Computers & Industrial Engineering 59 (2010) 552–560

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Computers & Industrial Engineering

journal homepage: www.elsevier .com/ locate/caie

Impact of demand correlation and information sharing in a capacityconstrained supply chain with multiple-retailers

Chanel Marchèi Helper a, Lauren B. Davis a,*, Wenbin Wei b

a Department of Industrial and Systems Engineering, North Carolina A&T State University, Greensboro, NC 27411, USAb Bank of America, Calabasas, CA 91302, USA

a r t i c l e i n f o

Article history:Received 2 September 2009Received in revised form 27 June 2010Accepted 28 June 2010Available online 3 August 2010

Keywords:Information sharingMarkov decision processSupply chain

0360-8352/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.cie.2010.06.014

* Corresponding author.E-mail address: lbdavis@ncat.edu (L.B. Davis).

a b s t r a c t

This paper considers a single product, two-echelon capacity constrained supply chain consisting of a sup-plier and two retailers facing correlated end-item demand. We use a decentralized Markov decision pro-cess with restricted observations to represent this system and conduct a numerical study to quantify thebenefits of information sharing to the retailers under varying levels of supplier capacity and supply allo-cation mechanisms. Our results show an inverse relationship between capacity and information and indi-cate the retailers can achieve significant benefits as a result of the information sharing partnership.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

As a result of recent advances in information technology, manycompanies, primarily in the retail industry, e.g. Wal-Mart, havebeen able to use electronic data interchange (EDI) and point-of-sale (POS) data to make better decisions about their ordering andinventory policies. With these technologies, information is imme-diately available within all the stages of the supply chain. As a re-sult, there is a general belief that capturing and sharing real-timedemand information is of key importance to improved supplychain performance. There has been significant research activity inthis topic over the past few years (see for example Huang, Lau, &Mak, 2003; Sahin & Robinson, 2002), typically along two dimen-sions. The first involves understanding the value of informationsharing. Research along this dimension compares traditionalinventory management strategies to information inclusive strate-gies and identifies the value of information sharing, discusseshow this value is measured, and analyzes the factors influencingthat value. The second dimension is related to supporting systemsor tools for information sharing. It addresses the necessary frame-work or technology required to ensure that information sharing beunbiased, timely, and accurate (Li, Yan, Wang, & Xia, 2005).

Many researchers have studied the process between the sup-plier and one retailer. In more recent years, however, studies havebeen conducted in situations with two or more retailers consider-ing capacitated or un-capacitated suppliers. Cachon and Fisher(2000) consider a supply chain consisting of N identical retailers

ll rights reserved.

and a single infinite capacity supplier and examine the impact ofthe supplier’s order and allocation decision on the value of inven-tory information sharing. Cheng and Wu (2005) consider the caseof one supplier and two retailers and evaluate the impact of shar-ing order, demand, and inventory information on the expectedoperating cost (holding and penalty) and inventory reduction ofthe supplier.

Capacitated suppliers have been considered by Gavirneni(2001), Zhao and Xie (2002), Gavirneni (2005), and Huang and Ira-vani (2005, 2007). Huang and Iravani (2005) determine the optimalproduction control policy of a manufacturer and the value of infor-mation sharing in a multiple-retailer environment when all retail-ers do not participate in the information sharing partnership. Zhaoand Xie (2002) examine the impact of forecasting error in a supplychain with one supplier and four identical retailers sharingplanned order information. Huang and Iravani (2007) consider asingle manufacturer and two non-identical retailers in a competi-tive environment sharing inventory information. They determinethe optimal production quantity and stock rationing decisions un-der this setting. The impact of constrained capacity of the manu-facturer/supplier on the value of information has been studied byGavirneni (2001) in a make-to-order environment under inventoryinformation sharing and in a make-to-stock environment (Gavirn-eni, 2005) in conjunction with scheduled order policies imple-mented by the retailers. In general, prior research reportssignificant benefit to the supplier under most information sharingschemes. However, a full understanding of retailer benefits undersimilar modeling conditions is not as extensively characterized inthe literature. One reason can be attributed to the treatment ofscarce supply.

C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560 553

Typically two modeling approaches are considered in handlingthe impact of limited supply: (i) assess a penalty cost for procuringthe missing items from an outside source (e.g. Gavirneni, 2005;Huang & Iravani, 2005) and (ii) strategic allocation of scarce supplyto the retailers (e.g. Gavirneni, 2001; Huang & Iravani, 2007; Zhao& Xie, 2002). Under the first approach, the retailer’s order quantityis met in full and information value is quantified from the sup-plier’s perspective only. The second approach allows for analysisof information sharing strategies from the retailer’s perspectivesince the retailers are more directly impacted by supply shortages.

For example, rationing or selectively allocating a portion of on-hand inventory to current orders and reserving stock for future or-ders is one approach examined by Huang and Iravani (2007).Gavirneni (2001) investigated the impact of using a retailer rank-ing procedure and stock reallocation among retailers.

The work presented here differs from prior research in the fol-lowing manner. We consider capacity constraints for both the sup-plier and the retailer and introduce the assumption of lost sales.Lost sales, capacity constraints, and delivery lags represent a fewof the conditions encountered when managing inventory in the re-tail sector (Downs, Meters, & Semple, 2001). The impact of thisassumption not only changes the structure of the assumed optimalpolicy of the retailer, but also allows us to further study the impactof information sharing on the retailer. Since many of the priorcapacitated supplier models assume the retailer receives all unitsdemanded, regardless of the supplier’s physical inventory limita-tion, the reported benefit of information sharing to the retailer isrelatively small or non-existent, with the supplier receiving mostof the benefits from the information sharing partnership. Further-more, we study the relationship between retailer demand correla-tion and information sharing. Raghunathan (2003) considers theimpact of retailer demand correlation in a multiple-retailer envi-ronment, where the level of correlation is modeled between peri-ods for each retailer, independently. However, the value ofinformation sharing is measured as a function of the cost reductionexperienced by the manufacturer, since the manufacturer guaran-tees supply to the retailer. Correlated retailer demand is alsoconsidered in Gavirneni (2005) in conjunction with the implemen-tation of scheduled order policies. However, only two cases forend-customer demand are investigated; independent (q = 0) andhighly correlated (q = 1). In addition, the benefits are quantifiedin terms of total supply chain cost. The goal of this research is toquantify benefits, to the retailer, supplier and the entire supplychain such that the supply chain profit is maximized.

A summary of the single-supplier multiple-retailer models(SSMR) based on retailer demand assumptions, information shar-ing type, and value of information evaluation measure is presentedin Table 1. As can be seen from the table, most models seek todetermine the optimal inventory policy for the supplier that min-imizes the expected holding and shortage costs under differentforms of information availability and flow. The papers do not quan-tify any benefits to the retailer in terms of cost or profit with theexception of Gavirneni (2001), where the supplier employs a

Table 1Comparison of proposed model with prior SSMR models.

Reference End-item demandbacklogged

Demand correlatedbetween retailers

Cachon and Fisher (2000) Yes NoCheng and Wu (2005) Yes NoGavirneni (2001) No NoGavirneni (2005) Yes YesHuang and Iravani (2005) No NoHuang and Iravani (2007) No NoRaghunathan (2003) Yes NoZhao and Xie (2002) Yes NoProposed model No Yes

make-to-order policy, holds no inventory and experiences no costs.Therefore, this paper merges the ideas proposed in Gavirneni(2005) with that of Raghunathan (2003), for a fixed allocationmechanism and correlated demand environment, in an effort tocharacterize the benefits to the retailer.

Our objective is to understand how information sharing bene-fits the retailer. Specifically, we seek to quantify the magnitudeof the benefit under varying levels of demand correlation andcapacity constraints. We model the information sharing problemusing an observation constrained Markov Decision Process, whichhas not been done in prior SSMR models. This approach allowsus to assume no general form of the optimal control policy forthe supplier and retailers.

The remainder of this paper is organized as follows. In Section 2,we present the model and formulate the information sharing prob-lem as a Markov Decision Process. In Section 3, we outline theexperimental design. Results from the computational study arediscussed in Section 4. Concluding remarks are provided inSection 5.

2. Model description

Consider a two-echelon supply chain with one capacitated sup-plier and two retailers. The supplier follows a make-to-stock policyand provides only one product to the retailers who are facing de-mand from end-customers. There is a one period lead-time, mean-ing that orders placed at the beginning of a period will not bereceived until the end of the period. The costs include variable or-der cost (m), holding cost (h), fixed setup cost (F), and stock out pen-alty cost (l). Both retailers sell their units for the same price (g)which is assumed to be based on the current market selling price.The sequence of events for each period is as follows: (1) Inventoryholding costs are incurred for the retailers and supplier; (2) Theretailers examine their inventory and then choose to place an orderincurring variable order cost; (3) The supplier examines his inven-tory and places an order incurring variable production and setupcosts; (4) Customer demand arrives and is satisfied from the retail-ers’ stock. Excess demand is lost and penalty costs are incurred; (5)The supplier receives the retailers’ orders and ships the availablequantity from inventory. If the supplier has insufficient inventoryto satisfy both retailers’ orders, the supplier must implement astrategy to allocate inventory among the retailers. The remainingunfulfilled items in each retailer’s order will be counted as lostsales; (6) The retailers receive their order at the end of the periodand place the items in inventory; (7) The supplier receives his or-der at the end of the period and places the items in inventory.

Three information sharing models are considered as depicted inFig. 1. In Model I (no information sharing) the retailers share noinformation with the supplier. The only information available tothe supplier is the orders received from the retailers each period,as well as his own inventory information. In Model II (partial infor-mation sharing), the retailers share their inventory information

Information sharing type VOI evaluationmeasure

Demand, inventory Supply chain costOrder, inventory and demand Supplier costInventory Retailer costInventory Supply chain costInventory Supplier costInventory Supplier costDemand and forecast Supplier costDemand forecast Retailer/supplier/supply chain costInventory Supply chain profit

S

R1

R2

S

R1

R2

S

R1

R2

(a) (b) (c)

Product flow

Information flow

Fig. 1. Information sharing models (a) no information sharing, (b) partial information sharing, and (c) complete information sharing.

554 C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560

with the supplier every period, but not each other. The suppliernow has a view of the entire system while the retailers can onlysee their local inventory level. Model III (complete information shar-ing) assumes all supply chain members share inventory informa-tion with each other and thus, have a complete view of theentire system. The purpose of Model III is to determine what thevalue of information sharing could be in a completely cooperativeenvironment. It allows us to quantify the magnitude of the devia-tion between Models II and III.

We formulate the supply chain model as a restricted observa-tion Markov Decision Process, where we seek the optimal inven-tory control policies for each supply chain member whichmaximizes the long-run expected supply chain profit. The re-stricted observation Markov Decision Process was first presentedin Serin and Avsar (1997) for the finite horizon case and extendedin Serin and Kulkarni (2005) for the infinite horizon, average re-ward model. Both models seek optimization for a single agent,and thus Wei, Davis, King, and Hodgson (2008) extend the modelto include optimization for multiple agents, where deterministicpolicies are desired. We formally describe the problem using theMDP framework under the average reward criterion as follows.

The state space S can be described by the vector (y, x1, x2) cor-responding to the inventory level of the supplier and retailers,respectively. We assume (y, x1, x2) is bounded by the capacity vec-tor (Cs, Cr1, Cr2).

The action space A is defined as (p, k1, k2) corresponding to theproduction quantity (p) of the supplier and order quantities of theretailers. The feasible quantities are constrained by the capacity ofthe supply chain member given they are in state s. Without loss ofgenerality, we let A(s) represent the feasible actions given the stateis s.

Transition probabilities are generated based on the distributionof demand experienced by the retailers, which is generated from aBivariate Poisson distribution shown below, where di representsthe realized demand for retailer i.

PD1 ;D2 ðd1;d2Þ ¼ expf�ðk1 þ k2 þ k3Þgkd1

1 kd22

d1!d2!

Xminðd1 ;d2Þ

j¼0

�d1

j

� �d2

j

� �j!

k3

k1k2

� �j

ð1Þ

Given random variables Zi, i = 1,2,3, follow independent Poissondistributions with parameters ki > 0, then the random variablesD1 = Z1 + Z2 and D2 = Z2 + Z3 follow jointly a Bivariate Poisson (BP)distribution with joint probability function defined in (1). Themarginal distribution functions follow a Poisson distributionwith parameters E(D1) = k1 + k3 and E(D2) = k2 + k3 Moreover,cov(D1,D2) = k3 and hence k3 is a measure of dependence betweenthe two random variables. The BP distribution allows for indepen-dence between two random variables. If k3 = 0 then the two vari-ables are independent and the BP distribution reduces to theproduct of two independent Poisson distributions (referred to asthe double–Poisson distribution) (Marshall & Olkin 1985).

The system transitions to a new state s0 ¼ ðy0; x01; x02Þ as a func-

tion of the random demand (d1, d2) and joint action (p, k1, k2) asfollows.

y0 ¼ ½y� ðk1 þ k2Þ�þ þ p ð2Þx0i ¼ ½xi � di�þ þ k�i i ¼ 1;2 ð3Þ

When y P k1 þ k2; k�i ¼ ki otherwise k�i is the quantity shipped

to retailer i based on a specific allocation rule. We examine threeallocation mechanisms. The first is a rationing based scheme,where the supplier allocates his inventory evenly to each retailer.The quantity shipped for each retailer is formally defined below.

k�1 ¼ miny2

h i; k1

� �ð3Þ

k�2 ¼ min y� k�1 ; k2� �

ð4Þ

The second allocation mechanism is one proposed by Gavirneni(2001). This approach attempts to bring the inventory level of allretailers to the same level. If it is not possible, it starts with the re-tailer with the lowest inventory level and brings it to the level ofthe next highest retailer. This allows for retailers with the largestinventories to receive smaller shipments. Note, this particularmechanism assumes the inventory levels of the retailers are knownby the supplier. As a result, we only examine the impact of this ap-proach relative to other supply allocation approaches under infor-mation sharing. The algorithm implemented for this method isformally defined in the appendix.

The last supply allocation approach is an equity based allocationscheme that allocates inventory to each supplier so that the frac-tion of satisfied demand is the same for both retailers. We formally,find a fraction (f) satisfying Eq. (5) below:

fk1 þ fk2 ¼ y ð5Þ

Using (5) we can easily find the value of f as a function of the retailerorder quantities and inventory level of the supplier.

Therefore, the quantity shipped for each retailer is defined asfollows.

k�i ¼ fki ð6Þ

The expected immediate reward (supply chain profit per peri-od) associated with choosing action a e A(s) while the system isin state s e S is defined as

rðs; aÞ ¼ Eðd1 ;d2Þ½g � ðminðd1; x1Þ þminðd2; x2ÞÞ �Lðx1; d1Þ�Lðx2;d2Þ � msp� hsy� Fsminð1;pÞ� ð7Þ

where,

Lðxi; diÞ ¼ hixi þ liðdi � xiÞþ: ð8Þ

Using (7), we can construct the supplier and retailers’ expectedper period profit as a function of each state and action pair, respec-tively, as follows.

Table 2Marginal distribution for correlation levels (dataset 1).

Correlation k1 k2 k3 E(D1) E(D2) j~q� qj

0.00 1 2 0 1.00 2.00 0.0000.25 1 2 0.479 1.48 2.48 0.0010.50 1 2 1.467 2.47 3.47 0.0060.75 1 2 3.914 4.91 5.91 0.0091.00 0.01 0.01 5 5.01 5.01 0.002

Table 3Marginal distribution for correlation levels (dataset 2).

Correlation k1 k2 k3 E(D1) E(D2) j~q� qj

0.00 4 4 0 4 4 0.0510.25 3 3 1 4 4 0.0300.50 2 2 2 4 4 0.0120.75 1 1 3 4 4 0.0011.00 0.01 0.01 3.99 4 4 0.003

Table 4Experimental parameters for correlation and capacity effect.

Correlation Cs Cr1 Cr2 hs h1 h2 l1 l2 Fs vs v1 v2 g

0.00 10 10 10 1 1 1 75 75 10 5 20 20 1000.25 150.50 200.751.00

C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560 555

r0ðs; aÞ ¼ m1k�1 þ m2k�2 � msp� hsy� Fsminð1;pÞ ð9Þriðs; asÞ ¼ g �minðdi; xiÞ � hixi � liðdi � xiÞþ � mixi; i ¼ 1;2 ð10Þ

Let Oi denote a finite set of observations for supply chain mem-ber i. Let Gi (�) denote a function that maps a state in S to an obser-vable output in Oi. Then for some k e Oi, Sk(i) = {(y, x1, x2)|Gi(y, x1,x2) = k}. Thus Sk(i) defines a partition of the state space accordingto the observation process of supply chain member i and satisfiesUk2Oi

SkðiÞ ¼ S. In the context of the supply chain information shar-ing problem, observable outputs correspond to inventory levels ofsupply chain members and are defined according to the specificassumptions of the information sharing policy as defined below.

� Model I: Oi correspond to the inventory level of the specific sup-ply chain member, where O0 = {O� � �Cs}, O1 = {O� � �Cr2}, andO2 = {O� � �Cr2}.

G0ðy; x1; x2Þ ¼ y ð11ÞGiðy; x1; x2Þ ¼ xi i ¼ 1;2 ð12Þ

� Model II: O1 and O2 are as defined in Model I. Since the supplierhas full visibility of the system Oo = S and G0(y, x1, x2) = (y, x1, x2).� Model III. Since each supply chain member has full visibility,

Oi = S "i.

For each information sharing model, we seek a stationary opti-mal control policy which maximizes the expected supply chainprofit per period expressed as a function of the immediate rewardsand steady state probability associated with each state as follows

J ¼ maxa2AðsÞXs2S

rðs; aÞpsðaÞ ð13Þ

When all supply chain members have information about theprocess (in particular inventory levels at each stage), a completelyobservable MDP can be used to represent this information sharingscheme (Model III). In this case, we assume a central decision ma-ker selects policies for each member which optimizes the supplychain. The solution to the optimization equation is determinedusing policy iteration (Puterman, 1994). When all inventory infor-mation is not known to the decision makers, then an observationprocess must be defined to represent the portion of the state thatis visible to each decision maker (Models I and II). A DecentralizedRestricted Observation MDP (DEC-ROMDP) is used to determinethe optimal policies for each supply chain member when partialinformation about the supply chain is known (Wei et al., 2008).For the DEC-ROMDP, the control alternatives and expected rewardare as defined in the completely observable model. However, anaction is admissible for an observable output k if it is admissiblefor all states defined in observation set Sk. The reader is referredto Wei et al. (2008) for a complete discussion of the DEC-ROMDPmodel and solution method. We use this approach to solve theno and partial information sharing models (I and II).

3. Experimental design

We perform a numerical study to investigate the value of infor-mation to both the supplier and retailer while maximizing the ex-pected supply chain profit. We are interested in determining underwhich settings the retailer benefits (monetarily) from informationsharing. We also investigate the relationship between informationvalue and the following problem specific parameters: demand cor-relation, capacity, cost, and supply allocation method. Two corre-lated datasets are constructed to generate the retailer demand.We select the mean rates (ki) to generate the desired level of cor-relation, with values ranging from 0 to 1.0. Note, we truncate the

BP distribution based on the capacity of the retailers. However,the parameter values are chosen such that the correlation of thetruncated distribution (~q) is close to its theoretical value (q). Thefirst set primarily changes the covariance term to achieve the de-sired correlation. We recognize changing the covariance termchanges the correlation as well as marginal means. Therefore, weconstruct a second set of demand parameters such that the mar-ginal means are identical across all correlation values. The correla-tion, corresponding demand rates, marginal means, and absolutedeviation between the theoretical correlation and computed corre-lation are shown in Tables 2 and 3.

In the first experiment, we evaluate the impact of suppliercapacity and correlation on the value of information. The relevantcost and capacity parameters are summarized in Table 4. We useboth demand datasets and the rationing based allocation method,which results in a total of 30 problems generated and solved.

In the second experiment we vary the correlation level, retai-ler’s holding costs and lost sales costs to distinguish how the valueof information is affected. The particular values are summarized inTable 5. We use demand dataset 1 (Table 2) and the rationingbased allocation method, which results in a total of 90 problemsgenerated and solved.

The third experiment uses demand dataset 2 (Table 3) alongwith cost and capacity values in Table 4 to examine the impactof the different supply allocation strategies on the value of infor-mation sharing.

To quantify the value of information sharing (VOI) we comparethe expected supply chain profit obtained from solving the variousMDP models. We calculate the relative increase in profit due toinformation as

VOI ¼ Jis

Jnis

��������� 1; nis ¼Model I; is ¼Model II: ð13Þ

When comparing information value between model II and III,Jnis represents the expected profit obtained from Model II, whileJis corresponds to the expected profit obtained from Model III. It

Table 5Experimental parameters for cost and correlation effect.

Correlation Cs Cr1 Cr2 hs h1 h2 li Fs vs v1 v2 g

0.00 10 10 10 1 1 1 65 10 5 20 20 1000.25 2 2 750.50 4 40.751.00

Table 7Average supply chain profit per period as a function of information strategy (dataset1).

Correlation NIS IS

0.75 32.74 636.231.00 127.82 650.66

00.20.40.60.8

11.21.41.61.8

0

.25

0.5

.75 1 0

.25

0.5

.75 1 0

.25

0.5

.75 1

Supp

ly C

hain

Val

ue o

f In

form

atio

n

Correlation

556 C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560

is obvious that if VOI > 0, information is valuable. The magnitude ofthat value depends on the magnitude of VOI. We can also use Eq.(13) to quantify the value of information for each supply chainmember using their respective profit Eqs. (9) and (10). Decompos-ing the total supply chain profit in Eq. (7) in terms of other param-eters, such as inventory investment and penalty cost, allows us toexamine the relative increase/decrease in the cost components aswell.

0 0 0 0 0 0

10 15 20Supplier'sCapacity

Fig. 3. Supply chain value of information using dataset 2.

VOI(S)

VOI(R1)

VOI(R2)

0 0.25 0.5 0.75 1

0.0090 0.0644 0.1670 0.6938 0.6407

0.0033 0.0079 0.1373 15.0192 7.4889

0.0042 0.0115 0.6962 4.2281 7.4696

0.000.100.200.300.400.500.600.700.800.901.00

Val

ue o

f In

form

atio

n

Correlation

VOI(S)VOI(R1)VOI(R2)

0.300.400.500.600.700.800.901.00

Val

ue o

f nf

orm

atio

n

VOI(S)VOI(R1)

4. Results

4.1. Effect of correlation and capacity

4.1.1. Supply chain value of informationWe first examine the impact of supplier capacity and retailer

demand correlation on the expected supply chain profit. This rela-tionship is characterized in Fig. 2 for dataset 1 and takes on valuesin [0.0019, 18.43]. Note, we restrict the scale of Fig. 2 to allow allthe values to be clearly viewed. For many cases, the relative valueof information is less than 0.50. The two largest information shar-ing values occur at the lowest supplier capacity level. In particular,when the supplier’s capacity is 10 and the correlation is 0.75 and1.0, the relative value of information is 18.43 and 4.09, respec-tively. This is largely due to the fact that the supplier’s capacityis slightly less than the combined mean demand of the retailers(Table 6), which results in extremely high penalty costs. Table 6summarizes the ratio of supplier capacity to mean demand whileTable 7 displays the expected supply chain profit for the supplyconstrained cases mentioned above. Clearly, it is not realistic fora supplier to operate at significantly lower capacity than the aver-age per period demand as this reflects a significant loss in profit forthe entire supply chain. In the absence of information, this profit

00.10.20.30.40.50.60.70.80.91

10 15

0 0.25 0.5 0.75 1

Val

ue

of

Info

rmat

ion

CapacityCorrelation

10 15 20 20 10 15 20 10 15 20 10 15 20

Fig. 2. Supply chain value of information using dataset 1.

Table 6Ratio of supplier capacity to total mean demand of retailers (dataset 1).

Correlation Cs = 10 Cs = 15 Cs = 20

0.00 3.33 5.00 6.670.25 2.53 3.79 5.050.50 1.68 2.53 3.370.75 0.92 1.39 1.851.00 1.00 1.50 2.00

VOI(S)

VOI(R1)

VOI(R2)

0 0.25 0.5 0.75 1

0.0226 0.0171 0.0335 0.1706 0.1366

0.0000 0.0027 0.0063 0.6566 0.5672

0.0010 0.0014 0.0093 0.5063 0.2423

0.000.100.20I

Correlation

VOI(R2)

Fig. 4. Supply chain partners value of information using dataset 1.

difference can be significant as indicated in Table 7. When thereis enough capacity to satisfy the mean demand, there is little valuethat can be achieved with information. When the supplier capacitylevel is 20, the relative increase in profit is <0.1%.

Fig. 3 illustrates the relative change in the expected supplychain profit using dataset 2. Recall dataset 2 removes the combinedeffect of changing correlation and average demand. The ratio ofsupplier capacity to the total demand of the retailers is 1.25,1.88, and 2.55 for supplier capacity of 10, 15, and 20 respectively,across all correlation values. Fig. 3 shows that the relative changein profit is larger when the capacity is tight relative to mean de-mand, similar to what was observed using dataset 1. In addition,when the supplier’s capacity is 15 (corresponding to a capacity

Fig. 5. Supply chain partners value of information using dataset 2.

VOI Penalty(R1)

VOI Penalty(R2)

VOI Inv.(R1)

VOI Inv.(R2)

0 0.25 0.5 0.75 1

-0.4373 -0.4559 -0.4852 -0.5047 -0.5224

-0.2728 -0.2892 -0.3125 -0.3292 -0.3330

0.1883 0.2008 0.2055 0.2200 0.2428

0.1011 0.1083 0.1096 0.1179 0.1200

0.00000.10000.20000.30000.40000.50000.60000.70000.80000.90001.0000

Val

ue

of

Info

rmat

ion

Correlation

VOI Penalty(R1)

VOI Penalty(R2)

VOI Inv.(R1)

VOI Inv.(R2)

Fig. 6. Relative change in penalty and holding costs when supplier capacity is 15(dataset 2).

C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560 557

ratio of 1.88), the relative value of information appears to increaseas the correlation between the retailers’ demand increases. Thiscorrelation effect is eliminated when the supplier’s capacity is 20,since there is sufficient production capability to satisfy demand ofboth retailers. The results obtained using both datasets illustratethat the supply chain value of information is more valuable whenthe supplier’s capacity is constrained relative to mean demand. Inaddition at moderate levels of supplier capacity, information valueincreases as the correlation between the end-item demand of theretailers increase.

4.1.2. Supply chain partners value of informationSince the magnitude of VOI(�) is relatively small at the largest

supplier capacity level, we initially focus our discussion on thecapacity constrained cases. Figs. 4 and 5 illustrate that all supplychain partners can benefit when the retailer’s inventory informa-tion is shared, since VOI(�) > 0. Recall, information value is mea-sured relative to the increase in profit incurred by each supplychain member as defined by their individual profit Eqs. (9) and(10). In most cases, we observe that information value is higherfor the retailers than for the supplier. In addition, Fig. 5b alsoshows that information value is increasing as the correlation be-tween the end-item demand of the retailers is increasing. The largebenefit achieved by the retailers, relative to the supplier, is largelydue to the fact that the retailers carry all of the risk associated withlost sales. Since increased information translates to fewer lostsales, the retailer benefit is larger. This relationship is illustratedin Fig. 6 for the scenario represented by Fig. 5b. As the demand cor-relation increases, the inventory investment of the retailers also in-creases which causes a reduction in penalty costs. This increasinginventory investment on the part of the retailer is a direct resultof the supplier’s use of information to increase the average per per-iod production. In general, the supplier’s average inventory is high-er when inventory information is shared than when it is not. Therelative increase in inventory costs incurred by the supplier is

0.98, 0.403, and 0.17 for corresponding capacity levels of 10, 15,and 20, using dataset 2. Similar results are seen using dataset 1with corresponding relative increase in supplier’s inventory costsof 0.618, 0.209, and 0.024.

The results in Figs. 4 and 5 also suggest that when capacity issignificantly lower than the total mean demand, the influence ofcorrelation on the value of information is not monotonic, thus indi-cating capacity is more of an influence at those levels. Since supplychain information value is more significant at lower capacities, thecorresponding benefit achieved by the supply chain partners is alsomore significant at lower capacities. When the supplier’s capacitytakes on the largest value (20), the relative change in profit is nearzero for both retailers and on average 1.6% and 2.25% for the sup-plier, using dataset 1 and 2 respectively. Therefore, the value ofinformation is more beneficial to the retailers when the supplier’scapacity is constrained relative to mean demand. In addition, atmoderate levels of supplier capacity, the benefit to the retailersis increasing as the correlation increases.

4.2. Effect of capacity and costs

It is obvious that increasing costs decreases the profitability ofthe supply chain and resulting supply chain members. Therefore,we primarily discuss the impact of these parameters on supplychain information value. The effect of capacity and costs on infor-mation value is summarized in Tables 8–10. Table 8 characterizesthe relationship between supply chain information value, supplierinventory investment, and penalty costs. The results are averagedacross all holding cost parameters for retailer 1. In most cases,information value is increasing with decreasing supplier capacityand increasing penalty costs. When supplier capacity is insufficientto satisfy the mean demand of the retailer, supply chain penaltycosts increase significantly. Since the supplier’s use of the informa-tion results in larger investments in inventory (as reflected in therelative change in inventory costs depicted in Table 8), informationsharing helps to mitigate the effects of shortages reflected in theincreased penalty cost of the retailers.

Table 9 quantifies the magnitude of the information benefit as afunction of the various holding cost factors and the ratio of suppliercapacity to mean demand. In most cases, the magnitude of the ben-efit increases as the ratio of capacity to mean demand decreases. Inaddition, we observe at the extreme values of capacity ratio (3.33and 0.92), information value is increasing in both factors.

We also summarize information value as a function of correla-tion using dataset 2. As illustrated in Table 10, information sharingprovides more value when demand is perfectly correlated and athigher penalty costs.

Table 8Average information value by penalty cost factors (h2 = 1).

Ratio of capacity to mean demand Supply chain information value Relative increase in supplier’s inventory cost

li = 65 li = 75 li = 65 li = 75

3.33 0.0056 0.0055 0.0499 0.03872.53 0.0176 0.0180 0.3096 0.30531.68 0.3214 0.3496 0.8470 0.85231.00 2.9008 4.1882 0.9431 0.94330.92 6.6186 20.6445 0.9887 0.9887

Table 9Supply chain value of information by holding cost factors (li = 75).

Ratio of capacity to mean demand h1

1 2 4

h2 = 13.33 0.0046 0.0051 0.00672.53 0.0173 0.0183 0.01861.68 0.3634 0.3475 0.33781.00 4.0905 4.1677 4.30630.92 18.4309 19.9285 23.5740

h2 = 23.33 0.0048 0.0054 0.00722.53 0.0166 0.0175 0.01781.68 0.3594 0.3495 0.32911.00 4.1684 4.2251 4.42450.92 20.0843 22.2602 27.2054

h2 = 43.33 0.0069 0.0077 0.00902.53 0.0155 0.0159 0.01641.68 0.3515 0.3507 0.32621.00 4.3084 4.4254 4.63770.92 24.5425 27.9342 38.7991

Table 10Information by penalty and holding cost factors (dataset 2, h2 = 2).

Correlation li = 65 li = 75

h1 = 10 1.427 1.7230.25 1.418 1.7110.50 1.410 1.7000.75 1.399 1.6851.00 2.872 4.168

h1 = 20 1.435 1.7370.25 1.427 1.7250.50 1.418 1.7130.75 1.407 1.6981.00 2.913 4.257

h1 = 40 1.452 1.7660.25 1.443 1.7530.50 1.434 1.7410.75 1.421 1.7211.00 2.983 4.424

558 C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560

4.3. Effect of allocation method on information value

We first examine the impact of the allocation method on supplychain information value, and then discuss its effect on the informa-tion value for each supply chain partner. Table 11 summarizes thechange in information value between the rationing based (RB)and equity based (EB) allocation mechanisms calculated asVOID = VOI(�)RB � VOI(�)EB. The sign of VOID provides some indicationas to which method has a higher impact on the change in supplychain profit as a result of information sharing. It should be noted thatthe second allocation method discussed in the model description as-

sumes inventory information sharing exists, and thus is not applica-ble when comparing the profit of a policy with information sharingto one without. For the supply chain information value, Table 11indicates that larger profit gains due to information are achieved ifthe supplier is operating under the RB method. This difference startsto diminish as capacity increases, which is intuitively obvious sincethe supplier has ample capacity to satisfy demand. However, whenthe information value is measured as a function of the profit of eachsupply chain member, a larger difference between the values is ob-served. For example, when the capacity of the supplier is tight, thechange in profit due to information is higher for retailer 1 underthe EB allocation method. In contrast, for retailer 2, the change inprofit due to information is higher under the RB allocation method.The reason for this behavior can be explained as follows. The RBmethod is more biased toward retailer 1 since his orders are allo-cated first by at most half of the supplier’s inventory. Therefore, thereis a chance that more of his order quantity will be satisfied than thatof retailer 2. As a result, under no information sharing and informa-tion sharing, the expected profit is higher with the RB method andthe corresponding information value is lower than that of the EBmethod. This is explained mathematically as follows.

Jis;r1ðRBÞP Jis;r1ðEBÞ ð14ÞJnis;r1ðRBÞP Jnis;r1ðEBÞ ð15ÞJis;r1ð�ÞP Jnis;r1ð�Þ ð16ÞJis;r1ðRBÞ � Jnis;r1ðRBÞ 6 Jis;r1ðEBÞ � Jnis;r1ðRBÞ6 Jis;r1ðEBÞ � Jnis;r1ðEBÞ ð17ÞRelations (14) and (15) represent what is observed in the exper-

imental results, while (16) follows based on the relationship be-tween the completely observable and restricted observationMDPs. Since Jis,r1(RB) � Jnis,r1(RB) 6 Jis,r1(EB) � Jnis,r1(EB), it followsthat the deviation in information value is negative indicating infor-mation value is higher for retailer 1 under the EB method. A similarargument can be made for retailer 2, since his profit is higher underthe equity based allocation method. The biases associated with theallocation method are minimized as capacity increases. Fig. 7 dis-plays the information value by allocation method for each supplychain member at every supplier capacity level.

We briefly discuss the effect of allocation method 2 on the ex-pected supply chain profits when information is shared. Whenthe capacity of the supplier is at the largest value, allocation meth-od 2 provides a slight benefit over methods RB and EB. However,the overall percent increase is less than 0.02%. The magnitude ofthe change in the expected profit is similar at the smaller capacitylevels. When the demand is perfectly correlated, all three methodsyield the same expected profit. With respect to the retailer profits,we observe that the second allocation method is always boundedabove and below by the other two methods, when the supplier’scapacity is most constrained.

4.4. Complete versus partial information sharing scheme

Models II and III allow us to compare the impact of partial infor-mation sharing (retailers only sharing their inventory information)

0

1

2

3

4

5

6

7

8

Val

ue o

f In

form

atio

n

Correlation

Allocation Method

VOI(S)

VOI(R1)

VOI(R2) 0

0.1

0.2

0.3

0.4

0.5

0.6

Val

ue o

f In

form

atio

n

Correlation

Allocation Method

VOI(S)

VOI(R1)

VOI(R2)

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0 0.25 0.5 .750.75 1

0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1

RB EB RB EB

RB EB

Val

ue o

f In

form

atio

n

Correlation

Allocation Method

VOI(S)

VOI(R1)

VOI(R2)

(a) Supplier’s capacity is 20

(a) Supplier’s capacity is 10 (b) Supplier’s capacity is 15

Fig. 7. Information value by allocation method (dataset 2).

Table 11Deviation in information value due to allocation method.

Supplier capacity Correlation Total supply chain Supplier Retailer 1 Retailer 2

Cs = 10 0 0.0032 0.0007 �0.0923 0.09670.25 0.0040 0.0002 �0.1032 0.10870.50 0.0036 �0.0004 �0.0975 0.10010.75 0.0025 0.0007 �0.1265 0.12041.00 0.0007 �0.0007 �0.0273 0.0382

Cs = 15 0 0.0101 0.0053 0.0119 0.01020.25 0.0084 0.0062 0.0107 0.00720.50 0.0065 0.0063 0.0094 0.00410.75 0.0044 0.0036 0.0185 �0.00741.00 0.0005 0.0004 0.1534 �0.1159

Cs = 20 0 0.0000 0.0009 0.0001 �0.00030.25 0.0001 �0.0003 0.0003 0.00000.50 0.0001 0.0032 �0.0006 �0.00030.75 0.0000 0.0001 0.0001 �0.00011.00 0.0003 0.0011 0.0000 0.0002

C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560 559

with that of complete co-operation within the supply chain. Therelative increase in profit between the two models is determinedusing Eq. (13) and in all experimental cases is less than 0.1%. Thissuggests that in this setting, sharing upstream inventory informa-tion with the downstream players may not be beneficial to the sup-ply chain since little additional value can be achieved undercomplete information sharing.

5. Conclusion

The approach presented in this paper illustrates the use ofconstrained MDP models to study the information sharing prob-lem for single-supplier multiple-retailer supply chains. We as-sume unmet demand at both stages is lost and the end-itemdemand of the retailers is correlated. The modeling approachused in this study permit us to not assume any particular formfor the inventory control policy, as the control policy for eachsupply chain member is determined from the model. Therefore,

we can focus on the possible benefits that could be achievedassuming all parties behaved optimally under the various infor-mation sharing schemes. As a result of an extensive computa-tional study, we have characterized the relationship betweeninformation sharing, capacity, demand correlation, and supplyallocation method. More importantly, we have been able to dis-cuss the effects both from a total supply chain profit perspectiveas well the perspective of each supply chain member. Prior mod-els report that the benefits to the retailers are small or non-exis-tent. These differences are attributed to the supply chainstructure and underlying dynamics of the inventory control pol-icy in use. Our results show that the retailer can benefit fromthe information sharing partnership and in many instances, thebenefit can be higher than that of the supplier. Additionally,the magnitude of the benefit is more significant when suppliercapacity is constrained (relative to the total mean demand ofthe retailers) and in highly correlated demand environments.This benefit is achievable because the supplier makes better pro-duction decisions as a result of viewing the inventory information

560 C.M. Helper et al. / Computers & Industrial Engineering 59 (2010) 552–560

of the retailer. This translates to higher inventory levels and thusa higher service level of the supplier in terms of a reduction inlost sales. When the supplier has ample capacity to satisfydemand, the supplier benefit due to information is higher thanthat of the retailers and more significant when the demand isuncorrelated.

Our results suggest that there is an inverse relationship be-tween capacity and information value. Information is more valu-able when capacity is tightly constrained relative to meandemand. Therefore, information allows for higher production andallocation of the scarce capacity. As capacity increases, informationbecomes less valuable since the supplier can meet the demand ofthe retailers and additional capacity helps to mask the effects ofpoor decision making. The effect of capacity on information valueobserved in this work is similar to what was presented in Gavirn-eni (2001) for a make-to-order production–distribution environ-ment, where retailer demand was not correlated.

Lastly, we have demonstrated the influence of supply allocationon information sharing value and characterized the conditions,where one retailer may prefer one method over another. Theseresults show the importance and impact of supply allocation inquantifying information value in capacity constrained environ-ments.

One limitation in our models is that we assume the retailer car-ries all the risk, in the form of penalty costs, for unmet demand.Once the steady state optimal control conditions of the MDP aredetermined, the steady state supply chain penalty costs can be cal-culated. As the information sharing is beneficial to the supplier, theretailer may negotiate with the supplier about the transfer of someof the penalty. Any transfer in penalty costs would only decreasethe information value to the supplier and increase the value tothe retailers.

Appendix A

The algorithm used to implement the allocation method definedin Gavirneni (2001) is formally defined below using the notation ofthe MDP. For simplicity, we omit the equations, where the shipquantity variables are initialized to zero. It should be noted thatwe illustrate this for the case when the inventory level of retailer1 is lower than that of retailer 2. A similar set of statements canbe defined to represent the opposite case.

If x1 < x2

k�1 minðx2 � x1; k1; yÞy0 y� k�1

Do

If x�2 < k2 and y0 > 0k2 k2 þ 1y0 y0 � 1

If k�1 < k1 and y0 > 0k1 k1 þ 1y0 y0 � 1

While y0 > 0

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