(1)a (2) (3) (4) (5)b C6)c (7)d
Case
manufacture/ Months Number of Number of Sample Cases remaining
acquisition in cases cases ratio number
date system purchased in sample (4) (3) proportion (3) X (6)

1-81 1 787 145 .1842 1 787
9-80 5 3,637 532 .1463 .794 2,888
2-80 12 2,132 221 .1037 .563 1,200
9-79 17 4,929 401 .0814 .442 2,179
5-79 21 5,197 353 .0679 .369 1,918
10-78 27 3,939 243 .0617 .335 1,320
5-78 33 3,443. 140 .0407 .221 761
12-78 38 2,644 138 .0522 .283 748

Totals -- 26,708 2,173 ------- 11,801


a
Case manufacture dates are shown here; ideally they should correspond
they do not, column (21 should be adjusted to reflect as nearly as possible
put into service, rounded to the nearest month.


Column (5C is calculated by
of cases bought of the same age.


to acquisition


dates. If


the date cases were actually


dividing the number of cases observed of a specific age by the number
For example, 145-787 = .1842, etc.


c
Column (6) is calculated by dividing every number in column (51 by the first number in column
(5L. For example, .1842L.1842 = 1, .1463t.1842-= .794, etc. The resulting numbers represent the
proportions of cases of each batch that remain in the system. For percentages, multiply proportions
by 100.

d
Column (71 is calculated by multiplying the proportion of cases remaining in the system
by the number of cases originally purchased, i.e., columns (3) and (6).









bought or acquired of the same age. For example 145 1 787 = .1842,

532 7 3,637 = .1463, etc. The resulting- numbers are termed the "sample

ratio" (Table 2). The sample ratios are then used to calculate column

(6), the proportion of cases of specific ages remaining in the system.

This technique has been used by another researcher to-analyze similar

problems (Hausman, 1979).

The values in column (6) are calculated by dividing every number in

column (5) by the first number in column (5) for example, .1842 .1842

= 1, .1463 .1842 = .794, etc. This calculation implicitly assumes

that none of the latest batch of cases is missing. The sample ratios

for all other batches of cases are expressed relative to the most recent

batch. The values calculated for column (6) represent the proportions of

cases remaining of each batch. For example, about 79 percent of the

cases are estimated to be in the system at the end of five months (those

acquired 9-80), but only 33.5 percent of those purchased 27 months

previously i.e., 10-78 (Table 2). Obviously, to calculate the proportion

of cases missing, one would subtract the proportion remaining from 1.0.

The proportions are converted to percentages by multiplying by 100.

After the proportions of cases remaining in the system have been

estimated (olumn 6),estimates of actual case numbers of each age group

can be calculated by multiplying the values in column 6 by the numbers

of cases originally purchased (Column 3). These estimates are shown in

column (7). Summing the remaining cases of all ages yields an estimate

of total inventory. In Table 2, an estimated 11,801 cases remain of the

26,708 purchased in the last 38 months.

The values in column (6) can also be plotted to give a visual or

graphic representation of case losses over time (Figure 2). If an












Percent

100

90

80

70

60

50 Free hand curve

40

30

20 -

10

| I '' S I j I I I '
1 5 12 17 21 27 33 38
Months

Figure 2. Percent of cases remaining in a distribution system over time (from Table 2, Column 6).










estimate of the percentage of cases remaining is desired for a point in

time between actual observations, a smooth, free hand curve can be drawn

through (among) the points, which attempts to minimize the deviations of

individual points (Figure 2). The approximate proportion of cases

remaining in the system can then be read off the graph for any time

period. If the values from column (6) are highly variable, it may be

difficult to draw an accurate, free hand curve through the resulting

plotted points. In such cases, the mathematical relationship between

the proportions of cases remaining (or lost) and time can be easily and

accurately estimated using a statistical procedure discussed in the

Appendix.

CONCLUSIONS


Data limitations precluded the determination of relative loss rates

for cases made of different materials or designs. However, the sampling

technique developed provides dairy processing plant managers with a

technique which can be used within their respective firms to estimate

case life for their own unique operations. It is important that managers

begin to have each new shipment of cases uniquely identified with legible

manufacture dates. The should also record the dates that cases are

actually put into service. This will allow case life to be monitored

using this procedure. An analysis of case life for different company

locations, case types, and management practices can help identify ways

to reduce case costs.
































APPENDIX













APPENDIX


Case loss can be expressed as a mathematical function of the form
Y = ebt where:

Y = the ratio of remaining cases, i.e., column (.6) from Table 2.,

also shown in Appendix Table 1.

e = logarithmic base, 2.7182818, a constant.
t = time (in months) that various batches of cases have been in
the system, ice. column (2) Table 1, also shown in Appendix

Table 1. Other time units such as days or years could be
used if desired.

The objective of this procedure is to estimate the value of the

parameter "b" in the above equation by using a simplified form of re-

gression analysis. The purpose of this mathematical approach is to be

able to calculate an "average" relationship between case loss and time,
resulting in a smooth, accurate curve such as the one shown in Appendix

Figure 1. This is especially useful when the calculated points (column

6) are highly variable. Points on the curve were calculated by allowing

"t" to take on values from 1 to 38 after "b" was estimated. To estimate
"b", the following steps are required:

1. Calculate columns (2) and (6) of Table 1, shown again in Appendix
Table 1.

2. Construct column (8) of Appendix Table 1 by taking the natural

log (base e) of column (6). Many inexpensive hand held cal-
culators wtll perform this operation.









3. Add the squares of the entries in column (2):

12 + 52 + 122 + 172 + 212 + 272 + 333 + 382 = 4162

4. Add the products of the entries in column (2) times the entries

in column (8):

(1)0 + 5(-.231) + 12(-.574) + 17(-.816) + 21(.-.997) + 27(-.1.093)

+ 33(-1.509) + 38(-1.262) = -170.1

5. The parameter "b" equals the result in step 4 divided by the

result in step 3:
-170.1 4162 = -.04087

6. The equation is y = e-'04087t

7. Cases remaining can now be estimated for any time period between

one and 38 months. For example, the estimated proportion of
cases remaining after 24 months in the system would be calculated

as follows:

Y = 2.7182818-.04087(24)

Y = 2.7182818-.98088

Y = .375 or 37.5 percent

8. The time required for a firm to lose a given proportion of cases

can also be calculated. The formula below will allow you to

solve for t given Y:

t = In Y
b

For example, to calculate the number of months it would take for
half the cases to leave the system, take the natural log of .50,

divid the resulting logarithm by -.04087, the estimated "b" value
discussed above.
t = -0.693147 = 16.96 months
-0.04087










Appendix Table l.--An example of data and calculations required to
determine case life using a statistical procedure.


Columnb
(2) (6) (8)
Months in system Cases remaining, proportion Log of column (6)

1 1 0
5 .794 -.231
12 .563 -.574
17 .442 -.816
21 .369 -.997
27 .335 -1.093
33 .221 -1.509
38 .283 -1.262


a
The statistical estimating procedure is regression analysis, used

to estimate the parameter b of the function Y = ebt where

Y = the ratio of remaining cases, column (6)

t = time (months) that various batches of cases have been in the
system, and

e = logarithmic base, 2.7182818.

b
Columns (2) and (6) are taken from Table 2 in the text. The
values in column (8) are natural logs (base e) of the values in column
(6).













Percent


100 -

90-

80-

70 -
Line drawn through points
60 calculated with mathematical
e function y = e-04087t
50- Points from/
Column (6)
40- Appendix Table 1 ,

30-

20-

10

I I i i S S S S S S I I I | I l l l I | l I i i I 1 i I l '
1 5 12 17 21 27 33 38
Months


Appendix Figure 1. Percent of cases remaining in a distribution system over time.















REFERENCES


Mathis, Kary and Robert L. Degner, Dairy Delivery Case Losses in
Florida: Costs and Controls, Industry Report 77-1, Florida
Agricultural Market Research Center, Food and Resource Economics
Department, IFAS, University of Florida, June 1977.

Mathis, Kary and Robert L. Degner, Dairy Delivery Case Losses in
Florida 1979, Industry Report 79-6, Florida Agricultural Market
Research Center, Food and Resource Economics Department, IFAS,
University of Florida, November 1979.

Hausman, Jerry A. "Individual Discount Rates and the Purchase and
Utilization of Energy Using Durables", The Bell Journal of Economics,
Vol. 10, No. 1, Spring, 1979.




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