The Pennsylvania State University CONTRACTING AND …

The Pennsylvania State University

The Graduate School

Harold and Inge Marcus Department of Industrial and Manufacturing Engineering

CONTRACTING AND ISSUING POLICIES FOR PERISHABLE GOO DS

SUPPLY CHAINS

A Thesis in

Industrial Engineering

by

Joohyun Cho

2010 Joohyun Cho

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

December 2010

The thesis of Joohyun Cho was reviewed and approved* by the following:

Paul M. Griffin Professor and Head of the Department of Industrial and Manufacturing Engineering Thesis Advisor

Jose A. Ventura Professor of Industrial and Manufacturing Engineering

M. Jeya Chandra Professor of Industrial and Manufacturing Engineering Graduate Program Coordinator

*Signatures are on file in the Graduate School

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ABSTRACT

Perishable goods are closely related to our daily life, which is represented by

groceries and pharmaceutical products. They differ from non-perishable items in that

they have limited shelf life and have an additional cost when they expire. Another issue

is how the dispatching order affects spoilage. From the perspective of individual

optimization, the FIFO issuing policy has higher profit than LIFO. However, from a

supply chain perspective, the upper stream’s issuing policy has an impact on the buyer

and the whole supply chain.

In this thesis, we examine a perishable good supply chain with a distributor and a

retailer. We assume the two entities use a continuous review policy for inventory

management with positive leadtimes. In addition, products have a limited shelf life and

decay at a constant rate. An expired product has no salvage value. For this supply chain,

we examine two things, 1) the feasibility of the buy-back contract as a coordinating

mechanism, and 2) the impact of the distributor’s issuing policy on the profit of the

retailer and the total supply chain. The results are that a buy-back contract can be

designed to coordinate the independent participants under a Q(r) policy with positive

leadtimes, and a LIFO issuing policy of the distributor can provide a higher profit to the

retailer.

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TABLE OF CONTENTS

LIST OF FIGURES ..................................................................................................... vii

LIST OF TABLES ....................................................................................................... ix

ACKNOWLEDGEMENTS ......................................................................................... x

Chapter 1 INTRODUCTION ...................................................................................... 1

Chapter 2 LITERATURE REVIEW ........................................................................... 6

2.1 Optimal Inventory Policy for Perishable Products ......................................... 6

2.1.1 Periodic Inventory Review ................................................................... 7

2.1.2 Continuous Inventory Review .............................................................. 8

2.2 Supply Chain Coordination ............................................................................ 10 2.2.1 Quantity Discount ................................................................................. 11

2.2.2 Revenue Sharing ................................................................................... 12

2.2.3 Buy-Back .............................................................................................. 13 2.3 Optimal Inventory Issuing Policy ................................................................... 15

2.3.1 Multi-Echelon Perishable Inventory ..................................................... 16

2.3.2 LIFO Perishable Inventory Issuing Policy ........................................... 18

Chapter 3 SUPPLY CHAIN MODELING ................................................................. 22

3.1 Modeling Introduction .................................................................................... 22 3.1.1 Retailer ................................................................................................. 23 3.1.2 Distributor ............................................................................................. 24 3.1.3 Types of the Supply Chains .................................................................. 25

3.2 Sets and Notations .......................................................................................... 27 3.2.1 Sets ....................................................................................................... 27 3.2.2 Notation for the Inventory Operations ................................................. 27

3.2.3 Notation for Inventory Issuing Process ................................................ 29

3.2.4 Issuing Policies and Dispatching Models ............................................. 30

3.2.4.1 FIFO Issuing Policy ................................................................... 30

3.2.4.2 LIFO Issuing Policy ................................................................... 31

3.3 Constraints ...................................................................................................... 32 3.3.1 Inventory Capacity ( nIC ) ..................................................................... 32

3.3.2 Service Level ( nSL ) .............................................................................. 33

3.4 Constants......................................................................................................... 33 3.4.1 Unit Price ( nP ) .................................................................................... 34

3.4.2 Unit Costs ............................................................................................. 34 3.4.2.1 Inventory Holding Cost (nH ) .................................................... 34

3.4.2.2 Waste Handling Cost ( nWH ) ..................................................... 34

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3.4.2.3 Lost Sales Cost ( nLS ) ................................................................ 35

3.4.2.4 Fixed Ordering Cost ( nOC ) ....................................................... 35

3.5 Decision Variables .......................................................................................... 36 3.6 Objective Functions ........................................................................................ 38

3.6.1 Decentralized Supply Chain ................................................................. 38

3.6.1.1 Distributor’s Objective Function ................................................ 38

3.6.1.2 Retailer’s Objective Function .................................................... 40

3.6.2 Coordinated Supply Chain .................................................................. 42

3.6.2.1 Distributor’s Objective Function ................................................ 43

3.6.2.2 Retailer’s Objective Function ..................................................... 43

3.6.3 Centralized Supply Chain ..................................................................... 44

Chapter 4 EXPERIMENTS SETTINGS AND RESULTS ANALYSIS .................... 47

4.1 Experimental Design ...................................................................................... 47 4.2 Optimal Order Quantity of Decentralized Supply Chain ............................... 49

4.3 Feasibility and Effectiveness of the Coordinated Supply Chain .................... 51

4.3.1 Buy-back Contract for LIFO Issuing Policy ........................................ 51

4.3.2 Comparison with Centralized Supply Chain ........................................ 54

4.4 Which Policy Is Better in Decentralized Supply Chain? ................................ 55

Chapter 5 CONCLUSION .......................................................................................... 67

5.1 Evaluation of the study ................................................................................... 67 5.2 Applications of the study ................................................................................ 69

Bibliography ................................................................................................................ 71

Appendix A Customer Demand Sets for Experiments ............................................... 73

Appendix B Order Quantities and Profits of Entities in Decentralized Supply Chain ..................................................................................................................... 79

B.1 Retailer’s Order Quantities and Profit Optimization ..................................... 79

B.2 Distributor’s Order Quantity and Profit Optimization under FIFO ............... 80

B.3 Distributor’s Order Quantity and Profit Optimization under LIFO ............... 80

Appendix C Retailer Performances in Decentralized Supply Chain according to the Distributor’s Issuing Policies .......................................................................... 82

C.1 Retailer’s Mean of Sales Volume under Distributor’s FIFO Issuing Policy ............................................................................................................. 82

C.2 Retailer’s Mean of Waste Volume under Distributor’s FIFO Issuing Policy ............................................................................................................. 83

C.3 Retailer’s Mean of Lost Sales Volume under Distributor’s FIFO Issuing Policy ............................................................................................................. 83

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C.4 Retailer’s Mean of Remaining Shelf Lives under Distributor’s FIFO Issuing Policy ................................................................................................ 84

C.5 Retailer’s Mean of Sales Volume under Distributor’s LIFO Issuing Policy ............................................................................................................. 84

C.6 Retailer’s Mean of Waste Volume under Distributor’s LIFO Issuing Policy ............................................................................................................. 85

C.7 Retailer’s Mean of Lost Sales Volume under Distributor’s LIFO Issuing Policy ............................................................................................................. 85

C.8 Retailer’s Mean of Remaining Shelf Lives under Distributor’s FIFO Issuing Policy ................................................................................................ 86

Appendix D Centralized Supply Chain Order Quantities and Profit .......................... 87

D.1 Supply Chain Mean Profit under the Distributor’s FIFO Issuing Policy ...... 87

D.2 Supply Chain Mean Profit under the Distributor’s LIFO Issuing Policy ...... 88

Appendix E URLs for C Language Programming Codes for Experiments ................ 89

E.1 The URL for Decentralized Supply Chain Codes ......................................... 89

E.2 The URL for Coordinated Supply Chain Codes ........................................... 89

E.3 The URL for Centralized Supply Chain Codes ............................................. 89

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LIST OF FIGURES

Figure 3.1: Transactions in Decentralized Supply Chain ........................................... 26

Figure 3.2: Transactions in the Coordinated Supply Chain ........................................ 26

Figure 4.1: Mean of The Retailer's Total Profit .......................................................... 49

Figure 4.2: Mean of The Distributor's Total Profit ..................................................... 50

Figure 4.3: Mean of The Retailer’s Total Profit under Distributor’s LIFO Policy..... 52

Figure 4.4: Mean of The Distributor’s Total Profit under Distributor’s LIFO Policy .................................................................................................................... 52

Figure 4.5: Total Profit of Centralized Supply Chain under the Distributor’s LIFO ..................................................................................................................... 54

Figure 4.6: Retailer’s Sales Volume Comparison when Q1=250 ............................... 58




Figure 4.10: Retailer’s Waste Volume Comparison when Q1=250 ........................... 60




Figure 4.14: Retailer’s Lost Sales Volume when Q1=250 ......................................... 62




Figure 4.18: Retailer’s Average Remaining Shelf Life when Q1=250 ...................... 64



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ix

LIST OF TABLES

Table 4.1: Unit Prices and Costs for the Objective Functions .................................... 48

Table 4.2: Constraints and Other Numerical Values for Experiments ....................... 48

Table 4.3: Buy-Back Contract Ratio under ( 21,QQ ) is (300,300) .............................. 53

Table 4.4: Supply Chain Mean Profit Comparison by the Distributor’ Issuing Policies .................................................................................................................. 55

Table 4.5: Distributor’s Mean Profit Comparison by Its Issuing Policies .................. 56

Table 4.6: Retailer’s Mean Profit Comparison by Distributor’s Issuing Policies ...... 57

x

ACKNOWLEDGEMENTS

At this moment of completing my thesis, I would like to give thanks to people. In

the first place, I would like to express the deepest appreciation to Dr. Griffin, my great

adviser. His taking care of me, and his patience encouraged me to keep doing research

and finally complete this work. In addition, his great advice and profound insight

inspired me to have fresh perspective on supply chain coordination. Without his

guidance and persistent help, this thesis would not have been possible. I also would like

to thank to Dr. Ventura, who gladly gave his time and energy for detailed reviewing and

feedback. With his help, this thesis became perfect with no error.

I thank to my family members in Korea, my father, mother, and the younger

brother. I do appreciate your all supports, especially your consistent praying for me, and

being the model to show what it is like living as a faithful Christian.

Finally, I would like to give all my appreciation to the Lord in Heaven. Though

others would say that it is all about coincidence, I cannot help but confessing it is God's

grace and providence that have guided me until now. God worked before me and gave

me abundant grace more than I was deserved. The Lord was always with me and saved

me when I was in desperate. What is more, He inspired me to see such an amazing

research topics, and prepared all these great people to meet. God is our refuge and

strength, an ever-present help in trouble. (Psalms 46:1)

Chapter 1

INTRODUCTION

“How many to order, when to order, and how to deliver it”. These three issues

are some of the most challenging but essential answers for supply chain managers. For

distributors and retailers, these questions are significant as they are directly related with

the level of service, operating costs, and profit. A large amount of research has been

conducted in order to find an optimal solution for a wide variety of environments, and in

order to better satisfy customer demand. Much of this research has focused on

optimization of individual components of a supply chain rather than the entire supply

chain system. However, as market competition has increased, industry requires that

every party in a supply chain works in a partnership.

Ideally, a company should operate as an integrated supply chain. In such a case, a

single decision maker chooses the best decision that yields the highest profit for the

whole supply chain. For example, Wal-Mart integrates all processes from procurement to

retailing activities. The result is that they take advantage of cost savings from internal

transactions. (Simchi-Levi, 2003) Dell’s innovative ways of customer sales is another

exemplary case. It reduces distributing and retailing activities for personal computer

production by taking orders directly from customers via phone calls or through their

website. Dell, therefore, does not hold assembled product inventory. On the other hand,

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most conventional PC manufacturers still have independent distributors and retailers that

place orders and hold inventory to manage customer demand. (Magretta, 1998)

Although business executives are already aware of the significance of centralized

supply chain, it is not easy organizing a centralized supply chain in practice for several

reasons. First, it requires not only an extensive amount of investment for purchasing, but

also for after-buying activities including HR training and re-shaping of the supply chain

stream. (ARM research, 2008) In addition, antitrust law in the U.S. prohibits vertical

integration in some industries. As a result, many companies operate as a decentralized

supply chain. (Froeb, 2004)

There is a recent research trend that focuses on finding methods to act as

autonomous distributors and retailers towards the direction that global optimization

suggests. This is called supply chain coordination, where all stages of a supply chain

collaborate often through incentives or other contracting mechanisms for maximizing

total supply chain profitability. (Chopra, 2007) While some research advocates

information sharing as a means to facilitate coordination, it is often not practical due to

the combination of the characteristic of relationship among supply chain entities and the

characteristic of information. As many experts including Lee (1997) mention, distrust

among supply chain members is the biggest obstacle for information sharing

implementation. As an alternative, the coordination with financial incentives has been

emerged as a means of supply chain coordination. Financial incentive motivates buyers

to change “voluntarily” their conventional decisions to perform closer to that of a

centralized supply chain. Three conditions need to be satisfied in order for the incentives

to work in practice: 1) incentives should motivate the buyer to order the “correct”

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quantity, 2) the incentive provider should have at least the same level of profit under the

new decision (i.e., should be Pareto improving), 3) the total supply chain profit should

strictly increase over the decentralized case. Three incentive types will be studied in this

thesis; quantity discount, revenue sharing, and buy-back contract.

Quantity discounts may be the simplest type of incentive. It works by offering a

lower unit price for larger order sizes. This motivates buyers to increase the order

quantity. However, there are some obstacles that prevent it from being widely practiced.

One is that there can at times be legal issues if too severe discount is given so that it

violates fair trade regulations. Another is the reaction of competitors that they would be

likely to offer similar discount program which can ultimately hurt the profitability of both

parties. (Monahan, 1984)

Revenue sharing works differently from the quantity discount. In this case, the

seller sells a product at a discount price in the exchange for a certain portion of the

revenue that the buyer generates from the item sold to customers. There are three major

problems in implementation. First, it is not attractive for competing retailers in the same

market. Second, it needs a fair method to monitor the sales operations of the retailers.

Finally, it has limited effectiveness when retailer’s costly activity affects retailer demand

such as promotions by the retailer.

Under the buy-back contract, suppliers buy unsold items from retailers at a certain

ratio of the wholesale price. As Pasternack (1985) shows, the most efficient structure is a

subsidy on a partial unit of total unsold goods at a partial ratio of the distributor’s price.

This allows for risk sharing between the distributor and retailer that lead to an increase in

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order quantity by the retailer. In practice, several industries, such as clothing and

publishing, use this type of incentive. (Chopra, 2007)

Different from non-perishable goods, perishable products need a special attention

in the inventory management as they keep aging and unsold ones are spoiled on the

expiration date with little or no salvage value. In this sense, suppliers have to decide

another factor that in what order they have to dispatch products to buyers. There are two

widely used inventory issuing policies; FIFO (First-In-First-Out) and LIFO (Last-In-

First-Out). In FIFO, inventories are issued to the buyer from the oldest, and they have

almost same period held waiting to be sold. Due to this, it also provides almost equal

opportunities for all items to be dispatched, and have similar inventory holding cost per

unit. In contrast, LIFO gives higher priority to the youngest products to be delivered to

the buyers, so products have fewer opportunities to be purchased as they are getting aged.

This contributes to unequal stored days of inventory and thus it is complicated to

calculate inventory holding cost in a brief way. While FIFO has more reasons to be used

as mentioned above, LIFO has an advantage in a case where prices are differentiated

according to the age of products. In this case, the supplier can take advantage by selling

younger products first for getting extra benefit, while there is a risk that this policy would

produce more wastes because items have fewer opportunities to be sold as aging

continues. However, these issuing policies have been viewed only for a single entity

optimization, and it is better worthy to widen the perspective to examine that how such

issuing polices from an upper stream entity would have an impact on the retailer and the

whole supply chain.

5

In this thesis, we will deal with a perishable goods supply chain with made of

single distributor and retailer, with positive leadtimes, and limited inventory capacities.

Under this setting, we will examine two topics; 1) the feasibility of the buy-back contract

where entities use continuously review their inventories 2) the impact of distributor’s

issuing policies on the profitability of the retailer and the whole supply chain. And the

layout of the thesis will be as follows. In Chapter 2, relevant work will be reviewed

including perishable inventory policy models with continuous review policy, impact of

the issuing policy on supply chain management, and supply chain coordination focusing

on buy-back contracts. In Chapter 3 model notation and formulations will be presented

for the both perishable coordination feasibility and issuing policy performance analysis.

Chapter 4 will present detailed experiments settings and then observation and analysis.

Finally, Chapter 5 will conclude the thesis providing a summary as well as suggestions

further research.

Chapter 2

LITERATURE REVIEW

In this chapter, we review research under the following categories; 1) optimal

inventory policies for perishable products, 2) supply chain coordination, and 3) optimal

inventory issuing policies for supply chains.

2.1 Optimal Inventory Policy for Perishable Products

Good inventory models for perishable goods are rather difficult to develop due to

the limited life time and aging of the product. Limited product’s life constrains the time

period over which products can be sold at full price. Those products that do not meet this

constraint will “spoil” with little or no salvage value. In some cases, additional waste

handling cost is occurred for outdated products. From a computational perspective, we

are required to keep track of items according to their shelf lives, resulting in numerical

and computational difficulties. Due to the complexities of perishable products, most of

the previous works make the assumption of periodic review rather than continuous

review due to the convenience of modeling and computation. An extensive work has

been done for periodic inventory review policy by Wagner(1958) and Veinott(1960) with

deterministic demand, and by Nahmias(1974, 1975a) and Friedman (1978) for random

7

demand, while there is a comparably small amount of research for continuous inventory

review policy developed by Nahmias(1982), Schmidt (1985), and Liu (1999)

2.1.1 Periodic Inventory Review

Arrow et al.(1958) set the life time of the product as a single time. Their study

shows that finding an optimal order size of a retailer is the same as searching an optimal

order policy for a series of simple newsvendor problems. Zyl (1964) finds an optimal

policy for a retailer with a two-period life time product. With unit order cost and unit

shortage cost, the condition is analyzed under which the expected cost of one period time

is minimized. This study also shows that if the starting level of one period old stock

increases only one unit, the optimal order quantity will decrease by less than one full unit.

Based on this, Nahmias(1974) also derives an optimal policy when the product life time

is exactly two with unit outdating and shortage cost. Therefore, the optimal order

quantity is less than that in the case of non-perishable goods.

Fries(1975) and Nahmias(1975a) are the first two researchers who extend life

time of a product into multi periods based on Zyl’s two period life time above. They

respectively set up the formulation as a cost-minimizing dynamic program with outdating

and shortage unit cost. The result is that the optimal policy is not fixed and dependent on

the age distribution of inventory. Though each work has different approaches in

modeling expected cost, it is shown that these two works have a different perspective in

analysis on the same phenomenon. Fries’s objective function is made of three parts;

ordering cost, holding and shortage cost function, and expected outdating cost of current

8

inventory. On the other hand, Nahmias’s one time expected cost function appears to

diverge from Fries’s since he uses an outdating cost of replenished products instead of an

expected outdating cost of current inventory as in Fries. However, it is shown by

Nahmias that the objective functions are consequentially equal. However, due to the

computational complexity from exponentially growing state space, some models aim to

find approximate quantity for the optimal policy, including Nahmias(1975b),

Cohen(1976), and Chazan and Gal (1977).

2.1.2 Continuous Inventory Review

Unlike the periodic review policy, defining an appropriate period can be

challenging under continuous review. Because of this, many researches set up an

objective to seek an optimal cost or profit for long term, not a single period, shown in

works by Weiss (1980), Schmidt and Nahmias (1985), and Liu and Lian (1999). In

addition to this, the limited product life complicates the inventory policy.

Weiss (1980) is credited to be the first to explore optimal inventory policy under

continuous review. Under zero lead time and instantaneous replenishment, the objective

is to issue items in order to achieve the optimal expected long term average cost. In

addition, the cost function incorporates fixed costs charged at every order. With the

backlogging and lost sales models, Weiss’ study shows that an optimal policy exists and

is unique.

Schmidt and Nahmias (1985) extend Weiss’s (1980) work by allowing a positive

lead time. For this order policy, they adopted (s-1, S) which places orders whenever

9

items are sold regardless of the amount. Viewing this problem as queuing problem with

impatient customers, they use a Markovian process for describing demand. Ravichandra

(1993) extends this study with an (s,S) order policy and positive random lead time.

Though the model is complex, the research shows through a numerical study that newly

replenished items begin aging after total depletion of the current inventory. Finally, Liu

and Lian(1999) prove that a tractable model can be built under continuous review policy.

Allowing back ordering, they adopted Markov renewal process, and derived a closed-

form solution for the steady state probability distribution of the inventory level. From the

analysis, they show that the optimal s and S can be easily computed, and the new policy

is also optimal for models with general renewal demand processes. Therefore, (s,S) is an

effective tool for perishable inventory systems as well.

As competition is getting severe in markets, inventory management is getting

more attention as one the enablers for sufficient service level as well as for the success.

Many industry-leading companies have innovate their supply chain in order to lower

inventory level while maintaining or improving customer service level, so as to keep a

competitive edge in a market. For example, AMD, a renowned CPU manufacturer

competing with Intel head to head, continuously focuses on supply chain in order to

achieve higher level of customer service and lower levels of inventory. Deere &

Company, which is one of the leading companies in agricultural and construction

machineries, implemented an optimization project on the whole supply chain of

Commercial & Consumer Equipment Division. Concentrating on finding the optimal

inventory levels, the company saves more than $1 billion by reducing inventor while

maintaining customer service level at 90 percent or better. (Chopra, 2007) What is more,

10

continuous review is a dominant inventory review policy in industries providing high

responsiveness for customer demand as it thoroughly observes the demand and its

inventory level. In spite of these advantages, continuous review strategies for a perishable

supply chain proves challenging and provides significant opportunities for future

research.

2.2 Supply Chain Coordination

While supply chain management is aimed at improving overall profitability and

efficiency, a great deal of research has focused on the individual’s improvement rather

than the improvement for the entire supply chain. It is not that hard to observe that an

individual’s myopic optimizing behaviors in the decentralized supply chain limit

performance as compared to strategies that consider the whole supply chain. In Lee’s

study (1997), he observes the Bullwhip effect in which an individual’s local optimizing

decision would bring a severe damage to the other partners with excessive inventory or

lost sales.

Therefore, supply chain coordination has received a great deal of attention as one

of the significant means to bring higher individual profit as well as that of the whole

supply chain. The basic concept is that a well designed contract motivates the buyers to

increase the order quantity, so that all individuals in the system will attain improved

operations performances under the agreement. The key issue to overcome is that the

buyer has to take the downside risk of carrying larger inventory quantities with additional

11

costs, including inventory holding and shipping costs. However, extensive research has

shown that this issue can be overcome with well designed contract schedules.

Thomas and Griffin (1996) review previous work on the supply chain

coordination and set up classification categories. They define three categories for

operational coordination according to interfaces within the supply chain; buyer-vendor,

production-distribution, and inventory-distribution. Also, they classify strategy decision

supporting models into three; methodological work, case study, and discussion. Many

complex modeling strategies such as mixed integer programming, have became practical

for driving numerical results due to decomposition algorithms and rapid-growing

computational efficiency. They also pointed out some unresolved issues from previous

research and as well as future opportunities.

Cachon (2001) reviews and summarizes extensive research on newsvendor

models with contracts. In this study, he categorized these agreements into several types

and introduced basic models for each type. Showing the fact that general wholesaler

price contract is not sufficient for initiating supply chain coordination, he suggests

several types of contract models that can be implemented in many cases. Among a

variety of contract terms, the two most frequently applied terms are revenue sharing, and

buy-back contracts. In addition, quantity discounts are also reviewed.

2.2.1 Quantity Discount

A quantity discount is offered from a supplier to a buyer to incentivize the buy to

purchase a higher order quantity. This type of contract is not always coordinating,

12

however. Weng (1995) incorporates a franchise fee in the quantity discount mechanism.

He considers the two perspectives: i) operating cost as a function of order quantities but

treating demand as a fixed constant, and ii) demand as a function of price while treating

operation costs as constant. The conclusion is that a fixed amount should be transferred

from the retailer to the supplier per period in addition to the wholesale price in order to

maximize joint profit of the supplier and the retailer.

Another concern about practicing the discount schedule is that buyers tend to stick

to their order size and do not easily increase order quantity worrying that the additional

order quantity would not bring any profit but extra costs, and many researches which

proved that the quantity discount schedule brings profit to a buyer by including operating

costs in its’ expected profit function in works by Lee and Rosenblatt (1986), Banerjee

(1986), Goyal (1988). Among them, Shin and Benton (2007) derive an all unit discount

model between a single buyer and a supplier. Named as buyer’s Risk Adjustment (B-

RA) model, the objective of the model is to increase both the supplier’s and buyer’s

profitability without changing the basis of both parties’ economic lot sizes. In addition to

this, the model shows that it also functions as a safety net for the buyer in the case of

overstocking under stochastic customer demand

2.2.2 Revenue Sharing

Revenue sharing is a revenue allocating contract between buyers and suppliers

based on the volume sold to the retailer’s customers. In order to have more titles on the

shelves in the debut time of a new movie, Blockbuster first came up with the idea on the

13

new contract term under the company agreed to pay its suppliers a portion of its rental

income in exchange for a reduction in the initial price per tape. This phenomenon

motivated Cachon and Lariviere (2005) to develop a refined revenue sharing model.

Assuming that the retailer price is fixed, they proved that revenue sharing is also effective

for the coordinating between the supplier and the buyer. Further, a single revenue

sharing contract can coordinate a supply chain with multiple noncompeting retailers even

if the retailers have different demand functions. For the contract term, sets of wholesaler

price and revenue sharing ratio are found for optimal supply chain coordination.

However, some limitations exist in adopting the revenue sharing into practice. First, it

does not coordinate retailers in a competing market as each retailer’s revenue depends on

its quantity, price, and the actions of the other retailers. For this, Berstein and

Federgruen’s (2005) adopt to a nonlinear price-discount contract and show that it is

effective in coordinating supply chain. Second is the administrative cost on the two

parties since a system is required for auditing the retailer’s revenues for the correct

amount of money to share. Finally, the retailer’s promotion activity can distort market

demands when there is no contract for the promotion support between the two.

2.2.3 Buy-Back

Buy-back is another form of contracts designed to motivate a buyer to increase

order quantity. Under the mutual contract, a supplier agrees to buy the unsold quantities

from retailer(s) at a pre-established price and quantity. The buy-back price should be set

higher than the salvage value, from which a supplier could make extra benefit by selling

14

it to second-hand market. Some studies uses return policy which basically referring the

same contract with a different title. In this thesis, buyback is the only term describing the

contact offering a subsidy for the leftover items at supply chain downstream.

Pasternack (1985) assumes a supply chain composed of a single vendor and a

buyer, one type of perishable goods whose salvage value is positive. Under these

assumptions, he derives a condition where the supply chain is coordinated. After

studying several return polices, he makes the conclusion that the optimal return policy is

supplier’s all unit acceptance at a partial wholesaler price, while full credit for all unsold

goods or partial credit for limited goods are achieving sub optimal. Furthermore, the

optimal return allowance is a function of retailer demand, which means that this optimal

function cannot be applied in models with multiple retailers. Lariviere (1999) shows that

the optimal contract quantity and price is independent of the customer demand

distribution. It is a significant problem from a managerial perspective, to assume that a

rational agent who is willing to accept a transaction even though one is unable to estimate

her expected profits from the deal.

Granot and Yin (2005) extend Paskternack’s work by adopting two types of price

dependent demand functions. They study the impact of the salvage value on the optimal

buy-back policy and find that a zero salvage value does not contribute to supply chain

coordination as much as it increases the manufacturer’s profit while hurting retailer’s

profit. However, when the salvage value is positive, it is observed that it brings a

significant effect on the buyback contract by improving the retailer’s and supplier’s profit

at the same time.

15

Recently, Wang and Zipkin (2009) extend a two-stage buy-back contract with

perishables by adding an “agent” for both the distributor and retailer. The agents are

compensated based on certain performance measures, and they act accordingly. The

study covers the impact of their behavior in both the supplier-as-leader and retailer-as-

leader settings. The analysis shows that channel stuffing takes place under both scenarios

showing more frequent under retailer-as-leader one. They conclude that incentives for

the agents are required to be carefully set in order to align them with the firm’s profit, in

order to avoid decisions that lead to a sub-optimal profit level.

One interesting note is that operation researchers and marketing researchers tend

to have differing perspectives with regards to customer demand and costs for supply

chain coordination. Operations researchers tend to assume that total cost are a function

that includes factors such as inventory, ordering, spoilage, etc. Marketing experts tend to

consider the whole cost as a one with constant margin or even a constant. Further,

operations researchers tend to assume that customer demand is according to stochastic

form. However, marketing researchers prefer to use real customer data from empirical

studies.

2.3 Optimal Inventory Issuing Policy

The optimal issuing policy of a distributor builds on multi-echelon supply chain

optimization and the conventional inventory issuing policy of First-In-First-Out (FIFO)

or Last-In-First-Out (LIFO). These two areas have much more contrasts than similarities.

16

Multi-echelon studies have focused on optimal allocation of a product with a single

distributor and multiple retailers. This decision making model sees the distributor as the

core in the supply chain whose decision would bring the optimal performance to the

distributor itself as well as to the whole supply chain. On the other hand, analyses of the

conventional issuing policy most consider a retailer who is facing customer demand. By

nature, the focus is rather myopic as the retailer’s optimality is the only concern under

some constraints. However, we also see a common idea preserved in both studies. Both

consider the age of the products in the inventory and view the shelf life as a significant

factor giving an impact on the profitability. In this chapter, research on multi-echelon

perishable inventory management and LIFO perishable inventory issuing are discussed

respectively in order.

2.3.1 Multi-Echelon Perishable Inventory

While there has been extensive research on two- or multi-echelon supply chains

with non-perishable products, relatively few works have been done with perishable

products. A majority of research with perishables has been made with item allocation

policies in order to satisfy the retailers’ demands efficiently. One thing that makes the

perishable echelon system complicated is that we have to consider inventories with

different ages. Therefore, the allocation problem has to also include how to distribute a

distributor’s stocks to retailers according to shelf lives of the products on hand. With

regards to specific issuing policy of a distributor, most of previous research develops the

17

optimal issuing policy for the perishable commodity considering shelf life of products in

the inventory.

Yen (1965) examines a two-echelon inventory model for perishables where

facilities at both echelons follow critical ordering policies. In his model, orders are

always satisfied and costs include shortage and outdating. He establishes conditions

where costs are convex with respect to the critical policy. He also establishes conditions

were a proportional allocation policy is optimal. In this case, an order form a retailer is

satisfied with inventory form each age category that is proportional to the fraction of total

orders represented by the facility’s order quantity.

Yen’s work is extended by Cohen et al.(1979) who compare the proportional

policy to a fixed fractional policy. The fixed fractional policy calls for the order to be

satisfied using a fixed fraction of inventory from each age category. The fixed fractional

policy enables proportional allocation among multiple retailers so that the designated one

may receive a larger or smaller share of fresher stock. They derive optimal, stationary

policies for the supplier operating under each allocation rule and specify conditions in

which they are identical.

Motivated by the blood bank management problem, Goh et.al. (1993) derive an

approach for dealing with different ages of item inventory. The first stage contains

inventory of fresh units and the second stage holds older, but still usable units. And

goods are issued from the first stage to the second stage. The issuing quantity to the

second stage is automatically determined by the age of the blood from the first stage.

Both supply chain withdrawals of inventory are assumed to occur randomly. The

demand specifies whether it must be satisfied with fresh units or if older units are

18

acceptable. The authors consider two two-stage FIFO policies: restricted and

unrestricted. In the restricted case, the request for older items can only be satisfied by

items in the second state. In the unrestricted case, request from older items can be

satisfied by items in the first stage, but only when there is no inventory in the second

stage. Results indicate that unless it is important to minimize the shortage of fresh units,

the unrestricted policy is better.

Fujiwara et.al. (1997) extend the two stage perishable inventory model with sub-

product problems. Finding an optimal ordering and issuing policy for a meat department

at a large grocery store, the fist state is considered to have a whole product that will be

divided into multiple sub-products. The second state is only composed of sub product

from the first state, and all demands are satisfied by sub-products at stage two. For the

case of dissatisfied demand, an emergency order is made with extra cost by processing

sub-products from stage one. They derive the optimal ordering and issuing policies in

this two stage system.

2.3.2 LIFO Perishable Inventory Issuing Policy

After Pierskalla and Roach (1972) and other studies proving that FIFO is

generally optimal as compared to LIFO for perishable items, a relatively small number of

supply chain management researchers adopt LIFO as an issuing policy in a supply chain.

Still, accounting researchers still are interested in comparing FIFO and LIFO policies

under a variety of exogenous changes using macro economics. For the case of perishable

19

items it is somewhat different than non-perishables not only due to the holding cost but

also due to the handling cost for outdated products.

Prastacos (1979) extends his previous research for the distributor’s optimal

allocating policy under a retailer’s FIFO policy with perishables into a retailer’s LIFO

policy. He derives two distributing systems of a distributor for managing inventories at

each retailer: a rotating policy and a retention policy. The rotating policy collects back

valid items from every retailer to a central distribution center at the end of the period, and

then re-allocates goods at the beginning of the next period. Under the retention policy,

each retailer keeps the quantity received by the distributor at the beginning of every

period until it is either used or outdated. He derives an optimal and approximately

optimal allocation policy for both inventory management systems. The results are

significantly different from the case where retailers use a FIFO policy. Specifically, the

optimal allocation in LIFO depends on the unit costs, and involves a trade-off between

shortages and outdated units, while another case with FIFO is optimal only with shortage

and outdates. In addition, the optimal quantity allocation in LIFO depends on age

segregation; some retailers would receive mostly fresh products whereas other would

receive mostly old products depending on the customer distribution. Finally, the optimal

policies in LIFO are the solutions to dynamic program whose solution is not easy to

compute, however, closed form solutions exist for specific demand distributions.

Cohen and Pekelman (1979) take a unique view by applying FIFO and LIFO

policy as inventory valuation methods to see the impact on tax liability and the

profitability. One particular assumption is that it is for a single retailer facing stochastic

demand with a single perishable product. They investigate the effect of the inflation and

20

corporate tax rate on the two policies. They derive closed form expressions of the

expected profit for FIFO and LIFO respectively. LIFO inventory levels tend to be larger

than FIFO levels. In addition, the best response of LIFO to an increase in the tax rate may

be to increase inventory while under FIFO it is always optimal to reduce inventory.

Finally, LIFO inventory levels increase as the size of the initial lower price layer

increases. Based on those closed form expressions, formulations are developed on multi-

period profit for FIFO and LIFO. For FIFO, it is easy to show that the optimal policy is

the myopic policy that is the sum of the profit of each period. However, for the case of

LIFO, the optimal policy is non-myopic but is able to be approximated by taking some

error terms which is acceptable. One of the important finding from this research is that

the LIFO issuing policy can be a very attractive policy under some conditions.

Keilson and Seidmann (1990) analyze the performance of a single retailer which

faces stochastic demand. Rather than simply comparing profitability, they evaluate the

performance based on spoilage rate, mean age at delivery to the customers, expected time

between stock outs, service level, and mean on hand inventory level. With regard to

product age, it is shown that LIFO can result in a much lower age of items delivered..

The service levels of FIFO and LIFO show similar levels of satisfaction under a low

demand rate. However, FIFO achieves a higher service level as the customer demand

rate increases. Finally, FIFO brings higher profits with lower supply rates when price is

independent of the products’ ages. On the other hand, LIFO is advantageous when fresh

items are more valuable than older ones in market.

Although the perception among many is that FIFO issuing policies are always a

better choice than LIFO, several studies have shown that LIFO can also useful. Such

21

analysis on the issuing policy of a retailer is meaningful, in that we can watch how the

customer demands are satisfied in the near future. However, there is a weakness on

analyzing the policy in that it is myopic by concentrating on a single relationship between

a retailer and customer. As it is more common that an item is supplied through a supply

chain with multiple layers of merchants, an issuing policy upstream would have an

impact on perishable items because the valid life is fixed and is getting shorter after the

production little by little. As a result, it is necessary to consider an approach to combine

issuing policy in a supply chain with the supplying hierarchy.

In this sense, multi echelon optimal policy modeling and LIFO issuing policy

analysis for perishable commodities offers a firm basis for developing an experiment on

multi-echelon supply chains with changing customer demands. As mentioned before, it

is not usual that multi-echelon supply chain models consider volatile customer demand or

consider end-to-end efficiency of a supply chain. In contrast, a retailer’s issuing policy

comparison merely pays attention to the end of the value chain while giving assumptions

on the supplier’s activities. As a consequence, connecting these two individual interests

in the supply chain will bring a broader scope for observing the multi-echelon supply

chain. Furthermore, contracts in supply chains such as buy-back agreements, gives an

actual motive for the supplier and retailer to cooperate as a team to satisfy the customer

demand. An analysis is needed that scrutinizes the decentralized perishable goods

supply chain to see the impact of distributor’s issuing policy on the individual members

as well as on the whole supply chain.

Chapter 3

SUPPLY CHAIN MODELING

3.1 Modeling Introduction

In this thesis, we study an independent distributor-retailer perishable supply chain

with the continuous review policy and leadtime. First, we investigate the feasibility and

effectiveness of the buy-back contract between the distributor and retailer. Specifically,

we find the optimal order quantity of an independent retailer and the distributor and using

a buy-back contract respectively. In addition, the effectiveness of coordination is

evaluated by comparing the decisions under the contract to the one from centralized

supply chain to determine how much coordinating mechanism enables the supply chain

profits. We also study the impact of the issuing policy of the distributor on the retailer

for a decentralized perishable supply chain. For this, we compare the profitability of the

retailer under two different policies, FIFO and LIFO, with a variety combination of order

quantities of the distributor and retailer.

We make several assumptions about the supply chain. First, the retailer and the

distributor do not share customer demand information, so that the retailer’s ordering is

the only information for the distributor to estimate actual customer demand. Second, we

assume that both retailer and distributor are given a leadtime for distribution. Most of the

23

previous studies on perishable products assume instantaneous replenishment, so that in-

transit-inventory or re-ordering points are not necessary. In this study, in transit

inventory must be considered. Third, we assume that the product begins aging at a

constant rate as soon as it is shipped into the distributor’s inventory. Finally, unsatisfied

demand is considered to be lost with penalty rather than backlogged. Detailed

assumptions follow for the retailer and distributor.

3.1.1 Retailer

The retailer is the only component of the supply chain that faces customer

demand. Fulfillment is accomplished by depleting on hand inventory in every time

period t. Because items have age until the end of their shelf lives, they get their

remaining shelf lives deducted as every time period passes one by one. At the same time,

the retailer receives the delivery from the distributor. Upon arrival, the incoming

inventory is categorized and shelved according to the remaining shelf life. Due to the

limited inventory storage of the retailer, overflow may occur. In this case, the oldest

inventory is removed in order to make space for the incoming product. For sales, the

retailer uses FIFO or the policy that let the older items to be sold first. All non-expired

items are sold at the same price regardless of age. If total demand is not satisfied during

a period, it is considered as lost sales and charged at a unit penalty. At the end of every

period, items whose shelf life is equal to one are discarded at a unit waste handling cost.

This quantity is recorded as per terms of the buy-back contract with the distributor.

Since the retailer uses the continuous review inventory policy, it always checks the

24

inventory level to see if the total amount left falls below the trigger point. If the ending

inventory is less than the safety stock level or the reorder point, then the retailer places an

order with pre-determined quantity.

3.1.2 Distributor

The distributor is the only source for bringing products to the supply chain. Since

there is only one retailer, the distributor does not determine how to allocate recourses

across retailers, but decides in what order to issue on-hand inventory. We adopt two

widely used issuing strategies, FIFO (First In First Out) and LIFO (Last In First Out). At

the beginning of period t, all perishable goods at the facility age by one just as occurs at

retailer, resulting in a reduced shelf life by one. Simultaneously, new items arrive that

are the freshest product in the whole supply chain. If overflow takes place, the needed

amount is selected on the basis on FIFO, and then thrown away at unit waste handling

cost. For sales, the distributor takes out commodities according to FIFO or LIFO so as to

fulfill the order placed at the end of the previous period (t-1) by the retailer. Any

unsatisfied order quantities are considered to be lost sales and charged with a penalty, and

no emergency order is made to fulfill the lost sales. The shipped items also age during

transportation at the constant rate. After sales, the distributor collects items whose shelf

lives are equal or less than the leadtime of the retailer. This is to prevent outdated

product from being sold or shipped. Because the distributor also uses the continuous

review policy, it monitors the total amount of the items left and uses a reorder point to

determine whether or not to place an order.

25

3.1.3 Types of the Supply Chains

One of the purposes of the study is to show the effectiveness of the buy-back

contract in coordinating a supply chain. In this study, we set up two additional supply

chains for comparison: a decentralized supply chain without coordination and a

centralized supply chain. We need the first case in order to investigate how much

improvement the coordination brings comparing to the conventional supply chain, i.e.,

one where a supplier and buyer makes local decisions by pursuing independent profit

maximization .

By contrast, coordination in a supply chain is designed to motivate cooperation

between the independent supplier and buyer in a decentralized supply chain in a way that

brings better results for the whole chain as well as for each individual. This is typically

done through the use of a contract where the distributor and retailer make their own

decisions in order to maximize individual profit. A common question is how close the

resulting cooperation is to a centralized supply chain. In order to answer to this question,

we will compare the results of from decentralized supply chain under a buyback policy

contract with a centralized one. However, a centralized supply chain is hard to

implement in practice due to financial burden for acquiring or merging a business unit,

managerial problems in integrating a new organization, and potential problems with anti-

trust law. However, as teamwork is given more emphasis in a competitive environment,

distributors and retailers also seek profitability for the total supply chain. In this research,

we choose the buy-back contract as a tool in coordinating the distributor and the retailer

in the supply chain because it is relatively simple to implement.

26

A transaction in a supply chain includes two types of flow; products and funds.

Figure 3.1 shows two flows between the distributor and the retailer in decentralized

supply chain where a simple transaction takes place. As seen from the Figure 3.1, each

flow goes in only one direction from one to the other. However, buy-back contract has

modified flows.

In Figure 3.2, a new fund transfer flow shows up from the distributor to the

retailer in the supply chain while shipments and payment flow remain the same as that of

decentralized supply chain. This new flow comes from the buy-back contract.

Figure 3.1: Transactions in Decentralized Supply Chain

Figure 3.2: Transactions in the Coordinated Supply Chain

27

3.2 Sets and Notations

3.2.1 Sets

Let T be the set for time period or day in the supply chain,

T = { 1, 2, … }

whose elements increase by one as each day passes. During every time t, each

transaction, shipment, and sales take place.

In order to denote facilities, let N be the sets for the individuals in the supply

chain.

N = { 0, 1, 2, 3 }

where 0, 1, 2, 3 represents the manufacturer, distributor, retailer, and customer

group, respectively.

Let SL be the set for remaining shelf life of the products.

SL = { SL_max, …, 2,1 }

SL descends from its maximum age of SL_max to 1. When SL reaches one at the

end of the time t while in the retailer’s inventory, it is considered expired.

3.2.2 Notation for the Inventory Operations

A function is needed to track the decaying product. Let nLT denote the leadtime

of n, which represents the time between placing an order and receiving it. Further

explanation will be given in the constraint description below.

28

Let sltnB ,, the amount of inventory at the inventory facility n, at the beginning of

time t, and whose remaining shelf life is sl. In considering the inventory in a two- or

multi-echelon supply chain, we define two kinds of inventories; on-hand inventory and

inbound inventory. As all products in the supply chain are losing remaining shelf life, we

can formulate this by adopting the following formula by Weiss (1982)

1,1,,, +−= sltnsltn BB

In addition, we also have to consider incoming inventories that were discharged

from facility (n-1) at 1−nLT , and stocked at facility n in the beginning of time t. We

therefore have

nn LTslLTnsltn SB +−= ,,1..

By aggregating both on-hand and inbound inventories, we can describe each batch

at place n at the beginning of time t

sltnB .. = 1,1, +− sltnB +nn LTslLTnS +− ,,1

Also, we can also calculatetnI , , the total beginning inventory at facility n, by

summing together all batches.

∑=sl

sltntn BI ,,,.

29

3.2.3 Notation for Inventory Issuing Process

The issuing policy is one of the significant comparison factors in this study, as it

determines the order of a products’ shelf life in sales. As mentioned before, we compare

the most commonly practiced inventory issuing policy, FIFO and LIFO.

Let tn,δ be the binary variable which equals to one when facility n places an order

nQ at the end of time t, and equals zero otherwise. The inventory issuing process is

initiated by an attempt to fulfill the order from the downstream demand 1,11 −++ ⋅ tnnQ δ or tD

in the case of the retailer customer demand. If the on-hand inventory is enough to satisfy

demand ( 1,11 −++ ⋅ tnnQ δ ) or tD , then the seller satisfies the order by shipping the quantity

requested. If any products remain whose remaining shelf life is one, they are to be

discarded at the appropriate handling cost because they do not have market value. On the

other hand, if demand exceeds the on-hand inventory, the upstream seller ships all

available products to the downstream, recording lost sales ( tntnn IQ ,1,11 −⋅ −++ δ ) for the

unfulfilled amount of the order. In order to simplify the notation for ordering, let tnO , be

the order or demand amount from place n at time t. Also, let tnS , be the amount of

supplies from facility n to n+1 at time t, which is made of available items in inventory.

As supplier n is not allowed to provide more quantity than asked for or than is present in

stock, the following expression holds.

),min( ,,, tntntn IOS =

Shipment tnS , is closely related to batches in that the inventory is composed of

products in all batches, and the products are actually dispatched from them according the

30

order imposed by the issuing policy. The batch dispatching models are described for

FIFO and LIFO respectively.

After sales, each location may have lost sales or perished units. Let tnL , be the

lost sales unit at place n at the end of time t. Also, let tnW , be the measurement for the

waste at place n at the end of time t.

3.2.4 Issuing Policies and Dispatching Models

As products in inventory have an opposite priority to those deployed according to

the issuing policies, we need to develop formulas to calculate the wasted amount and lost

opportunities for sales for each policy respectively.

3.2.4.1 FIFO Issuing Policy

In FIFO, products in older batches receive a higher priority to be sold to the

downstream buyer. As backlogging is not allowed according to the assumptions, the

supplier is allowed to fulfill the order 1,1 −+ tnO up to the on-hand inventory at the

beginning of time t, tnI , . For the case when the order quantity is less than the on-hand

inventory the seller n satisfies an order by picking up products from the batch in

ascending order of remaining shelf life.

∑=

=max_

1,,,

SL

slsltntn BS

31

If the order quantity 1,1 −+ tnO is smaller than tnI , , products are discarded with a

waste handling cost whose remaining shelf life equals to one.

tnshtntn SBW ,1,,, −= =

On the other hand, insufficient inventory leads to lost sales with penalty whose

amount is

tntntn IOL ,1,1, −= −+

3.2.4.2 LIFO Issuing Policy

In LIFO, products in younger batches are given a higher priority for dispatch to

the downstream buyer. Just as in FIFO, the supplier is allowed to fulfill the order

1.1 −+ tnO up to the on-hand inventory at the beginning of time t or tnI , , due to the

assumption of no backlogging. In the case when the order quantity is less than the on-

hand inventory ( 1,1, −+> tntn OI ), the seller n satisfies the order by selecting products from

the batch in descending order of the remaining shelf life. That is

∑=

=1

max_,,,

SLslsltntn BS

One distinct fact from FIFO issuing policy is that LIFO yields wastes whenever

product amount in the inventory exceeds order quantity or 1,1, −+> tntn OI , because products

about to expire have the lowest priority to be sold. In this sense, once it is recognized

that the total amount of the inventory at n exceeds the ordered quantity from n-1, then it

is certain that facility n will have excess. This wasted amount is determined as follows.

32

tntnshtntn SIBW ,,1,,, ,min( −= =

Just as with FIFO, insufficient inventory leads to lost sales which is calculated as

tntntn IOL ,1,1, −= −+

3.3 Constraints

Two explicit constraints are imposed on the supply chain; finite inventory

capacities of each facility and service levels for both facilities. These two requirements

work in a conflicting way in that limited inventory capacity limits the order quantities

while the service level satisfaction leads to increases in the quantities in order to satisfy

demand from downstream. We describe the characteristic and numerical value of the two

conditions.

3.3.1 Inventory Capacity ( nIC )

Inventory capacity of the facility n or nIC keeps the decision makers from having

an excessive amount of orders. Otherwise the residual units are discarded with a waste

handling cost. By providing an upper limit on the order quantity, it can help ensure

environmentally-friendly management by reducing the wasted amounts from the

distributor and the retailer, resulting in more efficient use of resources in the supply

chain.

33

3.3.2 Service Level ( nSL )

In a supply chain, lost sales is inevitable due to uncertain demand over delivery

leadtimes. As a result, most of the inventory decision makers set an optimal service

level. In order to decide how much of the expected demand to satisfy over the leadtime

in a supply chain, the service level of the facility n or nSL is needed in order to decide

expected demand during the leadtime. One of the factors linked to the service level is the

reorder point nR , which is used to determine the timing of placing an order of facility n

based on current inventory position. In order to meet the service level, inventory

managers typically use an inventory buffer. For the retailer, the re-order point is

calculated as below.

elServuceLev

LTi

it

ZDR ×= ∑+

=

2

22

The reorder point of the distributor needs an alternative analysis since it faces

orders with positive intervals from the retailer. It is better for the distributor to set a

reorder point which is equivalent to the order size of the retailer, so as to have at least as

much as to be ready for the single shipment to the retailer.

3.4 Constants

For the expected profit function in the objective, price, unit costs, and fixed costs

are treated as constants.

34

3.4.1 Unit Price ( nP )

We assume there is no volume discount or promotion, and so unit prices remain

the same regardless of the volume handled. We denote nP as the unit price of seller n

when it hand over the products to the buyer (n+1).

3.4.2 Unit Costs

We model three unit costs: inventory holding costs, waste handling, and lost sales

as unit costs.

3.4.2.1 Inventory Holding Cost ( nH )

Inventory Holding Cost or nH is the opportunity cost of the capital tied up in

inventories for a specific period of time at facility n. First, let nROI be the normalized

return on Investment rate required by facility n during the single time period. Then, the

inventory holding cost per a product stored at the facility n per period is calculated as

1−×= nnn PROIH

3.4.2.2 Waste Handling Cost ( nWH )

Waste Handling Cost ( nWH ) is the cost for handling each unsold unit at place n.

It is a significant factor that differentiates the perishable product supply chain from

35

others. Particularly in the case where perishables have no salvage value, it is one of the

critical factors for management as the environment protection requirements are yielding

higher standard at additional expenses. Violation of related regulations may result in a

serious damage to a company’s profitability with considerable amount of penalties and

following correction orders.

3.4.2.3 Lost Sales Cost ( nLS )

Lost Sales Cost at facility n or ( nLS ) is charged on every unsatisfied demand from player

(n+1). Though lost sales costs are not reflected to the profit loss sheet in financial

reports, it is one of the key performance indices for the operations marketing

management. It is reasonable to consider the lost sales cost as higher than the sum of the

sales price and other related costs since there is a loss of customer good will in addition

to the lost profit.

3.4.2.4 Fixed Ordering Cost ( nOC )

Fixed costs are differentiated from unit costs in that they do not increase in

proportion to the number of units. Hence, many are able to take advantage of economies

of scale for an order by distributing one time fixed costs over units ordered. As a result,

marginal fixed costs decrease as more units are ordered. In this study, we consider

ordering cost as the fixed cost which occurs by the retailer and distributor when they

place orders. It includes administrative costs, transportation cost in the case of full truck

36

load, transaction fee, and others related fixed for an order to be submitted and shipped

between a supplier and a buyer.

3.5 Decision Variables

One of the purposes of this study is to find the optimal order quantity for the

entities in the supply chain. As a result, it is one of the keys to finding the optimal order

quantities of the distributor and the retailer. Let be 1Q and 2Q the order quantity for the

distributor and the retailer respectively. We find the optimal solutions of ( 21,QQ ) for

three types of supply chains: decentralized supply chain, coordinated supply chain, and

centralized supply chain. For the case of decentralized supply chain, entities will

optimize 1Q and 2Q independently. On the other hand, a centralized supply chain will

find the combination of 1Q and 2Q that brings the highest total profit to the entire chain.

For the coordinated supply chain, some additional explanation is needed to for the

contract. In the coordinated supply chain with coordination, a transaction is made

between the distributor and the retailer at the end of every period based on the contract.

For a buy-back contract, the distributor “virtually” buys back the leftover from the

retailer at the end of every time t at a certain percentage of the distributor’s price1P . This

coordinating mechanism is strictly valid under two conditions; it improves the total profit

of the whole chain as compared to a purely decentralized on, and is Pareto Improving for

the distributor and retailer respectively. By satisfying the two conditions, a voluntary

37

agreement comes into effect between the two as Cachon (2001) suggests. In this sense,

optimization with coordination has two decision variables of order quantities and buy-

back ratio α on the distributor’s price. Increased order quantities would increase total

revenue of the supply chain, leading to higher profitability. Though it is obvious that the

distributor gets more profit from the contract, a concern may arise as the margin where

the retailer would not increase its order quantity. So, another decision variable is

necessary for the profit sharing to be executed. The coverage ratio α is the mechanism

that controls the individual profitability of the distributor and the retailer. Under the

contract, the seller pays back for the all expired units at a ratio α of the distributor’s unit

price. The optimal ratio is ranged where the retailer’s profit with the subsidy exceeds the

one without coordination, and the distributor’s profit with subsidy is still greater or equal

to the level without the contract. In summary, an effective coordination is supposed to

bring increased 1Q and 2Q than the ones without cooperation so as to yield higher profit to

the whole supply chain, and under new1Q , 2Q , and α on the distributor price should be in

the range, which guarantees Pareto improvement for the distributor and retailer

respectively.

Other than variables on order quantities, we also need a binary variable in order to

incorporate with the ordering cost. Let be the binary variable, which equals to one

when facility n places an order of nQ at the end of time t, and equal to zero when no order

is placed.

38

3.6 Objective Functions

In measuring profit, it is reasonable use a long term perspective. From the market

dynamic perspective, it is due to the fact that the market demand is changing rapidly

every time period, and a company may earn profit some times while losing money for

other times. From the perspective of modeling, aging of perishable goods complicates

finding optimal profit conditions. In addition, introducing leatime further complicates

things. As the profit for the all periods is calculated by summing up the results of every

period, we can simply calculate single period profit and sum all profits up for the whole.

3.6.1 Decentralized Supply Chain

In decentralized supply chain, the two entities are seeking individual profit

maximization without any means of cooperation. For this, we need objective functions

for the distributor and retailer respectively.

3.6.1.1 Distributor’s Objective Function

The distributor generates revenue only from transactions with the retailer,

indicating that it earns money only when the retailer places an order of 2Q . When

shipping to the retailer, it can sell as many as the order quantity from the retailer, and in

the case of insufficient inventory on hand, it ships all inventories to the retailer. As

mathematical modeling, it is written as Eq. (3.1),

39

The following parts is about total costs, which can be decomposed into four parts

of procurement, inventory holding, waste handling, and lost sales. First, procurement

cost is made up of fixed ordering cost and the unit cost purchased from a manufacturer.

The fixed ordering cost is charged to the distributor when receiving the order placed

( 1LTt − ) before. Eq. (3.2) shows how to calculate the order fixed cost.

In addition, the total unit cost for purchasing 1Q is calculated as Eq. (3.3) shows.

So, aggregating Eq. (3.2) and Eq. (3.3) produces total purchasing cost of the distributor at

time t, which is modeled as Eq. (3.4)

For inventory holding cost, we use average inventory of 2

,1 tI as the amount kept

in the storage during time t. And the inventory holding cost is calculated by multiplying

holding unit cost by the average inventory amount, which is modeled as Eq. (3.5)

Distributor’s Revenue = ),min( 1,22,11 −⋅⋅ tt QIP δ (Eq. 3.1)

Distributor’s Ordering Fixed Cost = 1,1 1OCLTt ⋅−δ (Eq. 3.2)

Distributor’s Purchasing Unit Cost = 10 QP ⋅ (Eq. 3.3)

Distributor’s Total Purchasing Cost = )( 101,1 1QPOCLTt ⋅+⋅−δ (Eq. 3.4)

Distributor’s Holding Cost = 2,1

1tI

H ⋅ (Eq. 3.5)

40

The next one is waste handling cost, which take care of expiring inventories.

With discarded amount of tW ,1 , waste handling cost is calculated as Eq. (3.6)

The last part of the costs is to compute the cost of lost sales, which is calculated

with Eq. (3.7).

In conclusion, we are able to compute single period profit function of the

distributor by aggregating all equation from Eq. (3.4) to Eq. (3.7), the multiple period

profit of the distributor is easily calculated by summing it up over t periods, as it is shown

in Eq. (3.8)

3.6.1.2 Retailer’s Objective Function

The retailer’s objective function is quite similar to that of the distributor as it has

parallel function of purchasing, sales, and operations. Only significant difference is the

revenue part, as the retailer faces end customer demand every time period. Eq. (3.9)

shows retailer’s revenue for a single period.

Distributor’s Waste Handling Cost = tWWH ,11 ⋅ (Eq. 3.6)

Distributor’s Lost Sales Cost = tLLS ,11 ⋅ (Eq. 3.7)

})

2)(((),min({(.max ,11,11

,11101,11,22,11 1∑ ⋅+⋅+⋅+⋅+⋅−⋅⋅ −−

ttt

tLTttt LLSWWH

IHQPOCQIP δδ

(Eq. 3.8)

41

Just like the distributor’s, total cost of the retailer is made up of four parts of

procurement, inventory holding, waste handling, and lost sales. First, procurement cost is

made up of fixed ordering cost and the unit cost purchased from a manufacturer. The

fixed ordering cost is charged to the distributor when receiving the order placed ( 2LTt − )

before. . Eq. (3.10) shows how to calculate the order fixed cost.

In addition, the total unit cost for purchasing 2Q is calculated as Eq. (3.11) shows.

So, aggregating Eq. (3.10) and Eq. (3.11) produces total purchasing cost of the distributor

at time t, which is modeled as Eq. (3.12)

For inventory holding cost, we use average inventory of 2

,2 tI as the amount kept

in the storage during time t. And the inventory holding cost is calculated by multiplying

holding unit cost by the average inventory amount, which is modeled as Eq. (3.13)

Retailer’s Revenue = ),min( ,22 tt DIP ⋅ (Eq. 3.9)

Retailer’s Ordering Fixed Cost = 2,2 2OCLTt ⋅−δ (Eq. 3.10)

Retailer’s Purchasing Unit Cost = 21 QP ⋅ (Eq. 3.11)

Retailer’s Total Purchasing Cost = )( 212,2 2QPOCLTt ⋅+⋅−δ (Eq. 3.12)

Retailer’s Holding Cost = 2

,22

tIH ⋅ (Eq. 3.13)

42

With discarded amount of tW ,2 , waste handling cost is calculated as Eq. (3.14)

And the cost of lost sales is calculated using Eq. (3.15).

With this part, we can set up retailer’s profit objective function for multiple

periods by assembling from Eq. (3.12) to Eq. (3.15) above. The multiple period profit of

the retailer is computed by summing it up over t periods, as it is shown in Eq. (3.16)

3.6.2 Coordinated Supply Chain

In the coordinated supply chain, the distributor and the retailer still work for

individual profit maximization. One thing different from decentralized supply chain is

that buy-back contract is introduced to the chain for coordination. This affects the

objective functions of the entities, by adding new term related to financial transactions

according to the contract. The buy-back amount is calculated as Eq. (3.17)

Retailer’s Waste Handling Cost = tWWH ,22 ⋅ (Eq. 3.14)

Retailer’s Lost Sales Cost = tLLS ,22 ⋅ (Eq. 3.15)

})

2)((),min({(.max ,22,22

,22212,2,22 21∑ ⋅+⋅+⋅+⋅+⋅−⋅ −

ttt

tLTttt LLSWWH

IHQPOCDIP δ

(Eq. 3.16)

43

This amount of money is transferred from the supplier to the buyer at the end of

time t if retailer discards products due to expiration. In consequence, they have to

recalculate for the new optimal order quantities under the modified objective functions.

3.6.2.1 Distributor’s Objective Function

Here, the distributor pays to the retailer as much as tWP ,21 ⋅⋅α , which covers α %

of the wholesale price on the expired goods at the retailer. So, it has to deduct that

amount from the objective function from centralized supply chain, while other terms

remain same. Eq. (3.18) presents the distributor’s objective function under the buy-back

contract for multiple periods.

3.6.2.2 Retailer’s Objective Function

Under the coordination, the retailer gets paid from the distributor as much as

presented in Eq. (3.17) for the perished quantities. And the retailer’s multiple period

objective function can be modeled as Eq. (3.19) which adds Eq. (3.17) to Eq. (3.16)

Buy-back Amount = tWP ,21 ⋅⋅α (Eq. 3.17)

)}))2

)(((),min({(max1

,21,11,11,1

1101,11,22,11 1∑=

−− ⋅⋅−⋅+⋅+⋅+⋅+⋅−⋅⋅t

tttt

LTttt WPLLSWWHI

HQPOCQIP αδδ

(Eq. 3.18)

44

3.6.3 Centralized Supply Chain

In the case of a centralized supply chain, the whole chain works as a single entity

for the highest profit with decision variables of 1Q .and 2Q . Thus, the distributor supplies

goods to the retailer at unit price0P , not taking margin a margin between 0P and 1P .

Retailer is the only source. This allows centralized supply chain to be districted, in that

the distributor is dedicated for purchasing and holding inventory, while the retailer only

works for sales and holding products. Thus, the distributor does not make profit from

internal transaction with the retailer.

Like other objective functions in other types of supply chain, centralized chain

has the objective function made up of revenue and costs equations. For revenue, as the

retailer is the only source of making money by selling products to customers, so that

Eq. (3.9) can be used for the revenue equation of centralized chain.

And the objective function has four types of cost equations pertained to

purchasing, inventory holding, waste handling, and lost sales. Due to the specialization

)})

2)((),min({(.max ,21,22,22

,22212,2,22 21 t

ttt

tLTttt WPLLSWWH

IHQPOCDIP ⋅⋅+⋅+⋅+⋅+⋅+⋅−⋅∑ − αδ

(Eq. 3.19)

Revenue of Centralized Supply Chain = ),min( ,22 tt DIP ⋅ (Eq. 3.20)

45

of functions in centralized chain, purchasing function part is only dedicated for the

distributor while the lost sales part is related to the retailer. And the rest two, inventory

holding and waste handling, are related with the both entities. As the distributor

purchases goods for the whole supply chain, we can use distributor’s total purchasing

cost equation, Eq. (3.4), from decentralized supply chain.

For lost sales, as the retailer is only party working for sales in centralized supply

chain, it is also the single source of lost sales with unsatisfied demands of the end

customers due to insufficient inventory. So, we can adopt the retailer’s lost sales cost

equation, Eq. (3.15), as the lost sales function of centralized supply chain.

As the both distributor and retailer holds inventory, we have to add them up to

compute the inventory holding cost. One thing to pay attention is that the distributor

holds and ships the products to the retailer, keeping the unit price P1. This allows the

retailer to use unit inventory holding cost of1H , distributor’s unit holding cost, which is

lower than that of retailer or2H . As a result, we compute inventory holding cost in

centralized supply chain as by adding inventories at the distributor and the retailer and

multiply by the holding unit cost. So, the formula is set up as Eq. (3.23).

Total Purchasing Cost of Centralized Supply Chain = )( 101,1 1

QPOCLTt ⋅+⋅−δ (Eq. 3.21)

Lost Sales Cost of Centralized Supply Chain = tLLS ,22 ⋅ (Eq. 3.22)

46

In calculating waste handling cost of centralized chain, we can simply add total

waste handling costs at the distributor and the retailer, which is displayed as Eq. (3.24).

Now we can set up the objective function of centralized supply chain by

assembling from Eq.(3.20) to Eq. (3.24). As a result, the objective function for

centralized supply chain for multiple periods can be presented as Eq. (3.25).

Inventory Holding Cost of Centralized Supply Chain = ∑=

⋅2

1

,1 2n

tnIH (Eq. 3.23)

Waste Handling Cost of Centralized Supply Chain = ∑=

⋅2

1, )(

ntnn WWH (Eq. 3.24)

∑ ∑=

− ⋅⋅−⋅−⋅−⋅+⋅−⋅t n

tnntn

tLTttt WWHI

HLLSQPOCDIP })2

()(),min({(.max2

1,

,1,22101,1,22 1

δ

(Eq. 3.25)

Chapter 4

EXPERIMENTS SETTINGS AND RESULTS ANALYSIS

In this chapter, we describe the experimental settings and introduce the criteria

which we applied to analyze performance. Finally, we analyze the two problems; 1) the

feasibility and effectiveness of the buy-back contract between the distributor and retailer,

and the impact of the issuing policy of the distributor in decentralized perishable supply

chain 2) the impact of the issuing policy of the distributor on the retailer in decentralized

perishable supply chain.

4.1 Experimental Design

As shown in Section 3.6 , all objective functions calculate the long-term profit in

order to find the optimal order quantities due to the practical problems and dynamic

changing market situation. As a result, we need to consider two factors in doing

simulation for deriving numerical results; the length of the operating days for the

experiment and frequencies of replications with different customer samples. For

operating days, we measure the long term expected profit for 100 days.

In addition to this, we use 10 independent sets of the customer demands, and then

calculate the mean of the long term profit of the ten results for each objective functions.

48

For customer demand sample sets, we assume each set follows normal distribution of

N~ , and they are independent and identically distributed.

Table 4.1 displays the numerical values for all constants in the objective functions

for the experiments, and Table 4.2 shows numerical values of constraints and other

experiment relevant data.

Table 4.1: Unit Prices and Costs for the Objective Functions

P1 $6/unit

P2 $10/unit

Waste Handling Cost

Lost Sales Cost

Ordering Cost

P0

LS2 $20/unit

OC1 $150/unit

OC2 $100/unit

WH1 $1/unit

WH2 $1/unit

LS1 $8/unit

UNIT PRICES UNIT COSTS

IH1 $1.005/day/unit

IH2 $1.003/day/unit

Inventory Holidng Cost$1/unit

Table 4.2: Constraints and Other Numerical Values for Experiments

Service Level

95%

R2 95%

100 days

N~(100, 30 2̂)

10

Inventory Capacity

IC1 1000 units

IC2 700 units

R1Days

Customer Demand Distirbution

Number of Replication

LT1 2 days

LT2 1 days

Sh_max 7 days

T

OTHER VALUESCONSTRAINTS

Leadtime

Maximun Remaining Shelf Life

49

4.2 Optimal Order Quantity of Decentralized Supply Chain

Before analyzing the impact of the coordination or the different issuing policies,

the basic step is to find the optimal order quantity of the distributor and the retailer in

decentralized supply chain, in which the two participants make their own decision on the

order quantity size independently. Figure 4.1 shows retailer’s averaged total profit in

dollar for 100 days according to retailer’s order quantities 2Q .

From the Figure 4.1, we can observe that the retailer yields highest profitability

when placing an order of 250 units. Under the optimal order quantity of the retailer, the

distributor’s mean of total profit is described for a range of candidate order quantity of

FIFO and LIFO issuing policies respectively in the Figure 4.2.

Figure 4.1: Mean of The Retailer's Total Profit

50

As seen the figure, the optimal profit exists when the order size is 250 regardless

of the issuing policy. The only difference is the level of the profits that LIFO yields

higher total mean profit than that of FIFO.

In conclusion, the optimal order quantity combination of ( 21,QQ ) is (250, 250),

which brings the best long term average profit to the retailer and the distributor

respectively. With the optimal order quantity when the two participants make their

optimal decision independently, we will compare the result with the one coordinated in

the next section, 4.3

Figure 4.2: Mean of The Distributor's Total Profit

51

4.3 Feasibility and Effectiveness of the Coordinated Supply Chain

The goal of coordination is to bring higher effectiveness to each individual and to

the overall supply chain through the use of incentives. As mentioned in chapter 3, a buy-

back contract is one means to achieve coordination. The opportunity for using this type

of contract occur when 1) the retailer is more beneficial from changing order quantity, 2)

the distributor’s profit also increases or at least remains at the same level even after

transferring funds according to the contract term, and 3) the total profit of the supply

chain is better off or stay at least at the level than before. From the following analysis,

distributor’s LIFO issuing policy satisfies these three conditions, showing for the contract

to work to coordinate the distributor and the retailer.

4.3.1 Buy-back Contract for LIFO Issuing Policy

In order to validate the impact of a buy-back contract, we analyze the results

based on the three conditions mentioned above. As shown in Figure 4.3, the retailer’s

profit shrinks as it increases the order quantity from 250 to 300. And in Figure 4.4, the

distributor’s profit increase greatly when ( 21,QQ ) is (300, 300), which is contributed by

the order quantity increment from the retailer.

52

Figure 4.3: Mean of The Retailer’s Total Profit under Distributor’s LIFO Policy

Figure 4.4: Mean of The Distributor’s Total Profit under Distributor’s LIFO Policy

53

Rate (α) 0.0 0.5 0.6 0.7 0.8 0.9 1.0

Distributor's Profit ($) $25,710.00 $26,679.73 $26,324.98 $25,970.23 $25,615.48 $25,260.73 $24,905.98Retailer's Profit ($) $22,045.00 $21,320.81 $21,832.67$22,344.53 $22,856.39 $23,368.25 $23,880.11

Supply Chain Profit($) $47,755.00 $48,000.54 $48,157.65 $48,314.76 $48,471.87 $48,628.98 $48,786.09

Here, the buy-back ratio α plays an essential role in distributing the marginal

profit of the distributor to the retailer, so that the retailer and distributor all are able to

achieve higher level of profit in the long run. In addition to this, the total profit of the

supply chain also gets higher with the new order quantities.

Table 4.3 shows mean profit of the distributor, retailer and the whole supply chain

with financial transaction from the buy-back contract. With mutually benefited coverage

ratio on the 1P increases, distributor’s profit decrease while retailer’s gets higher both

parties are able to agree by satisfying improved financial results. As seen in the table, the

satisfying range is limited as excessive subsidy gives too much burden on the distributor

while underrated one does not motivate much the retailer to increase the order quantity.

As the shaded values of each entity are higher compared to the profit without the

contract, each participant independently motivated to accept the contract incentive under

these coverage ratios. In detail, the distributor would accept the contract when α is less

than or equal to 0.7, while the retailer would agree on it where α is greater or equal to 0.7.

From whole supply chain perspective, all ranges of α is acceptable as it earns higher

profit than without it. The two entities would agree on α where it is 0.7.

Table 4.3: Buy-Back Contract Ratio under ( 21,QQ ) is (300,300)

54

4.3.2 Comparison with Centralized Supply Chain

Now, we will compare the results of coordinated supply chain in section 4.3.1

with centralized supply chain, in order to analyze the effectiveness of the buy-back

contract. As seen in Figure 4.5, the optimal order quantity combination of ( 21,QQ ) is

(300, 300), which is equivalent to the result of the coordinated supply chain. Under the

same optimal order quantities, the two supply chains yield unequal profit values due to

the differences in the components of the objective functions. The difference is primarily

due to centralized supply chain taking advantages of internal transaction by providing

products at no margin from the distributor to the retailer, so that the unit holding cost and

omitted intermediate margin helps the chain to be more profitable than the other one.

Figure 4.5: Total Profit of Centralized Supply Chain under the Distributor’s LIFO

55

In conclusion, the buy-back contract works in coordinating independent retailer

and distributor to decide effectively as much as that of centralized supplies chain.

4.4 Which Policy Is Better in Decentralized Supply Chain?

In this section, we will analyze the supply chain performance in order to compare

the impact of the distributor’s issuing policy on the retailer's profit and scrutinize possible

causes. In examining decentralized supply chain performances, an interesting result is

observed that does not align to intuitive thought. It is largely known that FIFO issuing

policy yields higher profit as it allows holding fresher product than FIFO. However, as

Table 4.4 shows, we can see that distributor’s LIFO provides gives higher profit to the

whole supply chain in general.

In addition to comparing the mean differences, we also conduct paired t-test under

the alternative hypothesis that distributor’s LIFO issuing policy makes higher profit than

Table 4.4: Supply Chain Mean Profit Comparison by the Distributor’ Issuing Policies

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

FIFO's Profit (A) $41,815.19 $34,588.78 $47,522.97 $21,776.06 $36,271.81 $28,014.82 -$4,935.83 $19,554.30 $16,134.80 $13,001.69

Standard Deviation 11,804 6,118 8,941 13,035 4,605 9,009 8,097 9,725 8,407 9,359

LIFO's Profit (B) $47,755.84 $42,891.79 $49,143.61 $40,773.84 $41,854.99 $32,464.35 $21,651.52 $32,477.24 $23,981.25 $5,855.87

Standard Deviation 5,485 5,914 6,563 7,331 9,291 5,572 3,000 7,395 8,302 14,567

Difference (A) -(B) -5,940.66 -8,303.01 -1,620.64 -18,997.78 -5,583.18 -4,449.53 -26,587.35 -12,922.94 -7,846.46 7,145.82

P-value 0.07 0.00 0.22 0.00 0.04 0.05 0.00 0.01 0.01 0.99

56

FIFO. The p-value results justify that distributor’s LIFO issuing policy gives higher

profit to the whole supply chain than FIFO. For almost combinations of order quantities

of the distributor ( 1Q ) and the retailer ( 2Q ), we can claim that distributor’s LIFO issuing

policy give better financial results to the whole supply chain with confidence level of

90%. However, we fail to justify the hypothesis with considerably high level of

confidence level where (1Q , 2Q ) equals to (300, 300). Also, the order quantities equals to

(400,400) has the opposite phenomenon that distributor’s FIFO provides higher profit to

the whole chain than LIFO does.

In order to find out the cause, first we compare the financial results of the

distributor and the retailer respectively to see which party is more responsible for the

issue. Table 4.5 shows that distributor’s financial results according to the issuing policy

with paired t-test ones which examines if the distributor earns larger profit under its’

LIFO issuing policy. As the both differences of the profits and the p-value indicate, it is

complicated to tell that the distributor enjoys higher financial results under LIFO.

Table 4.5: Distributor’s Mean Profit Comparison by Its Issuing Policies

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

FIFO (A) 29217.96 19199.77 33067.00 19691.46 26671.64 33109.38 6976.04 18618.46 23359.82 33307.60

Standard Deviation 5842.87 3016.00 3895.96 5626.79 2607.48 3682.56 4117.84 4645.96 3256.19 4109.81

LIFO (B) 25710.13 19880.93 30382.10 21942.32 26683.48 27779.69 12236.52 20894.92 26141.18 17616.68


Difference(A)-(B) 3507.84 -681.16 2684.91 -2250.85 -11.84 5329.68 -5260.48 -2276.46 -2781.36 15690.92

P-value 0.944 0.187 0.972 0.080 0.496 0.978 0.001 0.086 0.091 1.000

57

In contrast, we see the completely dissimilar phenomenon to the distributors in

analyzing the retailer’s performances. Table 4.6 shows retailer’s financial gain and

paired t-test results to check if the supplier’s LIFO policy allows the retailer to have

greater profit than the distributor’s FIFO policy.

According to the differences and the p-values at every given order quantity

combinations of ( 1Q , 2Q ), it is obvious that the retailer generates profits with a

comparably large differences when the distributor dispatch products with higher priority

to the younger ones. As a result, it would be reasonable to focus on the retailer’s

operations for the investigation.

First, we analyze the revenue with total volumes sold for 100 days. From

Figure 4.6, to Figure 4.9, each figure shows that retailer’s sales volume is higher under

the distributor’s LIFO policy regardless of Q1 or the distributor’s order quantity to the

manufacturer.

Table 4.6: Retailer’s Mean Profit Comparison by Distributor’s Issuing Policies

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

FIFO (A) 12,597.23 15,389.01 14,455.97 2,084.60 9,600.17 -5,094.56 -11,911.87 935.84 -7,225.02 -20,305.91

Standard Deviation 7,270.00 4,038.00 5,624.00 8,158.00 2,472.00 6,109.00 5,845.00 7,097.00 6,484.00 7,081.00

LIFO (B) 22,045.72 23,010.86 18,761.51 18,831.52 15,171.51 4,684.66 9,415.00 11,582.32 -2,159.92 -11,760.81


Difference(A)-(B) -9,448.49 -7,621.85 -4,305.55 -16,746.92 -5,571.34 -9,779.22 -21,326.88 -10,646.49 -5,065.10 -8,545.10

P-value 0.001 0.000 0.040 0.000 0.011 0.000 0.000 0.004 0.000 0.000

58

Figure 4.6: Retailer’s Sales Volume Comparison when Q1=250


59

For the analysis above, it is clear that distributor’s LIFO policy generates greater

revenue by selling more units at the retailer than the FIFO at almost order quantities.

However, it is not enough to attribute the supplier’s LIFO’s superior profit only to the

gap of the sales volume. Rather, we need to seek for the in-depth reason that gives the



60

LIFO more sales opportunity from operational perspective. So, we need to look on the

waste and lost sales units. From Figure 4.10 to Figure 4.13, the retailer’s waste volumes

are compared by the distributor’s FIFO and LIFO issuing policy. Except the case where

the distributor and the retailer makes order size of 300, distributor’s choice on

dispatching younger items first gives lead the retailer generate less waste amount.

Figure 4.10: Retailer’s Waste Volume Comparison when Q1=250


61

Figure 4.14 , Figure 4.15, Figure 4.16, and Figure 4.17 compare lost sales volume of the

retailer by distributor’s dispatching policies. Just like the waste volume, distributor’s



62

LIFO policy allows the retailer to have less waste volume except the order quantities

combination of (350, 300) in Figure 4.16.

Figure 4.14: Retailer’s Lost Sales Volume when Q1=250


63

Combining the waste and lost sales volume together, it can be concluded that the

distributor’s LIFO policy provides more opportunities to the retailer to sell to the retail

customers than the FIFO policy. In other words, as the remaining shelf life is longer,

fresher the products are, thus having more chance to be held in the retailer’s inventory



64

and sold. Figure 4.18, Figure 4.19, Figure 4.20, and Figure 4.21 compare retailer’s

average remaining shelf life between distributor’s issuing policies. One common

observation from the four figures is that remaining shelf lives get shorter as retailer’s

order quantity gets larger.

Figure 4.18: Retailer’s Average Remaining Shelf Life when Q1=250


65

As distributor sells fresher products to the retailer under LIFO policy than under

FIFO, it is natural that the retailer also receives benefit from the distributor’s choice in



66

that products distributed have longer remaining shelf lives, indicating more sales

opportunities than older one.

Chapter 5

CONCLUSION

5.1 Evaluation of the study

We analyzed a perishable goods supply chain composed of an independent

distributor and retailer. Under this setting, we assumed that the product has finite life

time continuously aging at a constant rate, and the entities use a continuous review policy

with positive leadtimes and finite inventory capacities. First, we showed that the buy-

back contract coordinates the decentralized when the distributor offers a portion of the

wholesale price on unsold quantities. While an independent distributor and retailer reach

its highest profit when order quantities were 250 respectively in the study, the buy-back

contract provided enough incentive to the retailer to increase the order quantity to 300.

Also, the distributor increased the order size from 250 to 300 in order to cope with the

updated retailer demand. Financially, the mean profit of the retailer for 100 days

increased from $22,045.72 to $22,344.53 with the help of the coordination contract, and

the distributor's improved from $25,710.13 to 25,970.23.

In addition, we examined the same perishable supply chain from the perspective

of the impact of the distributor's issuing policy on the profit of the retailer and the whole

supply chain. The analysis showed that the distributor’s LIFO issuing policy enabled the

68

retailer to have higher profit than distributor’s FIFO policy. Statistically, the retailer

earned higher profit for all ( 21,QQ ) points under the confidence level of 95% except for

the case of (300,300). The whole supply chain showed better financial gain from LIFO

than FIFO with 99% confidence.

There are several limitations of this study, however. Since closed-form solutions

are extremely difficult to derive, the work is based on empirical simulation with relatively

few examples. The experiments were run using simulation in order to handle the

discrepancy between placing an order and receiving it, continuous inventory review

policy, and aging of the product in the supply chain. Clearly there is opportunity for

future work to try to develop a closed-form model that includes all the three of these

complicating factors.

Another opportunity is to relax the assumption on customer demand. Most

researchers in supply chain management assume retailer customer demand follows a

specified probability distribution or a functional form with slight variation due to

unexpected events. However, in the real world, customer demand reacts to a variety of

factors including price change, bundling promotions, and penetration of a new product

into a market. This is especially true for the grocery industry where we see the case that

customers increase buying quantity responding to retailer’s price discount on the less

fresh products, which aimed to obtain more inventory space for the fresh incoming and to

save inventory holding costs by giving away aged products. What such customers’

reactions implies is that the end customers have different utilities based on the freshness

of the product and are willing to pay less as the goods are aging more. Based on this fact,

it might be suggested to integrate price differentiated customer demand on freshness into

69

supply chain optimization. Such a trial would be significant in that coordination efforts

have been mainly focused on organizations in the supply chain. However, it is the end

customer who actually brings monetary inflow to the supply chain through retailers.

5.2 Applications of the study

As this study dealt with the perishable items, it might be possible to apply the

study on the grocery, restaurant, and pharmaceutical industries where products have

limited shelf lives which are gradually lost with a constant rate or following a decaying

function of time and other exterior conditions. Like many supply chains, these industries

also have a lot of decentralized supply chains especially for franchise contracts, where

retail shops or the end supplying managers have the final authority on making a decision

regard to ordering, including the facts of how many and how often. As shown in the

previous chapter, a buy-back contract would work as a means of coordination for the both

the independent distributor and retailer with positive leadtimes and continuous review

policy, which many companies are facing and implementing into their operations. In this

case, persuading the retailer is the most challenging and essential process for the two

parties to move to the mutual agreement for cooperation. As retailers are likely to be risk

neutral or risk averse, the distributor has to initiate the deal by making the counter party

to realize that the buy-back contract functions as a safety net for the increasing order

quantity. At the same time, it should guarantee that information on the unsold goods

should be kept confidential so as not to punish for the wasted amount or share the data

70

with other retail competitors and distributors. To be financially beneficial, it has to

provide enough coverage ratio on the distributor price in order for the retailer to be

satisfied enough to accept the contract voluntarily. Finally, this contracting process must

be voluntary for a long-term partnership.

Another important rule is the issuing policy of the distributor in a perishable

supply chain. While most retailers recognize the significance of the issuing policy and

use FIFO, it is also important what kind of policy a distributor uses when it supplied

products to retailers. As we observed, the distributor holds the key to determining the

remaining shelf lives at the retailer, which directly pertains to the likelihood of sales

opportunity for the retailer and thus impact the profitability of the retailer and the

distributor, as well as the whole supply chain. Many distributors tend to operate their

inventories with FIFO concerning inventory holding cost and additional chances for sales

to the retailer under the situation that the distributor does not differentiate price

depending on the age of the stock. However, this research showed that intuition can be

wrong. The distributor first has to analyze the costs of implementing FIFO and LIFO

with discretion and precision respectively in order to find out which policy is really

better. By supplying fresher products first, the distributor is able to take advantage by

reducing lost sales as the stored inventories have longer shelf lives than those of FIFO,

and thus generating fewer discarded amounts. In addition, it is necessary to consider the

impact of lost sales on the order because consecutive unsatisfied orders downstream may

result in distrust between the two parties.

Bibliography

Arrow, K.A., Karlin, S and Scarf, H. E. Studies in the Mathematical Theory of Inventory and Production. Stanford, CA: Stanford University Press, 1958.

Banerjee, A. "A Joint Economic Lot Size Model for Purchaser and Vendor." Decision Sciences 17, no. 292 (1986): 31.

Bernstein, F. and Federgruen, A. "Decentralized Supply Chains with Competing Retailers under Demand Uncertainty." Management Science 51 (2005): 409-26.

Cachon, G.P. "Supply Chain Coordination with Contracts." University of Pennsylvania, 2001.

Cachon, G.P. and Lariviere, M.A. "Supply Chain Coordination with Revenue Sharing Contracts: Strengths and Limitations." Management Science 51 (2005): 30-44.

Chazan, D., and Gal, S. "A Markovian Model for a Perishable Product Inventory." Management Science 23 (1977): 512-21.

Cohen, M.A. "Analysis of Single Critical Number Order Policies in Perishable Inventory Theory." Operations Research 24 (1976): 726 -41.

Cohen, M.A. and Pekelman, D. "Optimal Inventory Ordering Policy with Tax Payments under FIFO and LIFO Accounting Systems." Management Science 25, no. 8 (1979): 729-43

Simchi-Levi, D. Kaminsky, P., and Simchi-Levi, E. Designing and Managing Supply Chain; Concepts, Strategies and Case Studies. 2 ed. New York: McGraw-Hill, 2003.

Friedman, Y. and Hoch, A. " A Dynamic Lot-Size Model with Inventory Deterioration." INFOR 16 (1978): 183–88.

Fujiwara, Okisugum, Soewandi, H. and Sederage, D. "An Optimal Ordering and Issuing Policy for a Two-Stage Inventory System for Perishable Products." European Journal of Operations Research (1997): 412-14.

Goh, C., Greenberg,B. S. and Matsuo, H. "Two-Stage Perishable Inventory Models." Management Science 39, no. 5 (1993): 633-49.

Goyal, S.K. "A Joint Economic Lot Size Model for Purchased and Vendor: A Comment." Decision Sciences 19 (1988): 236-41.

Granot, D. and Yin, S. "On the Effectiveness of Return Policies in the Price-Dependent Newsvendor Model." Naval Research Logistics 52 (2005): 765-79

Lee, H.L., Padmanabhan, V., and Whang, S. "Information Distortion in a Supply Chain: The Bullwhip Effect." Management Science 43, no. 4 (1997): 546-58.

Keilson, J. and Seidmann, A. "Product Selection Policies for Perishable Inventory System." MIT Operations Research Center 1990.

Lariviere, M.A. Supply Chain Contracting and Coordination with Stochastic Demand Quantitative Models for Supply Chain Management: Kluwer Acedemic Publisher, 1998.

Lee, H.L., and Rosenblatt, M.J. "A Generalized Quantity Discount Pricing Model to Increase Supplier Profits, ." Management Science 32, no. 9 (1986): 1177-85.

72

Liu, L. and Lian, Z. "(s,S) Continuous Review Models for Products with Fixed Lifetimes." Operations Research 47 (1999): 150-58

Nahmias, S. "Inventory Depletion Management When the Field Life Is Random." Management Science 20 (1974): 1276-83.

———"Optimal Ordering Policies for Perishable Inventory – II." Operations Research 23 (1975a): 739-49.

———"A Comparison of Alternative Approximations for Ordering Perishable Inventory." INFOR 13 (1975b): 175-84

——— "Perishable Inventory Theory; a Review." Operations Research 23 (1982): 680-708

Pasternack, B.A. "Optimal Pricing and Return Policies for Perishable Commodities " Marketing Science 4, no. 2 (1985): 166 - 76.

Pierskalla, W.P. and Roach, C.D. "Optimal Issuing Policies for Perishable Inventory." Management Science 18, no. 11 (1972): 603-14

Prastacos, G. "LIFO Distribution System." Journal of Operations Research Society 30 (1979): 539-46

Ravichandran, N. "Stochastic Analysis of a Continuous Review Perishable Inventory System with Positive Lead Time and Poisson Demand." European Journal of Operations Research 84 (1995): 444-57

Schmidt, C.P. and Nihmias, S. "(S-1, S) Policies for Perishable Inventory." Management Science 31 (1985): 719-28.

Shin, H. J. and Benton, W.C. "A Quantity Discount Approach to Supply Chain Management." European Journal of Operations Research 180 (2007): 610-16

Chopra, S. and Meindl, P. Supply Chain Management : Strategy, Planning, and Operation 3ed. Upper Saddle River, N.J.: : Pearson Prentice Hall, 2007.

Thomas, D.J. and Griffin, P.M. "Coordinated Supply Chain Management." European Journal of Operations Research 94 (1996): 1-15

Veinott, A.F. Jr. "Optimal Ordering, Issuing and Disposal of Inventory with Known Demand." Columbia University, 1960.

Wang, Y. and Zipkin, P. "Agents' Incentives under Buy-Back Contracts in a Two-Stage Supply Chain." International Journal of Production Economics 120 (2009): 525-39.

Weiss, H. J. "Optimal Ordering Policies for Continuous Review Perishable Inventory Models. ." Operations Research 28 (1982): 365-74.

Weng, Z.K. "Channel Coordination and Quantity Discounts." Management Science 41 (1995): 1509-22

Yen, H. "Inventory Management for a Perishable Product Multi-Echelon System." Northwestern University, 1965.

Zyl, Van G. J. J. "Inventory Control for Perishable Commodities." University of North Carolina, 1964.

Appendix A

Customer Demand Sets for Experiments

Set 1

79 68 104 97 134 156 91 105 99 69 112

132 48 98 127 103 97 109 116 98 63 128

101 111 129 139 44 108 139 124 162 125 96

73 85 124 158 135 150 58 106 97 115 85

70 112 164 77 95 77 115 97 96 102 104

55 40 114 123 77 127 153 84 105 119 71

106 120 137 148 118 125 146 106 133 122 153

52 139 112 73 75 59 31 115 85 106 135

119 78 91 104 82 76 136 101 82 82 104

135

Set 2

129 111 120 121 87 135 106 62 94 110 132

147 124 70 126 114 141 112 137 124 176 128

157 67 122 108 112 50 70 108 96 98 86

86 143 83 132 136 113 144 118 75 138 65

58 111 103 121 79 123 119 93 105 26 69

145 50 85 94 133 110 61 91 72 122 154

74

121 102 58 155 79 71 92 133 101 86 50

133 130 82 170 91 49 75 112 102 132 101

95 88 147 136 132 107 116 110 82 155 139

139

Set 3

128 103 49 106 78 140 143 86 51 125 142

80 125 92 139 33 112 132 85 98 131 105

136 103 84 136 78 133 91 110 141 141 90

170 126 115 109 140 114 68 78 155 149 64

69 122 96 126 126 106 90 109 86 126 60

56 131 125 99 120 48 97 100 87 117 89

48 98 104 71 76 87 104 76 115 132 90

89 106 104 70 82 128 79 83 110 108 121

82 114 110 122 129 99 51 120 60 53 132

130

Set 4

120 84 156 58 95 86 88 51 125 91 126

131 103 118 108 111 76 111 56 126 117 54

100 132 109 65 121 134 109 91 111 89 147

109 90 84 94 86 66 94 98 105 165 100

162 128 63 53 67 117 86 73 82 115 99

75

73 136 148 94 42 91 133 72 108 68 106

146 137 80 44 117 65 80 95 135 86 141

120 112 105 131 69 119 108 84 77 95 94

122 138 133 67 131 53 108 62 108 44 76

125

Set 5

63 96 123 107 124 38 78 108 115 55 163

119 88 79 86 93 110 125 102 51 85 54

22 40 65 151 87 134 75 126 143 58 83

113 96 50 93 70 115 85 146 88 90 63

141 79 118 74 83 95 111 107 90 97 82

99 117 113 85 72 103 133 113 108 60 82

89 164 39 95 133 122 56 99 69 69 67

78 132 88 87 95 111 78 122 114 86 58

67 129 84 146 123 120 63 124 123 118 57

87

Set 6

89 114 115 66 110 91 96 105 110 115 74

85 45 49 108 105 105 113 85 130 109 121

144 132 82 81 123 124 91 50 110 115 113

93 139 56 115 103 90 161 138 106 77 80

76

133 64 70 148 59 91 121 98 61 92 108

76 164 110 123 115 96 110 128 49 122 72

102 95 85 54 109 110 43 142 90 91 121

130 81 123 50 79 106 58 91 142 72 153

127 128 109 110 50 101 103 142 140 108 99

110

Set 7

40 38 73 131 112 78 98 128 50 112 95

87 150 25 149 105 102 129 56 97 127 57

100 64 131 106 103 140 39 50 140 111 108

46 147 112 85 122 97 78 41 74 89 95

164 128 92 116 81 103 118 68 105 117 108

94 57 91 75 104 155 109 100 113 115 119

121 156 95 144 92 150 121 122 108 74 93

83 132 114 108 73 54 84 62 93 52 63

76 64 138 73 120 98 128 106 108 119 114

144

Set 8

104 135 108 135 104 118 76 100 112 83 54

85 28 119 70 128 91 83 71 148 130 100

119 112 82 73 81 84 30 116 76 55 83

77

135 128 105 74 74 47 87 85 59 81 140

92 97 90 93 93 83 106 74 130 133 66

103 108 78 131 108 150 117 100 78 99 128

42 54 127 93 104 143 98 81 49 65 133

113 152 88 84 104 66 89 87 100 113 67

79 123 157 105 94 89 102 75 103 70 82

102

Set 9

121 71 158 118 83 76 103 65 127 89 102

71 41 125 163 112 132 122 131 153 110 91

117 90 57 120 119 88 114 102 39 121 102

73 118 172 131 117 88 111 102 160 153 123

101 97 91 78 56 95 139 98 127 53 60

40 101 120 146 51 103 54 144 132 130 176

84 161 81 96 103 116 67 82 102 72 113

186 129 65 165 80 33 123 113 137 128 79

125 115 137 89 119 58 88 106 130 133 136

76

Set 10

27 142 91 68 141 97 64 75 118 145 103

118 119 62 94 70 88 111 105 83 62 140

78

60 61 119 95 124 112 166 75 135 125 147

65 75 94 53 107 83 92 92 77 36 115

129 112 89 111 69 152 77 152 148 132 136

58 131 120 80 100 88 95 71 120 123 128

93 40 140 58 110 92 159 108 88 96 108

150 147 136 103 112 121 76 144 46 141 128

93 101 106 124 128 65 134 84 123 88 119

86

Appendix B

Order Quantities and Profits of Entities in Decentralized Supply Chain

B.1 Retailer’s Order Quantities and Profit Optimization

Q2 0 50 100 150 200 250 300 350 400 450 500 550 600

Test 1 -$224,200.00 -$163,512.59 -$114,387.94 -$60,806.34 $15,647.98 $37,969.44 $38,393.37 $31,743.95 $30,463.54 $31,007.83 $30,108.01 $28,392.36 $28,243.11

Test 2 -$224,160.00 -$166,706.59 -$117,257.78 -$64,601.16 $3,219.46 $36,439.15 $41,279.27 $32,951.59 $25,514.42 $23,200.83 $18,788.01 $19,730.01 $13,122.86

Test 3 -$215,640.00 -$158,048.55 -$108,695.52 -$58,462.92 $19,329.50 $40,576.79 $34,808.86 $24,801.73 $25,274.89 $25,717.89 $19,899.94 $17,769.75 $16,973.86

Test 4 -$210,260.00 -$152,710.56 -$103,765.64 -$52,281.40 $10,360.30 $39,644.41 $34,645.56 $22,837.09 $19,457.50 $17,777.06 $17,996.89 $14,938.19 $15,600.92

Test 5 -$200,180.00 -$142,780.59 -$94,590.05 -$41,336.99 $23,746.95 $35,348.08 $26,500.03 $17,482.02 $10,156.41 $4,034.77 $6,718.05 $8,590.16 $7,373.10

Test 6 -$212,540.00 -$154,942.55 -$106,181.66 -$54,653.62 $13,833.68 $41,077.37 $31,613.41 $28,604.42 $24,390.09 $25,494.39 $25,560.83 $25,038.29 $24,868.96

Test 7 -$208,620.00 -$151,082.56 -$102,869.84 -$50,694.23 $19,426.36 $36,090.01 $27,376.94 $22,640.42 $16,892.01 $15,400.43 $14,874.37 $15,187.84 $8,893.10

Test 8 -$201,960.00 -$144,386.56 -$95,453.61 -$45,481.67 $25,514.01 $37,540.39 $28,600.54 $19,151.01 $15,368.85 $12,094.63 $9,247.66 $9,523.49 $8,914.63

Test 9 -$222,000.00 -$164,402.55 -$114,677.42 -$65,100.64 -$3,238.60 $40,581.65 $38,197.33 $24,071.39 $20,779.74 $21,256.05 $18,671.99 $12,108.08 $7,875.12

Test 10 -$215,980.00 -$158,520.58 -$109,491.63 -$59,749.03 $11,882.46 $40,492.32 $36,274.20 $26,500.65 $16,627.46 $20,568.38 $20,751.80 $18,428.39 $16,115.63

Mean -$213,554.00 -$155,709.37 -$106,737.11 -$55,316.80 $13,972.21 $38,575.96 $33,768.95 $25,078.43 $20,492.49 $19,655.23 $18,261.75 $16,970.65 $14,798.13

Standard Deviation 8,543.38 8,145.36 7,764.97 7,921.75 8,939.80 2,152.58 5,061.63 5,008.54 6,007.83 7,735.15 6,904.07 6,347.06 7,185.28

80

B.2 Distributor’s Order Quantity and Profit Optimiz ation under FIFO

B.3 Distributor’s Order Quantity and Profit Optimiz ation under LIFO

Q1 0 50 100 150 200 250 300 350 400 450 500 550 600

Test 1 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 -$30,402.40 $36,738.00 $22,939.55 $27,936.50 $9,286.42 $16,780.65 $8,378.42 -$1,370.30 -$1,573.15

Test 2 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$22,353.70 $27,239.00 $20,740.35 $14,387.22 $8,286.55 $2,233.20 $3,579.57 -$6,019.95 -$5,172.13

Test 3 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$5,454.17 $28,488.38 $22,789.60 $25,635.47 $8,135.98 $2,632.95 -$5,470.45 -$10,570.17 -$15,372.85

Test 4 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$12,454.35 $26,138.88 $17,739.57 $18,885.90 $485.35 -$10,066.83 -$8,070.75 -$6,319.17 -$10,772.05

Test 5 -$211,000.00 -$168,600.05 -$133,700.09 -$96,950.23 $17,042.30 $25,786.63 $16,689.18 $17,085.82 $785.70 $6,031.90 $10,979.55 -$13,869.58 -$14,572.33

Test 6 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 -$354.70 $27,137.63 $20,940.38 $11,386.78 $13,236.05 $8,083.13 $1,878.57 -$4,169.10 -$8,022.05

Test 7 -$209,000.00 -$166,650.08 -$131,800.16 -$95,150.33 $17,142.38 $33,637.13 $13,739.70 $20,336.00 $6,236.58 -$1,566.20 $10,279.58 $879.47 -$2,423.70

Test 8 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 $5,943.17 $17,787.38 $18,589.53 $14,387.30 $11,586.42 $83.30 $5,279.00 -$319.80 -$7,322.58

Test 9 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$24,302.40 $37,089.50 $16,590.25 $26,637.53 $5,485.52 $2,082.38 -$970.63 $980.67 -$4,521.55

Test 10 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 $10,694.10 $32,137.13 $21,239.60 $20,236.10 $6,235.88 $2,132.43 $7,379.13 -$3,718.88 -$7,822.08

Mean -$211,800.00 -$169,380.04 -$134,460.08 -$99,175.14 -$4,449.98 $29,217.96 $19,199.77 $19,691.46 $6,976.04 $2,842.69 $3,324.20 -$4,449.68 -$7,757.44


Q1 0 50 100 150 200 250 300 350 400 450 500 550 600

Test 1 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 -$30,402.40 $34,389.25 $26,241.20 $25,137.93 $10,287.00 $5,883.42 -$2,871.70 $10,281.58 $5,578.50

Test 2 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$18,804.00 $31,389.88 $21,341.57 $23,136.90 $16,985.25 $14,631.97 $5,180.00 $8,832.97 $5,279.98

Test 3 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$3,553.88 $28,140.13 $21,840.63 $25,987.45 $16,088.80 $13,732.75 $10,779.80 $5,881.88 -$971.28

Test 4 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$3,054.63 $19,441.13 $20,690.53 $23,287.10 $7,837.02 $4,082.43 -$4,071.75 $4,382.15 -$971.03

Test 5 -$211,000.00 -$168,600.05 -$133,700.09 -$96,950.23 $5,293.70 $20,089.88 $14,340.60 $18,686.80 $7,286.60 $3,332.63 $579.13 -$2,619.10 -$6,922.13

Test 6 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 $1,595.70 $24,789.88 $19,140.82 $18,936.80 $12,187.28 $10,733.30 $8,429.55 $9,581.65 $4,778.40

Test 7 -$209,000.00 -$166,650.08 -$131,800.16 -$95,150.33 $1,244.35 $21,590.75 $16,090.75 $14,286.60 $9,536.55 -$5,318.33 -$8,921.63 -$3,618.88 -$6,921.80

Test 8 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 $6,843.65 $23,940.13 $19,440.43 $16,637.57 $14,885.17 $9,781.90 $1,979.15 $9,182.03 $1,478.82

Test 9 -$213,000.00 -$170,550.03 -$135,600.05 -$100,650.08 -$24,302.40 $23,440.38 $20,241.63 $26,737.88 $15,586.08 $10,032.65 $229.65 $3,782.55 -$2,020.47

Test 10 -$211,000.00 -$168,600.05 -$133,700.09 -$98,800.15 -$754.63 $29,889.88 $19,441.15 $26,588.13 $11,685.45 $9,132.53 $10,030.42 $12,682.15 $8,628.90

Mean -$211,800.00 -$169,380.04 -$134,460.08 -$99,175.14 -$6,589.45 $25,710.13 $19,880.93 $21,942.32 $12,236.52 $7,602.53 $2,134.26 $5,836.90 $793.79


81

B.4 Total Supply Chain Profit under the Distributor’s F IFO

B.5 Total Supply Chain Profit under the Distributor’s LIFO

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 $55,735.05 $41,026.31 $54,097.72 $36,653.89 $34,390.73 $20,658.58 -$4,571.00 $40,289.96 $25,273.72 $15,121.07

Test 2 $35,755.68 $36,654.63 $46,034.71 $7,101.55 $42,017.39 $33,216.29 -$5,178.65 $5,688.91 $23,638.00 $28,080.09

Test 3 $45,739.92 $42,136.08 $45,918.43 $37,990.33 $37,046.04 $38,293.27 -$2,537.11 $10,777.33 $25,603.62 $12,796.13

Test 4 $44,537.52 $33,295.61 $46,854.27 $26,579.63 $41,185.19 $19,421.88 -$9,592.05 $19,747.25 $20,443.67 $3,278.30

Test 5 $33,792.70 $26,033.77 $45,098.65 $16,394.62 $39,174.45 $20,344.78 -$12,763.64 $25,744.13 $6,966.46 $1,459.69

Test 6 $39,714.41 $40,719.98 $55,557.92 $5,156.91 $40,253.87 $24,910.41 $6,068.10 $13,360.18 $22,023.86 $5,593.46

Test 7 $42,997.80 $24,915.70 $48,696.42 $23,398.48 $35,884.41 $22,152.60 $301.37 $21,362.86 $12,648.59 $13,194.81

Test 8 $19,965.90 $29,995.02 $24,885.89 $3,272.48 $31,833.43 $23,473.64 $6,832.36 $21,626.03 $1,447.91 $5,237.75

Test 9 $62,619.33 $37,166.24 $54,955.20 $30,169.42 $33,469.12 $31,350.93 -$8,892.91 $24,189.27 $10,855.16 $18,875.94

Test 10 $37,293.58 $33,944.44 $53,130.52 $31,043.33 $27,463.51 $46,325.81 -$19,024.77 $12,757.11 $12,447.02 $26,379.66

Mean $41,815.19 $34,588.78 $47,522.97 $21,776.06 $36,271.81 $28,014.82 -$4,935.83 $19,554.30 $16,134.80 $13,001.69


Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 $58,194.00 $54,441.62 $47,849.43 $46,882.80 $32,559.55 $29,066.83 $20,373.79 $43,601.08 $28,075.38 $12,173.38

Test 2 $44,141.50 $47,590.75 $44,494.98 $37,739.30 $49,193.77 $36,326.07 $17,058.97 $38,730.42 $34,284.44 $23,329.64

Test 3 $54,904.60 $42,455.96 $55,467.95 $44,507.31 $54,849.02 $41,836.79 $24,354.78 $32,566.11 $28,416.39 -$1,708.26

Test 4 $47,173.80 $44,831.91 $52,327.91 $49,435.14 $44,135.67 $27,545.85 $25,561.52 $32,515.14 $21,056.82 -$1,544.77

Test 5 $39,732.73 $33,609.88 $50,444.31 $39,166.88 $40,242.65 $35,226.22 $17,943.99 $18,786.93 $6,744.96 -$16,265.30

Test 6 $45,519.70 $38,641.58 $50,324.98 $34,761.02 $41,868.98 $25,102.51 $24,488.45 $34,835.74 $24,998.29 $1,508.72

Test 7 $45,948.75 $36,958.13 $55,158.05 $28,925.33 $37,849.41 $27,874.55 $22,852.55 $32,659.08 $15,341.95 $3,361.24

Test 8 $47,496.63 $41,208.25 $34,203.41 $31,788.63 $22,560.26 $30,300.01 $18,631.72 $22,793.19 $21,252.91 -$10,564.98

Test 9 $43,758.30 $46,506.45 $55,464.50 $45,831.77 $49,175.77 $39,725.52 $21,776.53 $29,842.08 $26,597.95 $23,728.65

Test 10 $50,688.43 $42,673.41 $45,700.59 $48,700.20 $46,114.85 $31,639.17 $23,472.92 $38,442.67 $33,043.45 $24,540.39

Mean $47,755.84 $42,891.79 $49,143.61 $40,773.84 $41,854.99 $32,464.35 $21,651.52 $32,477.24 $23,981.25 $5,855.87


Appendix C

Retailer Performances in Decentralized Supply Chain according to the Distributor’s Issuing Policies

C.1 Retailer’s Mean of Sales Volume under Distributor’s FIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 10,040 9,837 9,820 9,703 9,763 9,126 8,830 9,985 9,327 8,996

Test 2 9,826 9,973 9,866 9,321 10,104 9,425 9,210 9,426 9,398 9,353

Test 3 9,768 9,697 9,389 9,781 9,583 9,240 8,843 9,196 9,439 8,806

Test 4 9,575 9,359 9,257 9,399 9,680 8,923 8,732 9,103 8,799 8,563

Test 5 8,902 8,847 8,963 8,711 8,983 8,385 8,236 8,906 8,260 8,195

Test 6 9,515 9,581 9,618 8,958 9,520 8,920 8,910 9,189 8,927 8,473

Test 7 9,323 9,174 9,252 9,062 9,379 8,567 8,823 9,098 8,567 8,456

Test 8 8,731 8,934 8,651 8,414 9,034 8,416 8,588 8,987 8,270 8,120

Test 9 10,406 10,027 9,897 9,604 9,767 9,302 8,964 9,600 9,101 9,196

Test 10 9,373 9,490 9,644 9,641 9,484 9,571 8,447 9,192 9,090 9,280

Mean 9,546 9,492 9,436 9,259 9,530 8,988 8,758 9,268 8,918 8,744


83

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 420 623 640 757 697 1,334 1,630 475 1,133 1,464

Test 2 882 735 762 1,387 604 1,283 1,498 1,282 1,310 1,355

Test 3 514 585 893 501 699 1,042 1,439 1,086 843 1,476

Test 4 438 654 756 614 333 1,090 1,281 910 1,214 1,450

Test 5 607 662 546 798 439 1,124 1,273 603 1,249 1,314

Test 6 612 546 509 1,169 607 1,207 1,217 938 1,200 1,654

Test 7 600 680 679 734 552 1,364 1,108 833 1,364 1,475

Test 8 867 664 947 1,184 564 1,182 1,010 611 1,328 1,478

Test 9 194 573 703 996 833 1,298 1,636 1,000 1,499 1,404

Test 10 926 809 655 658 815 728 1,852 1,107 1,209 1,019

Mean 606 653 709 880 614 1,165 1,394 885 1,235 1,409


C.2 Retailer’s Mean of Waste Volume under Distributor’s FIFO Issuing Policy

C.3 Retailer’s Mean of Lost Sales Volume under Distributor’s FIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 960 584 401 1,332 1,741 2,313 1,820 1,650 1,623 3,139

Test 2 1,063 577 634 1,518 1,435 1,564 1,868 2,074 1,777 3,080

Test 3 1,006 583 511 1,694 1,247 1,755 1,587 1,604 2,261 3,324

Test 4 948 716 844 1,576 2,245 2,450 2,041 1,922 1,952 3,682

Test 5 1,435 1,047 909 2,001 1,567 2,465 2,114 2,094 2,740 3,892

Test 6 1,192 372 739 2,092 1,797 2,040 2,090 2,511 1,832 3,637

Test 7 1,427 926 792 1,838 2,156 2,077 2,068 2,546 2,227 3,544

Test 8 1,553 1,116 1,433 2,336 2,118 2,434 1,896 1,615 2,880 3,982

Test 9 806 495 603 1,346 1,633 1,898 1,562 1,600 2,111 2,985

Test 10 1,213 676 607 1,402 1,621 1,365 2,254 2,413 2,160 3,120

Mean 1,160 709 747 1,714 1,756 2,036 1,930 2,003 2,156 3,439


84

C.4 Retailer’s Mean of Remaining Shelf Lives under Distributor’s FIFO Issuing Policy

C.5 Retailer’s Mean of Sales Volume under Distributor’s LIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 4.87 5.16 5.56 4.74 4.94 5.12 4.77 4.82 5.03 4.97

Test 2 5.02 5.25 5.57 4.90 4.97 5.22 4.89 4.82 4.98 5.06

Test 3 4.88 5.20 5.42 4.78 4.94 5.16 4.94 4.94 4.94 4.97

Test 4 4.98 5.23 5.41 4.79 4.90 5.03 4.85 4.75 4.95 4.97

Test 5 4.50 5.07 5.36 4.69 5.05 4.97 4.74 4.81 4.83 4.90

Test 6 4.72 5.30 5.47 4.77 4.99 5.09 4.87 4.62 4.95 4.97

Test 7 4.66 5.17 5.44 4.74 4.90 5.07 4.79 4.69 4.92 5.00

Test 8 4.63 5.10 5.26 4.87 4.97 5.13 4.87 4.94 4.87 4.97

Test 9 5.17 5.20 5.54 4.81 4.85 5.06 4.87 4.84 4.89 5.03

Test 10 4.60 5.02 5.47 4.88 4.99 5.25 4.73 4.67 4.92 5.03

Mean 4.80 5.17 5.45 4.80 4.95 5.11 4.83 4.79 4.93 4.99


Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 10,040 9,837 9,820 9,703 9,763 9,126 8,830 9,985 9,327 8,996

Test 2 9,826 9,973 9,866 9,321 10,104 9,425 9,210 9,426 9,398 9,353

Test 3 9,768 9,697 9,389 9,781 9,583 9,240 8,843 9,196 9,439 8,806

Test 4 9,575 9,359 9,257 9,399 9,680 8,923 8,732 9,103 8,799 8,563

Test 5 8,902 8,847 8,963 8,711 8,983 8,385 8,236 8,906 8,260 8,195

Test 6 9,515 9,581 9,618 8,958 9,520 8,920 8,910 9,189 8,927 8,473

Test 7 9,323 9,174 9,252 9,062 9,379 8,567 8,823 9,098 8,567 8,456

Test 8 8,731 8,934 8,651 8,414 9,034 8,416 8,588 8,987 8,270 8,120

Test 9 10,406 10,027 9,897 9,604 9,767 9,302 8,964 9,600 9,101 9,196

Test 10 9,373 9,490 9,644 9,641 9,484 9,571 8,447 9,192 9,090 9,280

Mean 9,546 9,492 9,436 9,259 9,530 8,988 8,758 9,268 8,918 8,744


85

C.6 Retailer’s Mean of Waste Volume under Distributor’s LIFO Issuing Policy

C.7 Retailer’s Mean of Lost Sales Volume under Distributor’s LIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 663 120 788 525 1,077 1,966 396 452 1,623 2,489

Test 2 888 392 695 787 632 1,656 1,106 680 1,753 2,553

Test 3 703 326 920 779 813 1,423 655 814 1,961 1,963

Test 4 187 289 800 879 719 1,606 516 866 1,720 2,210

Test 5 377 212 1,204 779 1,001 2,284 535 1,214 2,102 2,009

Test 6 360 532 1,154 816 785 1,620 439 754 2,068 2,585

Test 7 291 355 1,050 742 915 2,117 1,005 871 2,235 3,192

Test 8 443 492 687 699 1,514 1,980 1,194 1,137 2,143 2,989

Test 9 442 307 484 975 628 1,727 849 908 1,949 2,384

Test 10 192 330 749 647 530 1,624 694 568 1,902 2,682

Mean 455 336 853 763 861 1,800 739 826 1,946 2,506


Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 373 332 812 487 887 987 1,006 573 1,133 1,349

Test 2 707 350 688 745 410 1,025 1,186 749 996 1,146

Test 3 188 558 456 546 350 505 1,012 796 1,031 1,445

Test 4 249 452 390 192 624 769 605 778 958 1,315

Test 5 461 509 368 303 538 799 732 1,051 1,146 1,431

Test 6 528 510 379 593 762 688 803 724 1,188 1,372

Test 7 345 545 337 588 819 957 645 765 1,364 1,523

Test 8 308 406 483 563 990 728 920 918 1,014 1,603

Test 9 580 281 508 413 628 808 1,004 1,008 1,153 984

Test 10 542 463 548 423 663 789 859 674 951 965

Mean 428 441 497 485 667 806 877 804 1,093 1,313


86

C.8 Retailer’s Mean of Remaining Shelf Lives under Distributor’s FIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 5.77 5.88 5.56 5.56 5.50 5.36 5.92 5.81 5.29 5.31

Test 2 5.73 5.72 5.66 5.57 5.67 5.27 5.36 5.70 5.38 5.33

Test 3 5.77 5.58 5.63 5.46 5.68 5.45 5.84 5.62 5.27 5.41

Test 4 6.10 5.71 5.56 5.53 5.51 5.40 5.68 5.56 5.30 5.44

Test 5 5.82 5.82 5.53 5.54 5.54 5.25 5.73 5.57 5.24 5.50

Test 6 5.88 5.65 5.59 5.60 5.48 5.59 5.87 5.59 5.28 5.36

Test 7 5.90 5.64 5.61 5.46 5.50 5.34 5.54 5.69 5.19 5.17

Test 8 5.90 5.70 5.69 5.71 5.25 5.35 5.28 5.47 5.33 5.36

Test 9 5.76 5.70 5.61 5.40 5.64 5.36 5.58 5.53 5.21 5.31

Test 10 6.00 5.65 5.57 5.44 5.52 5.41 5.53 5.56 5.35 5.33

Mean 5.86 5.70 5.60 5.53 5.53 5.38 5.63 5.61 5.28 5.35


Appendix D

Centralized Supply Chain Order Quantities and Profit

D.1 Supply Chain Mean Profit under the Distributor’s FIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 $60,206.41 $58,600.14 $64,968.43 $48,326.81 $49,060.86 $35,526.87 $21,504.05 $50,760.47 $33,341.37 $27,982.71

Test 2 $50,728.80 $59,428.82 $62,805.62 $32,976.43 $55,887.64 $42,183.13 $28,296.55 $27,961.69 $29,304.76 $34,441.49

Test 3 $56,311.62 $58,009.06 $54,290.12 $51,362.89 $47,317.17 $44,259.00 $24,438.82 $29,449.02 $36,470.80 $25,657.81

Test 4 $57,108.63 $52,870.30 $55,225.17 $46,152.77 $54,754.37 $37,190.73 $24,983.69 $31,817.69 $26,010.64 $22,840.23

Test 5 $42,166.75 $46,808.17 $55,969.34 $34,967.82 $48,214.08 $32,111.99 $21,212.80 $32,814.49 $17,634.47 $21,022.81

Test 6 $50,286.94 $59,394.39 $64,027.84 $32,231.66 $47,323.65 $36,777.80 $29,342.80 $32,231.79 $27,590.99 $18,455.36

Test 7 $47,449.58 $51,560.37 $57,067.33 $41,722.14 $47,653.73 $30,919.22 $32,376.57 $31,933.30 $20,615.45 $22,755.35

Test 8 $36,640.25 $48,269.34 $43,257.71 $27,346.61 $43,903.31 $32,339.06 $31,606.98 $35,197.91 $17,016.56 $18,099.18

Test 9 $71,389.88 $63,240.23 $63,525.76 $44,641.35 $47,239.37 $37,517.80 $20,982.80 $35,359.61 $21,522.97 $31,738.03

Test 10 $41,566.55 $51,818.33 $61,500.83 $48,016.15 $45,335.12 $55,292.89 $12,150.80 $26,628.65 $28,015.15 $39,341.16

Mean $51,385.54 $54,999.91 $58,263.82 $40,774.46 $48,668.93 $38,411.85 $24,689.59 $33,415.46 $25,752.32 $26,233.41


88

D.2 Supply Chain Mean Profit under the Distributor’s LIFO Issuing Policy

Q1 250 300 300 350 350 350 400 400 400 400

Q2 250 250 300 250 300 350 250 300 350 400

Test 1 $62,565.84 $69,895.23 $58,819.48 $58,236.05 $47,431.62 $46,835.59 $40,348.99 $50,372.60 $36,143.20 $28,337.36

Test 2 $56,304.59 $72,964.87 $65,566.52 $50,512.24 $65,664.85 $49,684.10 $33,412.11 $46,190.50 $42,451.56 $39,493.00

Test 3 $68,046.25 $60,830.19 $66,538.64 $53,279.89 $60,518.32 $59,503.77 $42,628.77 $37,736.85 $36,583.67 $20,857.96

Test 4 $65,846.91 $60,505.49 $65,798.67 $60,406.50 $51,206.38 $48,014.32 $48,035.17 $38,385.80 $34,024.25 $24,221.11

Test 5 $51,905.98 $53,684.06 $61,315.25 $51,139.60 $47,812.94 $44,192.90 $38,118.91 $23,757.79 $19,713.38 $12,700.37

Test 6 $55,792.91 $60,416.75 $67,516.16 $48,634.49 $47,339.47 $51,471.18 $43,561.90 $39,905.73 $30,564.68 $24,073.47

Test 7 $61,691.42 $57,633.04 $67,668.41 $46,449.15 $43,990.07 $42,642.34 $45,026.55 $37,998.90 $23,408.78 $19,525.12

Test 8 $57,669.63 $57,681.47 $57,476.15 $45,762.01 $35,030.93 $45,067.14 $30,105.43 $27,763.74 $29,219.35 $11,999.83

Test 9 $60,531.57 $74,241.00 $69,795.16 $61,704.37 $56,945.78 $54,693.97 $39,449.49 $35,912.33 $34,765.30 $43,192.15

Test 10 $56,862.13 $64,748.25 $64,272.37 $59,172.91 $53,185.64 $52,207.93 $40,147.24 $44,313.02 $38,809.53 $40,703.59

Mean $59,721.72 $63,260.03 $64,476.68 $53,529.72 $50,912.60 $49,431.32 $40,083.46 $38,233.73 $32,568.37 $26,510.40


Appendix E

URLs for C Language Programming Codes for Experiments

E.1 The URL for Decentralized Supply Chain Codes

http://www.personal.psu.edu/jxc634/blogs/source_code/2010/08/c-language-

programming-codes-for-experiments-decentralized-supply-chain.html

E.2 The URL for Coordinated Supply Chain Codes

http://www.personal.psu.edu/jxc634/blogs/source_code/2010/08/c-language-

programming-code-for-coordinated-supply-chain.html

E.3 The URL for Centralized Supply Chain Codes

http://www.personal.psu.edu/jxc634/blogs/source_code/2010/08/c-programming-code-

for-centralized-supply-chain.html

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