The value of VMI beyond information sharing in a single suppliermultiple retailers supply chain under a non-stationary (Rn, Sn) policy

Devendra Choudhary n, Ravi ShankarDepartment of Management Studies, Indian Institute of Technology Delhi, New Delhi, India

a r t i c l e i n f o

Article history:Received 1 March 2014Accepted 9 September 2014Processed by FryAvailable online 18 September 2014

Keywords:Supply chainVendor-managed inventoryInformation sharingNon-stationary stochastic demandService-level

a b s t r a c t

This study aims to determine the value of vendor-managed inventory (VMI) over independent decisionmaking with information sharing (IS) under non-stationary stochastic demand with service-levelconstraints. For this purpose, we utilize mixed-integer linear programming formulations to quantifythe benefits that can be accrued by a supplier, multiple retailers and the system as a whole by switchingfrom IS to VMI. More specifically, we investigate the incremental value that VMI provides beyond IS interms of expected cost savings, inventory reductions, and decrease in shipment sizes from the supplierto the retailers by conducting a large number of computational experiments. Results reveal that thedecision transfer component of VMI improves these performance measures significantly when thesupplier's setup cost is low and order issuing efficiency is high. The benefits offered by VMI are negligibleunder the problem settings where the supplier's order issuing efficiency is low and the production setupserves solely a single replenishment under IS.

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1. Introduction

A VMI initiative encompasses two distinct components –

information sharing and a shift in decision making responsibilityfrom a downstream retailer to the upstream supplier [5]. In otherwords, under VMI, inventory is managed at both echelons by thesupplier. The academic literature and industry reports have shownmixed results from the implementation of VMI and relatedprograms. For example, Spartan Stores had to shut down its VMIinitiative due to higher inventory levels and planning inefficiencies[23]. The study of Blackhurst et al. [1] also suggests that theimplementation of the VMI initiative at a large electronics man-ufacturer actually resulted in increased inventory levels at thedownstream partners. Recently, companies like Toyota and Hondahave moved away from VMI, and are focusing on informationsharing as well as locating suppliers as close as possible to theirfacilities [10]. Nowadays, in spite of these unsuccessful VMIadoption occurrences, there has been growing interest in imple-menting VMI in many supply chains after successful executionby several world-class businesses such as Wal-Mart, Sara Lee,Nabisco, etc. ([17]). Several studies also provide analytical valida-tion for economic benefits offered by VMI by comparing it to atraditional system with no information sharing (e.g., [34,2,11]).

However, these industry reports and studies do not concludewhether benefits could have been achieved mostly through theinformation sharing or the decision transfer component of VMI.

In practice, adoption of VMI over retailer-managed inventorywith information sharing (IS) leads to greater implementationdifficulties and may increase operational costs. Thereby, switchingfrom IS to VMI can be justified if the decision transfer componentgenerates significantly higher value above information sharing.Distinguishing the incremental value that could be achieved fromVMI over IS is a difficult task, and there have been a few attemptsto do so under stationary stochastic demand (e.g., [6,22,20]) andnon-stationary deterministic demand (e.g., [4]). Furthermore, thecomplexity is substantially greater when demand is non-stationaryand stochastic, which is nowadays quite common because of shortproduct life cycles, seasonality, customer buying patterns, etc. [14].For example, while the product life cycle of a Hewlett-Packard (HP)personal computer could be as low as only three months, HP digitalcameras have an average life cycle of less than 12 months. Eventhrough the launch, ramp, peak, and end-of-life phases of theproduct life cycle, not only is demand non-stationary, but also theuncertainty changes (Fig. 1). The demand for many products has aseasonal component or experiences monthly/quarterly “hockeystick” patterns because of sales-force incentives and customerbuying behavior. For example, Microsoft experiences about 66% ofthe annual demand for its Xbox video game consoles during the last13 weeks before Christmas. Similarly, a peak in demand is observedfor Dell's enterprise products in the last week of every month.

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Omega

http://dx.doi.org/10.1016/j.omega.2014.09.0040305-0483/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: dceca@rediffmail.com (D. Choudhary).

Omega 51 (2015) 59–70

The extent and intensity of competitive advantage gained fromVMI above and beyond IS varies from company to companydepending on the demand process and business environment inwhich a supply chain operates. Realizing these facts, this studyaims to determine the incremental value offered by VMI beyondthat of IS alone under non-stationary stochastic demand withservice-level constraints. For this purpose, we first model a serialsupply chain consisting of a single upstream supplier and multipledownstream retailers under both the IS and VMI initiatives. Then,a comprehensive numerical study is carried out considering alarge number of business settings to figure out the conditionswhere the value of VMI over IS is significant. In the IS initiative, weconsider that the supplier and retailers manage their inventoryindependently. The retailers determine their own replenishmentschedules and place orders with the supplier. Moreover, theretailers provide full information to the supplier via informationtechnology tools such as electronic data interchange (EDI) orthrough internet [6]. In other words, the supplier gets an accessto the retailers' replenishment-up-to levels, expected inventorylevels, and timings of planned orders as well as demand distribu-tion data. Based on this information, the supplier decides itsproduction schedule to meet orders of the retailers. On the otherhand, under the VMI initiative, the supplier also manages inven-tory at the retailers along with full information sharing. Earlierstudies compare VMI with IS mainly in terms of the economicbenefits. It is less clear whether the benefits have been achievedthrough a decrease in inventory levels or consolidation of ship-ments at the expense of increased inventory levels. Also, there is alack of clarity on whether shipment sizes from the supplier toretailers increase or decrease using VMI [32,33,12]. In this paper,we assess the incremental benefits offered by VMI above andbeyond IS on various supply chain performance measures such asexpected cost savings, reduction in inventory levels and increasein replenishment deliveries at the retailers. A comparison of VMIwith IS based on these performance measures helps in clarifyingsituations where the economic benefits can be realized eitherthrough increased frequency of shipments and decrease in inven-tory levels, or through consolidation of shipments.

2. Problem statement and background

We consider a two-echelon serial supply chain in which aproduct is delivered from a common supplier to a set r¼{1,…, R}of retailers over a time horizon T. Each discrete time period t¼{1,…, T} is of the same duration. We assume that the retailers servegeographically dispersed (thus independent) retail markets. Theend-user demand at each retailer in each period is normallydistributed with a known probability density function. In addition,for each retailer, different periods have mutually independentdemands, which vary over time. In case of not fulfilling end-user

demand, stock-out occurs at the retailers' side and demand isbackordered. Moreover, the quantity of backorders at the retailersend is restricted by a cycle service-level requirement, which isvery common in practice where a stock-out situation is costly andindependent of its duration [30]. As is the case in practice, it isassumed that the supplier has several sources of the product suchas overtime production and/or subcontracting to meet the order ofretailers, which makes the supplier's production capacity suffi-ciently high. The quantity is produced or made available at mostonce in each period. We ignore the lead time of ordering andproduction and hence the required replenishment quantities aremade available in the same period. This assumption is in line withprevious studies [6,22,4]. The space available to store inventoryat the end of each period for both echelons is unconstrained.While the existing literature has considered stochastic single-itemdynamic lot-sizing problem at a single-echelon level, the same hasnot been studied so far at two-echelon level, even though it is awell known fact that an integrated approach may provide moreeffective means to reduce system-wide inventory.

Bookbinder and Tan [3] propose three policies – static, dynamic,and static-dynamic – to deal with non-stationary stochasticdemand. Under the static uncertainty policy, the replenishmentschedule and quantities are obtained in advance for the entireplanning horizon. However, under the dynamic uncertainty policy,one may revise the replenishment levels in subsequent periods byupdating the inventory status as demand evolves. While the formerpolicy is the most expensive because of larger safety stock require-ments, the latter policy suffers from quantity- and order-orientednervousness because each period's lot-size is chosen only at thestart of that period. The deviation in planned orders and timings isknown as quantity- and order-oriented nervousness, respectively.To combine the positive features of both the policies, Bookbinderand Tan [3] propose a static-dynamic uncertainty policy which isalso known as non-stationary (R, S) type of inventory control policy.This policy is characterized by two control parameters Rn and Sn

for each replenishment cycle n, where Rn denotes the length ofn'th replenishment cycle and Sn stands for the replenishment-up-tolevel of the n'th replenishment [26,15]. In this policy, at thebeginning of planning horizon, non-stationary review intervals Rn

as well as replenishment-up-to levels Sn are determined in advance.But the actual order quantity in each replenishment period isdecided only after the demands in the preceding periods have beenobserved. Although this policy is liberated from order-orientednervousness, but it suffers from quantity-oriented nervousness.

The sequential procedure of determining the timings andreplenishment-up-to levels ignores the interaction between thesetwo problem aspects. As a result, the heuristic approach of Book-binder and Tan [3] may not provide optimal solutions. Taking thisaspect into account, Tarim and Kingsman [25] formulate a mixed-integer programming model to determine both review intervalsand replenishment-up-to levels in a single step. This formulationoperates under the assumption that excess stock is carriedforward and not returned to the supply source if it exceedsthe replenishment-up-to level for a review cycle. As a result,the model only computes suboptimal policy parameters and anapproximate expected total cost [18]. Tempelmeier [27] extendsthe work of Tarim and Kingsman [25] by replacing cycle service-level requirement with cycle fill rate. A heuristic solutionprocedure is proposed by Tempelmeier [28] to determine thereplenishment schedules under a capacity constrained resourcefor multiple products.

The non-stationary (R, S) type of inventory control policy is amore accurate representation of industrial practice as pointed outby Sox [24] due to the fact that it is liberated from order-orientednervousness, which is considered to be most critical in practice [31].Even more, the (R, S) policy also dominates over the (s, S) policy in

0

50

100

150

200

250

300

350

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar

Dem

and

Non-stationary deterministic demand Non-stationary stochastic demandStationary stochastic demand

Fig. 1. Demand processes.

D. Choudhary, R. Shankar / Omega 51 (2015) 59–7060

terms of stability performance even when the inventory plan isregenerated throughout the planning horizon [13]. It is suggested byTunc et al. [31] that the (R, S) policy could be an effective strategy forcoordinating supply chain inventories across multi-echelons espe-cially when quantity-oriented system nervousness is not of muchconcern.

All the above researchers have studied a single-stage stochastic lot-sizing problem, where they have included setup cost, and cycleservice-level/fill rate constraints or stock-out costs. However, to thebest knowledge of the authors, no paper deals with all the followingaspects of the planning problem under consideration: a two-stagestochastic lot-sizing problemwith fixed setup and ordering costs, non-stationary demand, and a cycle service-level approach.

Fry et al. [6] investigate the benefits offered by VMI over ISunder a minimum and maximum (s, S) contract agreed onbetween a supplier and a retailer. Using renewal theory approach,Salzarulo and Jacobs [20] study a serial supply chain with andwithout IS and a VMI initiative under an (s, S) contract to quantifythe benefits offered by IS and to identify those benefits that areoffered by a shift in decision making responsibility alone. Theirstudy reports that VMI can offer an average cost savings of 2.2%over IS. Savaşaneril and Erkip [22] consider an (R, nQ) policy,where the reorder point R is a decision variable and the orderquantity Q is a parameter, to assess the motivation for the supplierbehind joining VMI with and without consignment beyond ISunder a service-level requirement. These studies consider station-ary stochastic demand. Even more, these studies do not considersetup and ordering costs, and multiple retailers at downstreamechelon, which are important cost components and businesssettings, respectively, in practice. Periodic review (s, S) and (R, nQ)inventory policies with a fixed replenishment-up-to level typicallydeal with a stationary stochastic demand. In most industrial context,however the demand is non-stationary stochastic with seasonalpatterns, trends, and limited-life business cycles [14,9]. Often, astationary demand is assumed even if it is actually non-stationarydue to less computational complexity. Tunc et al. [29] investigate thecost of using stationary demand as an approximation to the non-stationary demand. They find that such an assumption could be veryexpensive depending on the magnitude of demand variability. In caseof non-stationary demand, use of (s, S) or (R, nQ) inventory policyeither leads to a very high production level causing higher inventorylevels when demand is low, or to a low production level causing stock-out when demand is very high. Therefore, it is worthwhile toinvestigate inventory policy with non-stationary replenishment-up-to levels and review intervals for the problem under consideration inthis paper.

Particularly in this study, coordination of inventories along atwo-echelon supply chain comprising of a single supplier andmultiple retailers is optimized under a static-dynamic uncertaintypolicy. More precisely, we consider an (R, S) policy, also known asnon-stationary replenishment cycle policy. Under this policy,production and replenishment timings as well as correspondingup-to levels are considered as decision variables. In addition,production and replenishment quantities are considered as ran-dom variables and depend on the development of demand.In other words, real-time information about inventory levels ofthe retailers and supplier is taken into consideration whiledetermining production and replenishment quantities whendemands in the preceding periods have been realized.

A much more extensive motivation, literature review, andadditional discussion can be found in Choudhary et al. [4].They assess the value of shift in inventory ownership and shiftin decision making responsibility above and beyond IS for asupplier, a retailer and the system as a whole considering non-stationary deterministic demand. The present paper is differentfrom Choudhary et al. [4] in the sense that it investigates the value

of VMI above and beyond IS for a single supplier, multiple retailersand the system as a whole under non-stationary stochasticdemand with service-level constraints, that is a more realisticscenario. We have also extended the single-stage stochastic lot-sizing model of Tarim and Kingsman [25] towards a two-stage ISand VMI initiatives.

3. Analytical model development

This section details mixed-integer programming formulations usedin this study to determine optimal schedules of the retailers andproduction schedule of the supplier under both the IS and VMIinitiatives.

The mixed-integer programming formulation of Tarim andKingsman [25] allows simultaneous determination of the reviewintervals and order-up-to levels with some mild assumptions. Thismodel aims to minimize the expected costs of meeting non-stationary stochastic demand over some finite planning horizon,given a service-level constraint on the probability of stock-out.Therefore, without loss of generality, we extend the single-stagemixed-integer programming formulation of Tarim and Kingsman[25] to a two-stage serial supply chain consisting of a single supplierand multiple retailers under the IS and VMI initiatives. This will allowsimultaneous determination of the number and timings of replenish-ments and order-up-to levels for each retailer as well as to determinethe supplier's production schedule that will minimize expected costsof meeting end-user non-stationary stochastic demand for givenservice-level requirements.

Analytical models applied in this study to determine optimalschedules of the retailers and production schedules of the supplierunder both the IS and VMI initiatives are provided below.

3.1. Indices, parameters, and decision variables

The following notations are adopted in this study:

Indicesr set of retailers, r¼1,…, R.t set of discrete time periods, t¼1,…, T.j set of replenishment periods, j¼1,…, m.i set of production periods, i¼1,…, n.k length of the relevant risk period if a

replenishment is planned in period t – kþ1 tocover the demand of periods t – kþ1,…, t.

Parametersdrt mean demand (a random variable) for the retailer

r in period tort fixed cost incurred by the retailer r per order

issuing in period thrt inventory carrying cost per item per period at the

retailer r in period tαcr target cycle service-level requirement at retailer rSt fixed cost incurred by the supplier per setup in

period tht inventory carrying cost per item per period at the

supplier in period tβr supplier's efficiency for issuing an order on behalf

of the retailer r under VMI(1 – βr)ort supplier's cost of issuing an order on behalf of the

retailer r in period t under VMI

G�1Y ðt� kþ 1;tÞ ðαcrÞ α-quantile of the inverse cumulative distribution

function of dr(t-kþ1)þ…þdrtM a large number

D. Choudhary, R. Shankar / Omega 51 (2015) 59–70 61

Decision variablesRLrt target inventory level (replenishment-up-to

level) at the retailer r at the beginning of period tzrt binary variable indicating whether retailer r is

replenished or not in period tPLt target inventory level (production-up-to level) at

the supplier at the beginning of period tzt binary variable indicating whether supplier

produces or not in period t

Intermediate variablesIrt inventory level at the retailer r at the end of

period tIt inventory level at the supplier at the end of

period txrt replenishment quantity at the retailer r from the

supplier in period txt quantity that supplier produces in period tPrtk indicator variable: Prtk¼1, if the last

replenishment period at the retailer r prior toperiod t is period t – kþ1; Prtk¼0, otherwise

3.2. IS initiative

In the IS initiative, the supplier and retailers act independentlyand attempt to optimize their own cost objective with availableinformation under the given problem environment.

3.2.1. Retailers' model under ISEach retailer solves a Tarim and Kingsman [25] model as

defined in Eqs. (1)–(9) to obtain non-stationary replenishment inter-vals and replenishment-up-to levels over the planning horizon.

Minimize E TCISr

n o¼ ∑

T

t ¼ 1ortzrtþhrtE Irtf gð Þ r¼ 1; :::;R ð1Þ

subject to

RLrtZE Irðt�1Þ� �

t ¼ 1;…; T ð2Þ

E Irtf g ¼ RLrt�E drt� �

t ¼ 1;…; T ð3Þ

RLrt�E Irðt�1Þ� �

rMzrt t ¼ 1;…; T ð4Þ

E Irtf gZ ∑t

k ¼ 1G�1Y ðt � kþ 1;tÞ ðαcrÞ� ∑

t

u ¼ t�kþ1E dru� �" #

Prtk t ¼ 1;…; T ð5Þ

∑t

k ¼ 1Prtk ¼ 1 t ¼ 1;…; T ð6Þ

PrtkZzrðt�kþ1Þ � ∑t

u ¼ t�kþ2zru t ¼ 1;…; T ; k¼ 1;…; t ð7Þ

Prtk;RLrt ; E Irtf gZ0 t ¼ 1;…; T ; k¼ 1;…; t ð8Þ

zrtA 0;1f g t ¼ 1;…; T ð9Þ

The objective function (1) minimizes the sum of the orderingcosts and the expected inventory carrying costs, where the netinventory (Irt) is a random variable. The first term in (1) representsthe total order issuing costs while the second term gathers theexpected inventory holding costs for the entire planning horizon.It may be noted that ordering cost depends on whether the retaileris replenished or not in period t; therefore binary variable zrt isused in the expression of the ordering cost.

Constraints (2) ensure that the retailer cannot place negativeorder quantities. Hence, if the inventory at the end of periodt – 1 is greater than replenishment-up-to level planned for periodt, nothing is ordered or replenished. The inventory at the end ofevery period is gathered by Eq. (3). If RLrt¼ Ir(t-1), then no replen-ishment order is placed at the beginning of period t. The retaileris replenished at the beginning of period t, if the targetreplenishment-up-to level RLrt is greater than inventory levelIr(t�1) and the replenishment quantity is equal to the differenceRLrt – Ir(t�1), which is modeled with Constraints (4). In order tofind the exact periods when replenishment takes place, indicatorvariable Prtk is used to gather the exact knowledge of the relevantrisk period, which starts with a replenishment period and ends inthe last period prior to the next replenishment period. If the lastreplenishment period t is k – 1periods away, or, equivalently, if thelast replenishment period prior to period t is period t – kþ1, thenPrtk¼1. Thus, k is the length of the relevant risk period that mustbe covered by the replenishment quantity in period t – kþ1. If Prtkvalues are known, Constraints (5) ensure that the amount of stock-out at the retailer cannot be more than given cycle service-levelrequirement. The terms in square bracket of Constraints (5)actually calculate minimal safety stock levels required to meetuncertain demand and the expected proportion of replenishmentcycles with stock-outs not more than cycle service-level require-ment, αcr. Eq. (6) and Constraints (7) ensure that the Prtk are alwaysbinary variables, which take the value 1 if a replenishment isplanned in period t – kþ1 to cover the demand of periods t – kþ1,…, t. For a detailed discussion and calculation of G�1

Y ðt� kþ 1;tÞ ðαcrÞ andPrtk, we refer to Tarim and Kingsman [25] and Tempelmeier [27].Finally, Constraints (8) and (9) are used to force non-negativevalues and binary restrictions on the model.

The above model provides replenishment periods (τ1; τ2; :::; τm)as well as replenishment-up-to levels RLrτj (j¼1,…, m) for theseperiods at a retailer over the planning horizon. Let the unique

optimal solution consists of replenishment-up-to levels (RLISrτ1 ;RLISrτ2

; :::;RLISrτm ) and expected inventory positions EfIISrðτ1 �1Þg ;�

EfIISrðτ2 �1Þg ; :::; EfIISrðτm �1ÞgÞ at the beginning of each replenishment

period for every retailer. Let E TCISnr

n obe the minimum expected

total cost of each retailer. The actual replenishment quantitiesdepend on the development of the demands and therefore arerandom variables. For each retailer under the static-dynamicuncertainty policy, the actual replenishment quantity Efxrτj g inreplenishment period j is obtained from Eq. (10) only after thedemands up to period j – 1 have been observed. The actualreplenishment quantity at the retailer r is zero in period j, if theinventory level at the end of period j – 1 is greater than or equal tothe replenishment-up-to level required in the period j; otherwise,replenishment size is equal to the difference betweenreplenishment-up-to level required in the period j and inventorylevel available at the end of period j – 1, that is in other words,

Efxrτj g ¼RLrτj �EfIrðj�1Þg RLrτj 4EfIrðj�1Þg

0 otherwise

�j¼ 1;…;m; r¼ 1;…;R

ð10Þ

3.2.2. Supplier's model under ISUnder the IS initiative, the supplier has full knowledge of each

retailer's timings of orders (τ1; τ2; :::; τm), replenishment-up-to

levels (RLISr1;RLISr2; :::;RL

ISrT ), expected inventory levels at the begin-

ning of each period (EfIISr0g ; EfIISr1g ; :::; EfIISrðT�1Þg), and end-userdemand distributions over the planning horizon. Fry et al. [6],Salzarulo and Jacobs [20] and Choudhary et al. [4] incorporatesimilar assumptions to isolate the benefits offered by the IS and to

D. Choudhary, R. Shankar / Omega 51 (2015) 59–7062

identify those benefits that are offered by the decision transfercomponent of VMI. Under the static-dynamic uncertainty policy,information about inventory levels, replenishment timings andtheir corresponding up-to-levels is sufficient for the supplier tooptimize its production schedule. This information is utilizedby the supplier to plan production and inventory activitiesmore efficiently as compared to no IS. In other words, thereplenishment-up-to and expected inventory levels decided byeach retailer using Eqs. (1)–(9) are now parameters for thesupplier to decide optimal production timings ℓi (i¼1,…, n) andproduction-up-to levels PLt over the planning horizon throughfollowing model.

Minimize EfTCISSupplierg ¼ ∑

T

t ¼ 1StztþhtEfItgð Þ ð11Þ

Subject to

PLtZ ∑R

r ¼ 1RLISrt�E IISrðt�1Þ

n o� �t ¼ 1;…; T ð12Þ

E Itf g ¼ PLt� ∑R

r ¼ 1RLISrt�E IISrðt�1Þ

n o� �t ¼ 1;…; T ð13Þ

PLt�E It�1f grM:zt t ¼ 1;…; T ð14Þ

PLt ; EfItgZ0 t ¼ 1;…; T ð15Þ

ztAf0;1g t ¼ 1;…; T ð16Þ

while the first term in Eq. (15) represents the setup costs, thesecond term gathers the expected inventory carrying costs overthe planning horizon. It may be noted that setup cost depends onwhether production takes place or not; therefore binary variable ztis used in the expression of the production setup cost. We assumethat per unit variable production cost as well as transportation andshipment release costs per unit shipped from the supplier toretailers are stationary. Thereby, these costs have no effect on thedetermination of the optimal production schedule and can beexcluded from the supplier's objective function.

Constraints (12) relate the supplier's production-up-to levelswith the retailers' replenishment-up-to levels and expected netinventory. Eq. (13) gather net inventory at the supplier. It may benoted from Eqs. (12) and (13) that information about the retailers'expected inventory level leads to a reduction in inventory level atthe supplier. Constraints (14) ensure that the supplier would incurfixed setup cost in period t, if the target production-up-to levelPLt is greater than It – 1. Constraints (15) and (16) are used toforce non-negative values and binary restrictions on the model,respectively.

The above model gives a production schedule for the supplierat beginning of the planning horizon. However, only the timings ofproduction ℓi (i¼1,…, n) is useful information for the supplier asrandomness in order quantities of the retailers, given by Eq. (10),leads to uncertainty in quantities to be produced by the supplier.Additionally, the supplier would like to make use of real timeinformation about inventory levels of the retailers to reduce itson-site inventory requirements. Since in the static–dynamicuncertainty policy, the actual production quantities depend onthe development of the end-user demands and consequentlyrandom order quantities of the retailers; therefore they arerandom variables.

Expected total system cost under IS initiative can be expressedby the following equation.

EfTCISSystemg ¼ ∑

R

r ¼ 1EfTCISn

r g� �

þEfTCISn

Supplierg ð17Þ

3.3. VMI initiative

In the VMI initiative, we consider that the supplier and eachretailer agree to a contractual agreement with two conditions. Thefirst is certain service-level requirement set by each retailer, αcr.The second is benefit sharing agreement in which a potentially-efficient system (i.e., there are system-wide cost savings, andeither the supplier or the retailers are better-off) is to be turnedinto an efficient one (a win–win situation for all the partners)through order issuing cost sharing or a price discount [2].In addition, in line with the existing literature [2,4], we take intoaccount changes in the cost structures of firms involved due to theshift in decision making responsibility. More precisely, the VMIleads to transfer of the order issuing cost, ort, from the retailers tothe supplier. There are often many steps involved in an orderingprocess. Each ordering step consumes time and resources, andmany return little or no value to the retailers. The VMI offersa promise of reduced ordering costs as compared to IS byeliminating several non-value added steps involved in the order-ing process. The supplier's ability to eliminate non-value addedsteps for issuing an order on behalf of the retailer is termed asorder issuing efficiency (βr), where 0rβro1. Thus, under VMI, thesupplier pays (1 – βr)ort for issuing an order where ort representsorder issuing cost of the retailer r under IS.

With this background, we extend Tarim and Kingsman [25]model under the VMI initiative as follows:

Minimize E TCVMISupplier

n o¼ ∑

T

t ¼ 1StztþhtEfItgð Þ

þ ∑R

r ¼ 1∑T

t ¼ 11�βr� �

ort :zrtþhrtE Irtf g� �ð18Þ

Subject to

PLtZ ∑R

r ¼ 1RLrt�E Irðt�1Þ

� �� �t ¼ 1;…; T ð19Þ

E Itf g ¼ PLt� ∑R

r ¼ 1RLrt�E Irðt�1Þ

� �� �t ¼ 1;…; T ð20Þ

Constraints (2)–(9) for r¼1,…, R, and Constraints (14), (15) and(16).

The objective function optimizes expected total system-widecosts under VMI. The first and second terms in Eq. (18) gathersupplier's setup costs and expected inventory carrying costs,respectively. The third term represents that the supplier pays(1 – βr)ort for each order (s)he places on behalf of the retailers.Finally, the retailers are charged expected holding costs for eachunit of inventory stored at their premises, which is gathered by thelast term in the objective function.

The above stated stochastic dynamic VMI model determinesoptimum production schedule of the supplier as well as optimumreplenishment schedules for agreed upon cycle service-levelrequirements for every retailer. Thus, at the beginning of theplanning horizon, the production periods ℓi (i¼1,…, n) andproduction-up-to levels at the supplier, as well as the replenish-ment periods τj (j¼1,…, m) and replenishment-up-to levels forevery retailer, are determined in advance. In the static–dynamicuncertainty policy, the actual production and order quantities aredetermined at future production and replenishment periodsrespectively, and depend upon the development of the demandsrealized period by period over the planning horizon. The actualreplenishment quantities are obtained for each retailer usingEq. (10) for the replenishment schedule decided by the supplier

D. Choudhary, R. Shankar / Omega 51 (2015) 59–70 63

under VMI. Similarly, the actual production quantities are com-puted for the supplier.

4. Computational experiments

In this section, we conduct numerical experiments to explorethe value of VMI beyond IS, the allocation of benefits across supplychain partners, and the impact of system parameters on the supplychain performance measures such as reduction in expected costsand inventory levels, and increase in replenishment frequencies atthe retailer(s). We consider two types of serial supply chains, onewith a single retailer, and other with multiple retailers.

4.1. A supply chain with single supplier and single retailer

Here, we investigate how large the value of VMI can be above andbeyond IS when a product is produced by a supplier (or manufac-turer) and then sold to end-consumers through a single retailer.

To insure that the results are reflective of the general type ofbusiness environment and not a specific scenario, we use a test setinvolving a variety of demand and cost parameters. We conduct afull factorial analysis comprising of 972 test instances by using thefollowing set of parameters: demand patterns DP ϵ {RAND1,RAND2, SIN1, SIN2, LCY1, LCY2}, coefficient of demand variationCV ϵ {0.10, 0.30, 0.50}, cycle service-level requirement αcr ϵ {0.90,0.95, 0.99}, order issuing cost ort ϵ {200, 600, 1200}, supplier'ssetup cost St ϵ {50, 500, 1500} and order issuing efficiency βr ϵ {0,0.3}. In all the experiments, we set ht¼1and hrt¼2. We do not varyinventory holding costs at both echelons, because replenishmentand production decisions depend on the trade-off between hold-ing cost and ordering/setup cost. In other words, the impact ofincreasing holding cost is the same as that of decreasing order/setup cost. The planning horizon is set to 12 periods with no initialinventory in all the experiments.

Fig. 2 illustrates the demand patterns under consideration. Weconsider three demand patterns, namely, random (RAND), sinu-soidal (SIN) and life-cycle (LCY). Even more, we set two levels foreach demand pattern to investigate the impact of demand lumpi-ness on the incremental value offered by VMI over IS. The demandlumpiness is set at a higher value for RAND2, SIN2 and LCY2 thanRAND1, SIN1 and LCY1. Furthermore, to abandon any effect thatmay occur due to variation in the total demand, these demandpatterns are designed in such a way that the total demand overthe planning horizon is same for all the demand patterns. Thetotal mean demand summed over the planning horizon for eachdemand pattern is 1200 units. In other words, for all demandpatterns the average of mean demands over the planning horizonis fixed at 100 units. We consider stationary values for theremaining parameters to investigate how supply chain

performance measures are affected by varying the levels of theseparameters.

The results are summarized in Table 1. Beyond IS, the system-wide cost savings vary from 0% to 7.17% due to the shift in decisionmaking responsibility when order issuing efficiency βr is zero. Theincremental value of VMI is at the lowest level when the supplier'sorder issuing efficiency is low and a single production setup isused to serve solely a single replenishment under IS. Experimentalresults indicate that the VMI offers an average cost savings of 1.43%over IS even when βr¼0. However, system-wide inventory levelsincrease by 4.58% on average due to decrease in replenishmentfrequencies at the retailer by 12.48%. This observation suggeststhat the decision transfer component of VMI offers cost savingsdue to aggregation of replenishment and production quantities ina few settings when βr is zero.

We observe that increase in βr has significant positive impacts onall the three supply chain performance measures considered in thisstudy. The VMI offers an average cost savings of 12.50% over the ISwhen βr increases by 30%. In addition, system-wide inventory levelsdecrease by 3.67% on average due to increase in replenishmentfrequencies at the retailer by 1.8%. Under VMI, as compared to IS, theresults further reveal that system-wide inventory levels and ship-ment sizes from the supplier to retailer decrease in the majority ofbusiness settings only when βr¼0.30. This suggests that a VMIinitiative outperforms an IS initiative on all the performance mea-sures considered in this study only when a supplier places orderswith significant efficiency on behalf of the retailer.

The effect of varying the system parameters on the supplychain performance measures is more unidirectional when βr is at ahigh level. Fig. 3 reflects the impact of system parameters on the

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Table 1Experimental results: a study of single supplier–single retailer supply chain.

Independent systemparameters

Dependent supply chain performance measures

Expected costsavings (%)

Exp. inventoryreduction (%)

Exp. increase inrep. freq. (%)

βr¼0 βr¼0.30 βr¼0 βr¼0.30 βr¼0 βr¼0.30

Demand pattern (DP)RAND1 1.39 12.59 �5.45 5.41 �14.77 2.41RAND2 1.53 12.67 �2.95 5.06 �8.16 5.30SIN1 1.33 12.12 �4.13 1.76 �13.00 �0.09SIN2 1.40 12.65 �5.34 3.76 �12.12 1.84LCY1 1.52 12.38 �6.58 2.28 �15.51 1.05LCY2 1.40 12.58 �3.04 3.74 �11.32 0.27

Demand coefficient of variation (CV)0.10 1.93 13.39 �6.42 1.09 �15.73 �4.110.30 1.27 12.35 �4.50 5.53 �12.27 4.740.50 1.08 11.76 �2.83 4.38 �9.44 4.77

Service-level (αcr)0.90 1.46 12.73 �4.67 3.90 �12.78 1.090.95 1.34 12.48 �4.57 3.61 �12.39 1.840.99 1.49 12.29 �4.51 3.50 �12.27 2.46

Order issuing cost (ort)200 1.29 10.97 �3.09 2.88 �11.52 0.60600 1.40 12.67 �2.50 7.20 �12.45 3.601200 1.59 13.87 �8.16 0.92 �13.47 1.19

Setup cost (St)50 0.17 15.91 �5.25 9.65 �3.36 11.03500 2.06 12.08 �9.47 �2.15 �14.81 �2.741500 2.05 9.51 0.97 3.52 �19.27 �2.88

All test instancesMean 1.43 12.50 �4.58 3.67 �12.48 1.80Minimum 0.00 5.22 �86.35 �60.67 �50.00 �25.00Maximum 7.17 19.57 31.47 45.06 28.57 57.14Std. deviation 1.50 3.28 14.22 12.93 12.29 14.19

D. Choudhary, R. Shankar / Omega 51 (2015) 59–7064

supply chain performance measures for a general type of businessenvironment by taking average values of two extreme cases of theorder issuing efficiency. It is evident from Table 1 that demandpattern and its lumpiness have an influence on the supply chainperformance measures. For example, when βr is zero, the costsavings vary from 1.33% to 1.53% as demand pattern changes fromSIN1 to RAND2. For these demand patterns, the cost savingschange from 12.12% to 12.67% when βr¼0.30. In general, examina-tion of Fig. 3 reveals that higher level of demand lumpiness resultsin a substantial improvement in all the supply chain performancemeasures derived from the VMI. For example, with a change indemand pattern from RAND1 to RAND2, the cost savings increasefrom 6.99% to 7.10% on an average. Similarly, while inventory levelsreduce from �0.02% to 1.06%, the variation in percentage increasein replenishment frequency changes from �6.18% to �1.43%. Thisresult differs from previous studies (e.g., [19,4]), which suggestthat an increase in demand lumpiness provides less opportunityfor shipment consolidation, as well as synchronization of produc-tion and replenishment cycles under non-stationary deterministic

demand. However, under non-stationary stochastic demand usinga static–dynamic uncertainty policy in particular, the risk period isshorter, which leads to less safety stock requirements as thedecision on the amount ordered is postponed as late as possible.Due to this fact, even if the demand is lumpy, the VMI facilitatesbetter synchronization of supply and demand in comparison to IS.Consequently, a reduction in safety stock requirements leads todecrease in the system-wide inventory and thus total cost.

It is apparent from Table 1 that demand coefficient of variation(CV) has significant impacts on the three supply chain perfor-mance measures. The cost savings decrease as CV changes fromlow level to high level. In other words, moving from IS to VMIoffers greatest cost savings when CV is at the lowest level. Onthe other hand, Fig. 3 shows that the VMI offers significantimprovement in terms of percentage inventory reduction andincrease in replenishment frequency performance criteria whenCV is large. Thus, from a cost savings perspective, switching fromIS to VMI is more attractive when CV is low. On the contrary, ifremaining two performance criteria are taken into account, then

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D. Choudhary, R. Shankar / Omega 51 (2015) 59–70 65

moving to VMI beyond IS is more attractive when CV is large.This counter-intuitive behavior can be explained by observationthat the cost savings are achieved either by consolidating replen-ishment and production quantities, and/or through reducinginventory. The lower value of CV enables to take advantage ofaggregating replenishment and production quantities. Theseobservations can be verified from Table 1 which shows thatinventory levels at the retailer increase under VMI compared toIS with decrease in CV due to large shipment sizes even when βr islarge. These observations are consistent with previous study(e.g., [16]), which shows that VMI is more attractive for productswith stable demand and IS remains to be more valuable forproducts with high demand variance. However, our result differsfrom previous studies of Fry et al. [6] and Savaşaneril and Erkip[22], which show that VMI offers higher cost savings than IS whenCV is large under stationary stochastic demand conditions.

The experimental results indicate that the influence of varyingαcr is not unidirectional on the percentage cost saving measurewhen βr is zero. In such a situation, one can see that increasein system-wide inventory level is lower when αcr is large. This canbe explained by observing shipment frequency, which changesfrom �12.78% to �12.27% as αcr varies from 0.90 to 0.99. Incontrast, when βr¼0.30, delivery frequency from the supplier toretailer improves from 1.09% to 2.46% as αcr changes from low levelto high level. In general, examination of Fig. 3 reveals that theperformance of VMI over IS in terms of both the expected cost andinventory reduction criteria, marginally deteriorates with increasein αcr. Our observation of lower cost savings with increase in cycleservice-level requirements also corroborates with the finding ofSavaşaneril and Erkip [22].

Moving from IS to VMI, results in Table 1 show that the costsavings increase as ordering cost changes from low level to highlevel. A significant reduction in inventory levels and shipmentsizes is observed when ort¼600 and βr¼0.30. It is interesting toobserve that the cost benefits are almost negligible when bothsetup cost and order issuing efficiency are at low levels. This isbecause of the fact that such a situation does not provideadditional opportunity under VMI as compared to IS, to aggregateproduction and delivery quantities or reducing order costs. Thisobservation suggests that no value can be realized by moving fromIS to VMI if ordering process of downstream partner is already leanand setup cost of the upstream partner is low because of usingsingle-minute exchange of die (SMED), which is the businessscenario for companies like Toyota and Honda and their suppliers.Thereby, our observation explains to some extent why thesecompanies have recently moved away from the VMI and arefocusing more on the information sharing as pointed out byHandfield [10]. On the contrary, when βr¼0.30, greater cost savingis offered by VMI in comparison to IS when setup cost is lower.A low setup cost and a high order issuing efficiency enable thesupplier to produce more frequently and replenish the retailerusing smaller shipment sizes. Thus, switching from IS to VMI ismore attractive when setup cost is at a low level and βr is at a highlevel. For example, when St¼50 and βr¼0.30, expected systeminventory reduces by 9.65% and delivery frequency at the retailerimproves by 11.03%. In a general business environment, examina-tion of Fig. 3 reveals that shipment sizes from the supplier to theretailer increase under VMI as compared to IS when setup costchanges from low level to high level. However, system-wideinventory may not increase even when setup cost is large. This isdue to the fact that a shift in decision making responsibilityprovides the flexibility to the supplier to decide upon productionand replenishment schedules in such a way that it enables greaterreduction in the supplier's inventory level, as compared toincrease in the retailer's on-site stock. Taking into account all thethree supply chain performance measures, Fig. 3 exhibits that

VMI is likely to be more valuable beyond IS when setup cost issignificantly lower.

Experimental results show that the economic benefits arerealized mainly through consolidation of the replenishment quan-tities into the economic production lot-sizes, particularly whensetup cost of the supplier is high and the retailer places smallersize orders frequently under IS. In such situations, if the supplierhas a limited capacity, then production lot-sizes cannot beincreased, and hence switching from IS to VMI may not beattractive. Therefore, it is logical to conclude that the significanceof VMI over IS is greater when higher capacity is available at thesupplier, and vice-versa. This logic is consistent with previousstudies (e.g., [8,7,21]). On the other hand, when setup cost is lowand order issuing efficiency is high, experimental results revealthat replenishment and production quantities decrease underVMI as compared to IS. In such situations, higher benefits canbe realized using VMI over IS, even if capacity available at thesupplier is tight.

In the above discussions, we analyze benefits offered by VMIover IS for the system as a whole. The value of VMI beyond IS forthe supply chain partners is summarized in Table 2. The results ofexperimental study reveal that average on-site inventory level atthe retailer is higher under VMI than IS by 163 units over theplanning horizon due to decrease in shipment frequencies. Whensetup cost is at a low level, we observe that reduction in retailer'son-site stock can be at most 60 units on average. The inventorylevels at the retailer can increase considerably in several testinstances, particularly when the retailer orders more frequentlyunder IS than the supplier replenishes under VMI. This finding is inline with Blackhurst et al. [1], Savaşaneril and Erkip [22] andChoudhary et al. [4]. Beyond IS, the shift in decision makingresponsibility allows the supplier to reduce its inventory level by

Table 2Value of VMI over IS for the supplier and retailer.

Independent systemparameters

Dependent supply chain performance measures

Expected cost savings (inmonetary units)

Expected inventoryreduction (in units)

Retailer Supplier Retailer Supplier

Order issuing efficiency (βr)0.00 2794 �2651 �303 2470.30 3358 �2259 �22 122

Demand lumpinessLow 3053 �2433 �184 187High 3099 �2483 �141 180

Coefficient of variation (CV)0.10 2690 �2101 �227 2010.30 3093 �2485 �144 1840.50 3445 �2780 �116 168

Service-level (αrc)0.90 2927 �2332 �170 1900.95 3039 �2433 �162 1830.99 3261 �2600 �156 180

Ordering cost (ort)200 1765 �1395 �92 108600 3096 �2477 �147 2101200 4367 �3494 �250 234

Setup cost (St)50 3522 �2985 60 0500 2963 �2327 �219 1161500 2742 �2053 �329 437

Mean (all test instances) 3076 �2455 �163 184

D. Choudhary, R. Shankar / Omega 51 (2015) 59–7066

184 units on average over the planning horizon. However, weobserve that on-site stock of the supplier may not decrease underVMI in a few settings when it is economical to produce in lessnumber of setups, and the retailer's stock is replenished morefrequently as compared to IS. In such a situation, under VMI ascompared to IS, service-level may decrease as demand evolvesusing a static-dynamic uncertainty policy, particularly when CVis large.

Beyond IS, while cost savings of the retailer decrease with anincrease in the setup cost, the benefits are greater when remainingparameters are at high levels. On the other hand, an increase in thecost incurred by the supplier is lower when setup cost is high andremaining parameters (excluding βr) are at low levels. It isinteresting to note that higher level of βr makes VMI more valuableto both the partners. One can see from Table 2 that the retailergains on both the cost saving and inventory reduction perfor-mance measures when βr changes from low level to high level.Whereas, with increase in βr, the performance of the supplierdeteriorates on inventory reduction criterion, but improves on thecost saving measure.

Under VMI beyond IS considering non-stationary deterministicdemand, Choudhary et al. [4] exhibit that the retailer may becomeworse-off when the cost burden to carry additional stock due toincrease in shipment sizes is more than the transfer of totalordering costs to the supplier as a result of shift in decisionmaking responsibility. In such a situation, they propose that thesupplier needs to decrease unit price and/or consign the stock atthe retailer for VMI to work. Under non-stationary stochasticdemand, however, examination of Table 2 reveals that the retaileralways gains by moving from IS to VMI under the problem settingsconsidered in this study. On the contrary, the cost incurred by thesupplier is higher under VMI than IS in all the settings. Thus, forVMI to work, the retailer has to share ordering cost or make side-payment to the supplier.

4.2. A supply chain with single supplier and multiple retailers

In this section, we consider a serial supply chain in which aproduct is produced by a supplier (or manufacturer) and then soldto end-consumers through multiple retailers. We are particularlyinterested in investigating the benefits offered by VMI above andbeyond IS, especially when number of retailers as well as systemparameters such as ordering and setup costs, demand coefficientof variation, cycle service-level and order issuing efficiency change(i.e., increase). In doing so, we compare the performance of VMIand IS initiatives on the various supply chain measures such aspercentage reduction in system-wide costs and inventory levels, aswell as increase in replenishment frequencies at the retailer(s).

The following set of parameters is used in the experiment:Number of retailers ϵ {1, 2, 3}, CV ϵ {0.10, 0.60}, αcr ϵ {0.85, 0.95},

ort ϵ {200, 800, 1500}, St ϵ {50, 500, 1200, 2500}, βr ϵ {0, 0.3}, ht¼1,hrt¼2 and T¼10.

Non-stationary random demand for each retailer is generatedfrom uniform distribution U(5, 250). We consider 336 cases underIS and 672 cases under VMI (i.e., 336 cases at each level of βr) in afull factorial analysis. Table 3 reports benefit for a single retailer bytaking average values for all the three retailers when examinedindividually, i.e. three different random patterns are considered.Similarly, all combinations are taken into account in case of thetwo retailers.

We observe from Table 3 that the cost benefits decrease, butthe performance on inventory reduction improves under VMI ascompared to IS when βr¼0 and number of retailers changes from1 to 3. For example, while cost savings reduce from 1.21% to 0.98%as number of retailers changes from 1 to 3, the percent reductionin expected inventory level varies from �5.67% to 0.61%. On the

other hand, when βr¼0.30, the VMI offers significant improve-ments over IS on all the three performance measures as thenumber of retailers increases. For example, while expected costsavings improve from 11.63% to 13.65% as number of retailerschanges from 1 to 3, reduction in inventory level increases from4.29% to 11.92%. This observation suggests that a large base ofdownstream retailers can be more attractive on the cost savingcriterion under VMI as compared to IS, only when the supplierincurs lower ordering cost than the retailers.

Additional insights can be drawn from the study by investigat-ing the impact of increase in number of downstream retailers andchanges in the values of remaining system parameters on thesystem-wide performance measures. For this purpose, we considera general type of business environment by taking average valuesof two extreme cases of the order issuing efficiency. In suchan environment, Fig. 4 indicates that the expected percent costsavings improve under VMI compared to IS, as the number ofdownstream retailers increases. In addition, the benefit of movingfrom IS to VMI is higher for lower values of CV. It is seen that thelower values of cycle service-level requirements and increase innumber of retailers provide marginal opportunity for cost benefitsto be realized through VMI over IS.

Fig. 5 summarizes the results for the number of retailers andordering cost, where the cost benefit increases with increase innumber of retailers, or increase in ordering cost, or both. Theperformance in terms of inventory and shipment size reductioncriteria also improves with an increase in the base of downstreamretailers. However, a moderate value of ordering cost (i.e.,ort¼800) provides a greater opportunity in decreasing system-wide inventory and shipment sizes through VMI as comparedto IS.

We observe that moving from IS to VMI can be attractive whensetup cost is low and as the number of retailers increases. As

Table 3Experimental results: a study of single supplier–multiple retailers supply chain.

Independent systemparameters

Dependent supply chain performance measures

Expected costsavings (%)

Expectedinventoryreduction (%)

Expectedincrease in rep.Freq. (%)

βr¼0 βr¼0.30 βr¼0 βr¼0.30 βr¼0 βr¼0.30

Number of retailers1 1.21 11.63 �5.67 4.29 �8.82 4.782 1.16 12.95 �2.31 8.82 �6.84 9.183 0.98 13.65 0.61 11.92 �4.38 13.74

Coefficient of variation (CV)0.10 1.38 13.83 �5.01 8.79 �9.40 6.590.60 0.86 11.66 0.09 7.90 �3.96 11.88

Service-level (αrc)0.85 1.05 12.86 �0.24 10.43 �5.92 11.510.95 1.19 12.63 �4.66 6.26 �7.44 6.96

Ordering cost (ort)200 0.84 10.11 �1.18 4.87 �3.07 7.68800 0.83 13.41 1.43 9.96 �4.80 12.591500 1.70 14.70 �7.62 10.19 �12.18 7.43

Setup cost (St)50 0.10 16.68 �6.39 15.73 �1.69 18.85500 1.00 13.24 �6.46 4.49 �5.16 10.231200 1.71 11.55 1.36 7.14 �7.87 5.022500 1.67 9.50 1.66 6.01 �12.00 2.83

All test instancesMean 1.12 12.74 �2.45 8.34 �6.68 9.23Minimum 0.00 4.89 �84.55 �46.99 �38.89 �27.28Maximum 6.13 20.32 37.59 41.85 16.67 44.44Std. Deviation 1.25 3.82 13.73 11.32 9.89 12.32

D. Choudhary, R. Shankar / Omega 51 (2015) 59–70 67

illustrated in Fig. 6, an increase in setup cost from 50 to 2500deteriorates the performance of VMI over IS on cost savings andincrease in replenishment frequency criteria. However, the impactof interactions between setup cost and number of retailers is notunidirectional on the percent reduction in inventory levels. It isapparent from Fig. 6 that the gain of retailers is higher under VMIin comparison to IS as number of retailers changes from low levelto high level due to decrease in shipment sizes. In contrast,benefits of the retailers deteriorate as setup cost changes fromlow level to high level due to increase in shipment sizes. Weobserve that on-site stock of the supplier also reduces as thenumber of downstream retailers increases. For example, as com-pared to IS, the VMI reduces the supplier's inventory level by 337units on average over the planning horizon. The reduction ininventory of the supplier increases from 183 to 497 units asnumber of retailers changes from 1 to 3.

5. Conclusions, limitations, and directions for future research

The incremental value of VMI over IS varies greatly dependingon the structure of the supply chain being investigated, the

inventory control policy employed, and the values of systemparameters used in the analytical or simulation study. Priorresearch investigates the value of VMI beyond IS under stationarystochastic demand using (s, S) and (R, nQ) inventory controlpolicies. In this paper, we assess the benefits offered by VMI overIS for a supplier, multiple retailers and the system as a whole usingan (R, S) inventory policy under non-stationary stochastic demandconditions. For this purpose, we apply mixed integer linearprogramming formulations, and report the findings consideringvarious supply chain performance measures through a detailednumerical study carried out for a finite planning horizon.

The experimental results reveal that the decision transfercomponent of VMI can offer benefits over the information sharingcomponent in this particular environment. The magnitude ofbenefits, however, depends mainly on the order issuing efficiencyof the supplier. When order issuing efficiency of the supplier iszero, the VMI facilitates the supplier to aggregate the replenish-ment quantities into economic production lot-sizes in a fewsettings, and results in an average expected cost savings of1.43%. As a result, the system-wide inventory and shipment sizesincrease significantly under VMI as compared to IS. On the otherhand, increase in the level of order issuing efficiency reducesordering related fixed costs and system-wide inventory. Forexample, increasing supplier's order issuing efficiency by 30%improves cost savings by 12.20%, reduces inventory levels by3.67%, and increases replenishment frequencies at the retailer by1.80%. The managerial implication of this finding is very encoura-ging as it supports in choosing the most appropriate supplier forVMI partnership beyond IS.

The findings also indicate that the value of VMI over ISsignificantly depends on a large number of system parameters.Other than order issuing efficiency, these are demand pattern andits lumpiness, demand coefficient of variation, number of retailers,ordering cost, service-level requirement, and setup cost. As theseparameters get different levels, the benefits offered by VMI over ISalso change substantially. For example, the benefits of switchingfrom IS to VMI are maximumwhen order issuing efficiency is high,

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demand coefficient of variation, as well as setup cost are low. Thisobservation suggests that supply chain managers must assess thesuitability of VMI over IS considering all the performance criteria,particularly when the supplier's order issuing efficiency is low.

This study provides important insights by distinguishing incre-mental value of the decision transfer component over the informa-tion sharing component of VMI. This study is also constrained by afew limitations. First, we consider a serial supply chain structure,where the retailers operate under full backordering. In practice, wegenerally observe backordering with lost sales at the retailers.Second, we study the problem under a cycle service-level criterion.Therefore, in future, extending the results obtained from thisresearch with considerations such as fill rate criterion and lostsales at the retailers are well justified.

Acknowledgment

We are grateful to the anonymous referees and editorial boardfor suggesting a number of improvements to an earlier draft of thispaper. The authors would also like to acknowledge the valuablefeedback received from Prof. S. Armagan Tarim at the initial stageof preparing this research paper.

References

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