Omega 43 (2014) 54–63

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Omega

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Managing consumer returns in high clockspeed industries

Rocío Ruiz-Benítez a,n, Michael Ketzenberg b, Erwin A. van der Laan c

a Business Management Department, Pablo de Olavide University, Sevilla, Spainb Department of Information and Operations Management, Texas A & M University, College Station, TX, USAc Rotterdam School of Management, Erasmus University, Rotterdam, The Netherlands

a r t i c l e i n f o

Article history:Received 13 February 2012Accepted 13 June 2013

Processed by B. Lev

where the operational decision of interest is the frequency in which returns are picked up from acollection point and then processed at a centralized location. Returns decay in value over time according

Available online 6 July 2013

Keywords:Reverse logisticsConsumer returnsValue of information

83/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.omega.2013.06.004

esponding author. Tel.: +34 954977972; fax: +ail addresses: rruiben@upo.es (R. Ruiz-Benítezberg@tamu.edu (M. Ketzenberg), elaan@rsm

a b s t r a c t

In this study, we address control policies to manage the collection of products that have been returned byconsumers to retailers after they have been sold. Specifically, we model a consumer returns process

to their industry clockspeed. Hence there is an intrinsic tradeoff in the decision – a longer intervalbetween collections not only reduces transportation cost, but also reduces the value of asset recovery.

We analyze a stylized model with a single collection point and a centralized returns processingcenter. Given an asset decay rate and a fixed transportation cost we determine the optimal collectioninterval. We later expand the analysis to the case of a capacitated returns processing center. We alsoexplore the value of information (number of returns held at the collection point) sharing between acollection point and the central processing facility. We find that the VOI is quite sensitive to parametricsettings ranging upwards to over 20% with a median value of 5.0%. We find that the VOI increases withrespect to the asset value decay rate and the rate of returns, while it decreases with respect to theshipping cost.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

It is surprising to find that with the tremendous increase inconsumer returns over the past decade and the problems that theypose for supply chain management, there has been limitedresearch on control policies for their management, particularlywith respect to collection. In 2008, retail returns were over 8% ofsales, representing more than a 20% increase from the prior year[1]. According to a study conducted by Accenture, return rates inthe consumer electronics industry range between 11% and 20% [2].For other retail segments like department stores, the rate exceeds15%.

Not only are return rates high and increasing, but also they canbe quite costly. According to Accenture, the total landed cost ofreturns for manufacturers ranges between 5% and 6% of sales.Moreover, most product returns are in perfect working order – thatis they have no defects. These returned products are commonlyreferred to as false failure returns and they constitute more thantwo-thirds of all returns. Even the cost of handling false failurereturns can be high. For computer manufacturers it can be as highas 25% of the product price [2].

ll rights reserved.

34 954348353.),.nl (E.A. van der Laan).

One would think that a simple solution to the problem ofproduct returns is to enforce strict return policies. Indeed, part ofthe growth in product returns arises from a liberalization ofpolicies that allow their return. However, this liberalization is alsocoincident with a significant growth in “remote” purchases. That is,situations in which consumers buy remotely, from home or office,via the Internet, phone facsimile, or from mail order catalogs. Inthis light, the liberalization of return policies that has beenobserved arises because of both the value that consumers placeon the ability to return products after purchase, and the need forfirms to provide a competitive offering to the marketplace [3].

From the consumers perspective, a lenient return policyreduces the cost of reversing a bad decision and thus enablesconsumers to make decisions while maintaining flexibility. Inconsumer electronics, Accenture reports that 27% of returns arisedue to buyer's remorse [2]. Since liberal return policies are valuedby consumers, such policies provide a means to stimulate demand[3,4], and perhaps by as much as setting price. Conversely, makingreturn policies strict may not be attractive or even reasonablesince doing so may negatively affect demand. As stated in Shulmanet al. [4], “such a policy may also harm the firm by discouragingconsumers from trying the product in the first place.” From thisperspective, returns have become an endemic part of doingbusiness and there is a real need for management guidance onhow to best handle them. This need, coupled with a scarcity ofacademic research in this area, motivates our study.

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–63 55

We observe different practices for consumer returns thatdepend on the complexity of the process needed to put theproduct back on the shelf. In the apparel sector, for example, mostof the returned products, after a quick visual inspection, can be putback on the shelf and sold again as new products. However, sectorssuch as consumer electronics or domestic appliances need morethan an inspection process in order to decide whether the productcan go back to the shelf. In this case some rework may have to bedone in the product in order to make it suitable for sale. Thisrework can be made at the retailer site, if the product needsminimum changes, or most probably, the returned product willhave to go back to the OEM or to a refurbishing center for a morecomplex refurbishing process. Evenwhen returns processing couldbe performed at the retail level, OEMs may require that all returnsbe sent back to them for the purposes of brand management.Additionally, high depreciation of the product is experienced inthese sectors, which makes the recovery process a key factor tomaintain the profitability of the business. In fact, value depreciationis one of the biggest challenges regarding returns that big consumerelectronics retailers are facing. We will first focus on sectors inwhich the returned product needs to go back to a recovery facilityto be processed and product value depreciation is high. However,we later extend our model to the case in which inspection ofreturns can be handled at the retail level such that false-failurereturns may be immediately returned to the shelf for resale.

Therefore, returns, even non-defective returns, are costly fora variety of reason that include collection, transportation, testing,sorting, cleaning, packaging, and redistribution. Returns can alsobe damaged in the returns process itself. Common disposal methodsfor returned products are reselling through the primary channel,discounting through a secondary channel, or returning the productto the vendor. Regardless of their disposition, the process can takeconsiderable time. The time it takes to process returns arises froma lack of management attention as well as a need to rationalizefixed costs and resources in the reverse logistics chain such thatmost processing is often done at a centralized location. At thesame time, the longer product returns sit in the supply chain, themore value they lose, particularly in fast clockspeed industries. Forthat matter, the longer it takes to retrieve the value of a returnedproduct, the lower the likelihood of economically viable reuseoptions.

To most companies, consumer returns have been viewed as anuisance. Consequently, their legacy today is a reverse supplychain process that was designed to minimize costs and theseprocesses are not necessarily fast. Research has shown that forhigh clockspeed industries there may be significant opportunitiesto improve asset recovery of product returns by reducing costlytime delays in the reverse logistic processes [5]. Even so, thepotential improvement in asset recovery must be effectivelybalanced with the cost of making the investments to do so.

In this paper, we address control policies for product returnsmanagement. Specifically, we explore the tradeoff between timedelays on asset recovery opportunities with the cost of transporta-tion from a collection point to a central processing location. Givenan asset decay rate and a fixed transportation cost we determinethe optimal collection interval. We later expand the analysis to thecase of a capacitated returns processing center. We also explorethe value of information sharing between the collection point andthe central processing facility and assess its impact on the optimalpolicy.

The rest of this manuscript is outlined as follows. Section 2positions our research within the literature on consumer returnsmanagement and the value of information. Section 3 introducesour base model and Sections 4 and 5 provide extensions. Finally,Section 6 concludes our study with discussion and future researchdirections.

2. Literature review

The literature on economic inventory/transportation decisionsis abundant. We focus on consolidation practices which have somesimilarities with our work. Temporal consolidation requires hold-ing shipments over a period of time in order to obtain some costefficiency. Burns et al. [6] focus on minimizing the cost ofdistributing freight by truck from a supplier to many customersand determine the optimal trade-off between transportation andinventory costs. They compare two strategies: direct shipping toeach customer in isolation and delivery to multiple customers inthe same trip. The optimal solution depends on the shipment size.In the case of direct shipping the optimal size is given by theeconomic order quantity (EOQ) model while in the case of multiplecustomers the optimal size is a full truck. Also trying to minimizetransportation and inventory costs, Gupta and Bagchi [7] calculatethe minimum cost-effective load which should be accumulated ata consolidation center before shipment in just-in-time procure-ment environments. Çetinkaya and Lee [8] integrate inventory andtransportation decisions in a single model that determines thefrequency of outbound shipments and the replenishment inven-tory quantities.

Bookbinder and Higginson [9] explore cost-saving opportu-nities arising with shipment consolidation under different policiesbased on time or quantity. A time-based policy ships an accumu-lated load every T periods and a quantity-based policy ships anaccumulated load when an economic freight quantity is available.For the case of deterministic demand both policies are equivalent.

Time-based shipment consolidation policies have become apart of transportation contracts between supply-chain partners.Such contracts are particularly useful for VMI systems. In thissetting, [10] calculate the optimal replenishment quantity anddispatch frequency in order to minimize inventory and transpor-tation costs. Diaby and Martel [11] also study the lot sizingproblem considering simultaneously purchasing, inventory andtransportation costs for a multi-echelon distribution system.

Beyond the literature on consolidation policies, our research isclosely related to two separate research streams: closed loopsupply chains (CLSC) and the value of information (VOI). In theremainder of this section, we review the key related literature ineach stream and then position our research at their intersection.

From the operations and supply chain literature, productreturns management falls under the general umbrella of closedloop supply chain management. For a fairly comprehensive discus-sion of the field see [12–14] that also contain extensive references toresearch on production, planning, and control in reverse logistics. Foran extensive review on strategic and tactical aspects of CLSC pleaserefer to Ferguson [15].

Most of the research in the field of CLSC concerns managing thereverse flows of products that are at their end of use or end of life.The focus for these types of return flows is on cost-efficientrecovery and meeting environmental standards. With consumerreturns, however, the focus is on maximizing asset recovery whichgenerally requires flexible and responsive reverse supply chains.There are contributions, however, that do address management ofconsumer returns and we position our research with respect torepresentative examples.

Guide et al. [16] present a network flow model of consumerreturns that they use to identify the drivers of reverse supply chaindesign. Using illustrative examples from practice, they show thatfor high clockspeed industries the returns network should beresponsive and for low clockspeed industries the returns networkshould be efficient. We build on this research by developingoperational policies that balance the tradeoff between efficiencyand responsiveness. Ferguson et al. [17] also address consumerreturns and, in particular, contracts to reduce false failure returns.

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–6356

Essentially, there is a misalignment in incentives between retailersand manufacturers for reducing false failure returns. Manufac-turers absorb the majority of costs for returns and therefore willbenefit the most by reducing them. However, retailers incur themost cost for reducing returns, while benefiting little by doing so.The authors proceed by introducing a target rebate contract toalign interests.

Vlachos and Dekker [18] introduce a single period model withresalable returns. They show that the order quantity of new productshould be adjusted for returns that occur during the period. Later,[19] extend the literature by relaxing some restrictive assumptions –most notably that returned product can be resold only once and thata fixed percentage of returns are resalable.

Ketzenberg and Zuidwijk [3] introduce a model where thereturn policy is a decision variable along with the price and orderquantity in a two period model. Returns in the first period can berecovered and used to satisfy demand in the second period. In thiscontext, the return policy modeled has an explicit tradeoff – arestrictive policy limits the rate of returns, while a lenient policystimulates demand. Their results show that for a wide range ofscenarios an intermediate policy (neither completely strict norcompletely lenient) is optimal. Moreover, Ketzenberg and Zuidwijk[3] is one of the few contributions that addresses the value ofvarious supply chain investments, including the VOI.

The vast majority of the research in the area of CLSC is related toremanufacturing processes and the design of the network toinclude such activities. Savaskan et al. [20] search for the optimalreverse channel structure for the collection of used products fromconsumers. Jayaraman et al. [21] propose a closed-loop logisticsmodel to include remanufacturing activities and solves for thelocation of remanufacturing/distribution facilities, as well as thetranshipment, production and stocking quantities of remanufac-tured products. Min et al. [22] determine the number and locationof reverse consolidation points (or centralized return centers) forreturned products from retailers or end-customers. In such reverseconsolidation points, returned products are collected, sorted andconsolidated into large shipments destined for manufacturers’ ordistributors’ repair facilities. Srivastava [23] designs a cost effectiveand efficient reverse logistics network that determines the loca-tion of collection centers and rework facilities. Francas and Minner[24] compares two different network structures, one that includesmanufacturing and remanufacturing processes in the same plantand a second one that performs remanufacturing activities in aseparate plant. They show that the choice of the network config-uration depends on investment cost of remanufacturing capacityand market structure. Baker and Zabinsky [25] also analyzesdifferent network configurations, developing a decision makingmodel that considers multiple criteria to design the number andlocation of test and collection sites.

Inventory and production planning problems in remanufacturingenvironments have been widely studied. Part of this CLSC literaturehas focused on the development of optimal policies includingdispose-down-to policies. Inderfurth [26] provides an optimaltwo-parameter policy, characterized as “order-up-to L, dispose-down-to U” for situations in which the return volumes areexcessive (at the end of the product lifecycle). A Dispose-down-to policy is also present as part of the optimal policy for aproduction and remanufacturing multi-period CLSC problem,which is given by three parameters, a produce-up-to level S, aremanufacture-up-to level M and a dispose-down-to level U [27].Mitra [28] considers a two-echelon inventory system with returnsand develops deterministic and stochastic models. Jonrinaldi andZhang [29] develops a mathematical model for coordinatingproduction and inventory decisions in a manufacturing supplychain that includes a reverse flow of returned products. Differentsolution methods based on centralized and decentralized decision

making processes are also developed. See Akçali and Çetinkaya[30] for a recent review on the field.

With respect to the VOI literature, there are a few articles thatprovide literature reviews and taxonomies. Sahin and Robinson[31] and Huang et al. [32] are representative examples and eachprovides a very broad overview of the literature and uses its ownclassification scheme. Ketzenberg et al. [33], in addition to provid-ing an extensive literature review, develops and tests a frameworkusing the collective studies on the VOI in the literature. Thesereviews indicate that a preponderance of research in this areafocuses on the value of demand information to improve supplychain performance.

While both the literature on the VOI and CLSC have grownconsiderably over the past decade, not many bridge these fields.Generally, these contributions address the value of advanced yieldinformation in remanufacturing environments. For example, [34]address a remanufacturer that faces a tradeoff between limitedinformation regarding remanufacturing yield and potentially longsupplier lead-time. The authors develop four decision-makingmodels to evaluate the impact of yield information and supplierlead-time on manufacturing costs. Ferrer [35] and Ketzenberget al. [36] are other illustrative examples in the literature that,although addressing the VOI in CLSC, do neither explicitly addressconsumer returns nor do they address the use of information incollecting returns.

In this study, we model a consumer returns process where theoperational decision of interest is the frequency in which returnsare picked up from a collection point and then processed at acentralized location. The returns decay in value over time accord-ing to their industry clockspeed. Hence there is an intrinsictradeoff in the decision – a longer interval between collectionsreduces transportation cost, but also reduces the value of assetrecovery. While there are a few papers that explicitly addressacquisition policies for end of life returns such as Teunter andFlapper [37] and Guide et al. [38], we are not aware of any othercontributions that specifically address operational policies foracquisition of consumer returns.

We also examine the VOI. Specifically, we look at the value ofknowing the count of returns at a collection point in each periodwithout having to physically make a visit. In essence, the decisionto visit and collect returns can then be made dynamically in everyperiod, instead of the more traditional static policy, where collec-tion occurs over a fixed interval of time. In the next section weintroduce our model.

3. Model

The general setting is a manufacturer that produces and sellsconsumer products through retailers. For a variety of reasons thatextend to include buyer's remorse, unmet expectations, anddefects, consumers may return products to the same retailerswhere they made their purchases. The retailers serve as collectionpoints, holding the returns until the manufacturer decides tocollect them. Hence in our exposition, retailers and collectionpoints are synonymous. On collection, the returns are transportedto a central processing facility. This central processing facility isdevoted to certain type of products with similar processingcharacteristics. To the extent necessary, the central processingfacility inspects, tests, refurbishes, and repackages the returnsafter which they are reintroduced into the marketplace. We beginwith a simple model consisting of a single collection point. Theoperational decision of interest for the manufacturer is thefrequency or interval between collections at the collection point.

All consumer returns have an asset value to the manufacturerthat decays at a rate of α per time unit for a specific product

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–63 57

category, as suggested by Blackburn et al. [5] and Guide et al. [39].We consider that the manufacturer is deciding about the pick upfrequency for a product category or different product categorieswith similar decay rates and similar processing characteristics.Consumer returns are stochastic, arrive at a mean rate λ perperiod, with density function ϕð:Þ, and are i.i.d. across periods.Each time returns are picked up from the collection point andtransported to the central processing facility, the manufacturerincurs a shipping cost K that corresponds to the labor, fuel, andother costs associated with transportation.

We explore two cases that differ in the information available tothe manufacturer in deciding when to collect returns from thecollection point. In the first case, referred to as the static case, themanufacturer knows the relevant costs and the probability dis-tribution for returns. The objective of the manufacturer is tochoose a collection interval T so that the manufacturer's per periodexpected cost is minimized, where the collection interval Tcorresponds to the number of periods that elapse between visitsto the retailer. Since costs and the returns distribution arestationary over time, the optimal collection interval T is alsostationary over time. In effect, there is an explicit tradeoff betweenasset recovery value and transportation cost such that as Tincreases, the transportation cost decreases and the asset recoveryvalue decreases.

In the second case, referred to as the dynamic case, themanufacturer not only has the same information available as inthe static case, but also knows the number of returns that are heldat the collection point in the current period. In this case, themanufacturer can make its decision dynamically, deciding eachperiod whether or not to visit the collection point. Hence thecollection interval may vary from one collection cycle to the next.Below, we first introduce the static case policy and then proceedon to the dynamic case.

3.1. Static case

If xi denotes the returns realized in period i, i∈f1;2;…; Tg, thenthe expected asset value loss for a collection cycle of length T isgiven by L(T) where

LðTÞ ¼ α ∑T

i ¼ 1∑1

xi ¼ 1xiðT�iÞϕðxiÞ:

Letting πsðTÞ denote the manufacturer's total cost function forthe static case, then

πs Tð Þ ¼K þ α∑T

i ¼ 1∑1xi ¼ 1xiðT�iÞϕðxiÞT

:

Since

∑T

i ¼ 1∑1

xi ¼ 1xi T�ið Þϕ xið Þ ¼ ∑

T

i ¼ 1T�ið Þ ∑

1

xi ¼ 1xiϕ xið Þ ¼ ∑

T

i ¼ 1T�ið ÞE xi½ � ¼ λ

TðT�1Þ2

;

then

πs Tð Þ ¼ KTþ αλðT�1Þ

2

where λ¼ E½xi�. Note that technically T is an integer, but here weassume a continuous approximation.

The first derivative of πsðTÞ is∂πsðTÞ∂T

¼ �K

T2 þ αλ

2:

Setting equal to zero, we obtain a closed form solution

T ¼ffiffiffiffiffiffiffi2Kαλ

r:

Taking the second derivative we obtain that this solution is aglobal minimum:

∂2πsðTÞ∂T2 ¼ 2K

T3 40:

Note that the optimal collection interval, T, for the static casedoes not depend on the distribution of returns just on the returnsmean, λ.

3.2. Dynamic case

Now consider the case that the collection cycle ends wheneverY or more product returns are collected. We call such a policy adispose-down policy. The total value loss up to period n is therandom variable Zn ¼∑Xn

i ¼ 1Wi, where Xn is the number of collec-tion cycles up to period n and Wi is the cost in the ith cycle. Sincethe Wi are i.i.d. with finite expectation E(W), the elementaryrenewal theorem for renewal reward processes tells us thatlimn-1Zn=n¼ EðWÞ=EðSÞ with E(S) the expected length of a cycle(see e.g. [40]). The value loss in a particular period when k productreturns were collected prior to the period and x products werecollected during the period equals αðxþ kÞ. Summing over allpossible xmultiplied with its probability ϕðxÞ gives us the expectedvalue loss in the period given k:

LðkÞ ¼ α ∑Y�k�1

x ¼ 0ðxþ kÞϕðxÞ:

Define ϕiðkÞ as the probability that after i periods since the lastcollection, the number of returns equals k. Given k returns in thefirst i periods of a cycle, the expected value loss in the ðiþ 1Þthperiod equals LðkÞϕiðkÞ. Summing over all possible values of i and kand noting that Lð0Þ is the expected value loss in the first period ofa cycle we have that the fixed collection cost plus total expectedvalue loss during a collection cycle is given by

EðWÞ ¼ K þ Lð0Þ þ ∑1

i ¼ 1∑Y�1

k ¼ 0LðkÞϕiðkÞ:

Next define ΦiðY�1Þ ¼∑Y�1k ¼ 0ϕ

iðkÞ as the cumulative probabilitythat during i periods demand does not exceed Y, then the renewalfunction MðYÞ ¼∑1

i ¼ 1ΦiðY�1Þ represents the expected number of

periods before cumulative returns equal or exceed Y. Dividing thetotal value loss plus costs per replenishment cycle by the expectedlength of a cycle, EðSÞ ¼ 1þMðYÞ, we get the average total costfunction πdðYÞ where

πd Yð Þ ¼ EðWÞEðSÞ ¼ K þ Lð0Þ þ∑1

i ¼ 1∑Y�1k ¼ 0LðkÞϕiðkÞ

1þMðYÞ :

Note that due to the complexity of the expression we cannotfind a closed-form expression for Yn. In the next section wewill carry out an extensive computational study to analyze thisproblem.

We still need to prove the optimality of the dispose-downpolicy in the dynamic collection problem. Note that our disposalpolicy optimizes a fundamentally different decision (all productsare recovered, but the timing is optimized with respect to fixedtransportation costs on the one hand and value deterioration costson the other) than the dispose-down policies that are defined inthe closed loop supply chain literature (see e.g. [41,26]). The latterpolicies refer to the decision to use products for recovery orthrowing them away ‘disposal’ if inventories of returned productsbecome too high. Because of this fundamental difference wecannot use the available optimality results that apply to the latterdispose-down policies.

Our collection problem is as follows. For each period n we haveto optimally set the numbers Yn, which sets the inventory level atwhich to ship the returns, and yn the dispose-down-to level.

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–6358

We want to prove that a (Y,y) dispose-down policy is optimal withy¼0, that is, Yn ¼ Y and yn¼0 for all periods. The formal proof isconstructed as follows: (1) we show that, with the proper variabletransformation, our problem is equivalent to a standard inventoryproblemwith infinite horizon and stationary demand, (2) we showthat the cost structure for the transformed problem is linear,which proves optimality of an (s,S) policy, which transforms backto the (Y,y) dispose-down policy, and (3) we show that for ourparticular cost structure y¼0 is optimal.

(1) Equivalence of (s,S) policy. Define In as the inventory ofreturned products at the end of period n, Rn as the number ofreturns in period n, and consider the transformation Xn ¼�In,sn ¼�Yn and Sn ¼�yn. Fig. 1 illustrates the link between thedynamics of the original problem and the transformed one.

In the transformed problem, product returns decrease inven-tory X until the critical level sn is reached and inventory is restoredto level Sn. Obviously, the transformed problem with stationary‘demand’ R has the dynamics of the dynamic inventory problem(see e.g. [42]). Since the dynamics of the two problems are thesame, the original problem has exactly the same functionalequation to describe the cost of an n-period problem:

f nðxÞ ¼ min0≥y≥x

cðy�xÞ þ LðyÞ þ ∑1

k ¼ 0f n�1ðy�kÞϕðkÞ

( )

with f 0ðxÞ≡0. Here, y�x is the quantity shipped in period n, �y isthe number of returns left at the end of the period, L(y) is theperiod cost, ϕðkÞ is the probability that the number of periodreturns equals k and c(z) is defined as

cðzÞ ¼0; z¼ 0K ; z40:

(

A sufficient condition for optimality of the ðs; SÞ policy, that isst ¼ s and St ¼ S for all t, is that L(y) is convex [42]. Veinottand Wagner [43] show that this also implies optimality for theinfinite horizon problem under an average cost criterion, that is,limn-1ð1=nÞf nðxÞ.

(2) Convexity of L(y). The period cost is given as

LðyÞ ¼ �αy;

which is a linear function in y, so convexity is ensured and we canconclude that the (s,S) policy is optimal, which corresponds to a (Y,y)dispose-down policy in our original problem.

(3) Optimality of y¼0. Suppose that an ðyþ 1þ Q ; yþ 1Þdispose-down policy has average cost Cy, for fixed Q40 andy≥0. The ðyþ Q ; yÞ policy has exactly the same dynamics withthe same fixed transportation cost per time unit, but inventory at

Fig. 1. Equivalence of the collection problem (left) with the dynamic inventoryproblem (right).

each time period is 1 unit lower. Hence, the average deteriorationcost per period is α lower. Hence, CyoCyþ1 for all y≥0, so y¼0must be optimal. This completes the proof.

3.3. Numerical study

We carry out a numerical study to evaluate both the magnitudeand sensitivity of the VOI across a broad range of operatingenvironments. This study is predicated on a factorial design ofthe parameter values summarized in Table 1. For each permuta-tion of the parameters, we compute the optimal policies and theresulting average cost per period for both the static and dynamiccases. Additionally we calculate the VOI, where the VOI is measuredas the percentage reduction in average cost in the dynamic case,relative to the static case. We assume that returns are distributedaccording to a negative binomial distribution. Agrawal and Smith[44] discuss the appropriateness and relative advantages for usingthe negative binomial distribution to model retail demand pro-cesses and the same discussion applies for retail returns processesas well.

Given the analytical expression for the optimal collectioninterval Tn in the static case, it is no surprise to find that Tn

increases with respect to K, decreases with respect to α and λ,and does not change with respect to the coefficient of variation inthe returns distribution. Although the number of periods in acollection cycle varies from one cycle to the next in the dynamiccase, we find the same relationships between the expectedcollection cycle and the parameters. Except, however, that as thecoefficient of variation ðCVÞ increases, we find that the expectedcollection cycle tends to increase. This arises because there are anincreasing number of periods with little or no returns so that thefrequency of visits will decrease. It is true that the number ofperiods with a large number of returns also increases as thecoefficient of variation increases. However, the negative binomialdistribution, assumed for this numerical study, is a left-skeweddistribution such that increasing the coefficient of variation willincrease the number of periods with a small number of returns toa greater extent than the number of periods with a larger numberof returns. Hence, while the degree of uncertainty with respect tothe returns process has no bearing on the optimal decision in thestatic case, it does influence the dynamic case policy.

As for the VOI, we find that it ranges from 1.3% to 20.7% acrossour numerical results with a median value of 5.0%. Information inthe dynamic case has value because it can be used to avoidunnecessary trips (and therefore cost) when there are no or fewreturns at the collection point and to make more frequent tripswhen a large number of returns are realized and thereby avoidexcessive loss in asset value. In half the cases, information enablesa reduction in transportation cost and in two-thirds of the cases,information enables a reduction in asset value loss. In certainscenarios, a slight increase in transportation cost was offset by amuch more significant decrease in asset value loss and the reversesituation was also observed.

Clearly, the VOI is sensitive to model parameters. Generally, theVOI is greatest in conditions that favor small values for T in the

Table 1Parameter values.

Parameter Values

Rate of returns (λ) 10, 15, 20Coefficient of variation (CV) 0.35, 0.5, 0.85Shipping cost (K) 25, 50, 100Asset decay rate (α) 1, 1.5, 2

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–63 59

static case. In Table 2 we report our sensitivity analysis whereinthe VOI is reported as an average across all numerical experiments,except for one fixed parameter value. For example, the average VOI

across all experiments in which λ¼ 10 is 6.5%. Similarly, we alsoreport the average cycle for the static and dynamic cases. Weobserve that the VOI decreases with respect to K and increases withrespect to α, λ, and CV. Consider that when Tn is large in the staticcase, there is less uncertainty with respect to the number of returnat the collection point since there is, in effect, risk pooling overtime. That is, the variability in the number of returns that arecollected from one collection cycle to the next collection cycledecreases as Tn increases. Hence, additional information that isavailable in the dynamic case becomes less valuable since there isless uncertainty with respect to the number of returns at thecollection point in the static case.

In Table 3 we summarize our sensitivity analysis and also reportsensitivity of the components to the VOI (savings in asset value loss andsavings in shipping cost) to the parameters. The symbols denote thefollowing: ↑¼ increases, ↓¼ decreases, ∪¼ convex, and ∩¼ concave.Hence, as shown in Table 3 the savings in asset value due toinformation is concave with respect to K. Note that the tradeoffbetween asset value and shipping cost is clearly evident. As thesavings in asset value increase, the savings in transportation costdecrease and vice versa.

Additionally, if we relate the VOI results to the optimal visitingfrequency in the static case (1/T) we observe that there exists avery strong, positive correlation, between visiting frequency andthe VOI. Fig. 2 is composed of three successive charts. Each chartreports the visiting frequency 1/T on the horizontal axis and the VOI

on the vertical axis for a subset of experiments that correspond toa fixed value for the coefficient of variation. Clearly, we can seethat the relationship between 1/T and the VOI becomes stronger asthe coefficient of variation increases. Note that as the coefficient ofvariation increases from 0.35 to 0.50, the associated R2 increases

Table 2VOI and average cycles for different parameter values.

Parameter Value VOI (%) Avg. cycle

Static case Dynamic case

10 6.5 2.8 2.8Rate of returns (λ) 15 7.7 2.4 2.3

20 8.1 2.0 2.1

0.35 2.8 2.4 2.4Coefficient of variation (CV) 0.50 5.5 2.4 2.4

0.85 14.0 2.4 2.5

25 9.6 1.7 1.7Shipping cost (K) 50 7.1 2.3 2.3

100 5.7 3.2 3.2

1.0 6.4 2.8 2.8Asset decay rate (α) 1.5 7.7 2.4 2.3

2.0 8.1 2.0 2.1

Table 3VOI Sensitivity analysis.

Parameter Staticcycle

Dynamiccycle

VOItotal

Savings inasset value

Savings inshipping cost

Rate of returns (λ) ↓ ↓ ↑ ∩ ∪Coefficient of

variation (CV)↑ ↑ ↑ ↓

Shipping cost (K) ↑ ↑ ↓ ∩ ∪Asset decay

rate (α)↓ ↓ ↑ ∩ ∪

Fig. 2. Relationship between VOI and visiting frequency (1/T).

from 0.43 to 0.62 and as the coefficient of variation increasesfurther to 0.85, the associated R2 increases to 0.77.

4. Extending the model to the capacitated case

In this section, we extend our analysis to the case of a system inwhich the processing center is capacitated. As such, at most Nreturns can be processed in a period. Moreover, inventory maynow be held across periods at both the collection point and theprocessing center. Let Ic and Ip denote the respective quantities atthe beginning of the current period.

The added complexity imposed by a capacity constraint on theprocessing center precludes the derivation of a closed formsolution, even for the simple static case. We can, however, modelthe behavior of such a system as a Markov Decision Process (MDP)and thereby evaluate the impact of a capacity constraint on boththe optimal policy and the VOI.

Our objective, as it is for the policies introduced in the priorsection, is to determine an optimal schedule to visit the collection

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–6360

point that will minimize average long-run expected cost perperiod. We begin with describing the static case policy. In thiscase, the inventory level at the processing center is known, whilethe inventory level at the collection point is unknown.

Given starting inventory Ip and a collection cycle every Tperiods, the infinite horizon cost-to-go, if future periods behaveoptimally, is f sðIp; TÞ. The optimal cost-to-go that results is ΠsðIpÞ.As is the custom with average cost dynamic programming, we letcs denote the optimal average cost per period in the static case.We can explicitly write the infinite horizon recursion as

f sðIp; TÞ þ cs ¼ K þ LðTÞ þ α ∑T

i ¼ 1ðIp�minðN; IpÞðT�iÞÞ

þ ∑1

x ¼ 0f sðIp�minðT � N; IpÞ þ x; TÞϕðxÞ ð1Þ

and the optimal cost-to-go is given by ΠsðIpÞ where

ΠsðIpÞ ¼minT≥1

f sðIp; TÞ þ cs: ð2Þ

The right hand side of Eq. (1) computes expected total costwhich consists of four terms: (1) the collection cost, (2) the valueloss function for inventory returned to the collection point duringthe cycle, (3) the value loss of returns held at the processingcenter, and (4) future expected cost. The decision space for T isrestricted to the set of positive integer values greater than zero.Since the state space and decision spaces are discrete andcountable and the total cost related to inventory is bounded, thereexists an optimal stationary policy that does not randomize [45,pp. 102–111].

With information, the inventory at the collection point isknown with certainty and hence, the decision to visit, collect,

Table 4% VOI for different parameter values and level of capacity.

Parameter Value Capacity factor level (F) (%) Average (%)

1.05 1.10 1.20 1.50 1.75 2.00 1

λ 10 11.0 11.0 8.5 7.4 7.6 7.7 6.5 8.515 12.4 9.9 8.7 7.9 8.4 8.8 7.7 9.120 12.4 10.5 8.3 7.9 8.8 9.4 8.1 9.4

CV 0.35 7.8 4.6 2.5 3.3 4.0 4.1 2.8 4.20.50 13.2 10.8 7.4 6.0 6.6 7.1 5.5 8.10.85 14.8 16.0 15.6 14.0 14.1 14.6 14.0 14.7

K 25 11.3 10.3 8.7 9.1 10.3 11.0 9.6 10.050 12.6 11.1 9.2 8.3 8.6 8.8 7.1 9.4100 11.8 9.9 7.6 6.0 5.9 6.1 5.7 7.6

α 1.0 12.2 10.5 8.5 7.4 7.5 7.6 6.4 8.61.5 12.0 10.6 8.7 7.9 8.4 8.8 7.7 9.22.0 11.5 10.2 8.4 8.0 8.9 9.4 8.1 9.2

Average 11.9 10.5 8.5 7.8 8.3 8.6 7.4 9.0

Table 5Relationship between average, per period cost and capacity factor levels.

Parameter Value Capacity factor level (F)

1.05 1.10

Static case Total cost 99.1 74.3Shipping cost 32.7 32.7Asset value loss 66.5 41.6

Dynamic case Total cost 86.6 65.6Shipping cost 26.0 27.9Asset value loss 60.7 37.7

VOI 11.9% 10.5%

and transport the returns to the processing center can be madedynamically. Hence, the decision to visit V ;V∈f0;1g is made eachperiod, where V¼0 denotes no visit is made and V¼1 denotes avisit is made. The state space is now expanded from the static caseto include inventory held at the collection point waiting forpickup. Here, the infinite horizon, cost-to-go is given by f dðIc; IpÞand cd is the optimal average cost per period that results iffuture periods behave optimally. The infinite horizon recursion isexpressed as

f dðIc; IpÞ þ cd ¼ minV∈f0;1g

V � K þ α � ð1�VÞ ∑1

x ¼ 0½Ic þ x� � ϕðxÞ

þα ∑1

x ¼ 0½V � ðIc þ xÞ þ Ip�minðN;V � ðIc þ xÞ þ IpÞ�ϕðxÞ

þ ∑1

x ¼ 0f dðð1�VÞ � ðIc þ xÞ;V � ðIc þ xÞ

þIp�minðN;V � ðIc þ xÞ þ IpÞÞ � ϕðxÞ: ð3Þ

4.1. Numerical study

We carry out a numerical study to evaluate both the magnitudeand sensitivity of the VOI using the same experimental design aspresented in Table 1. We replicate the design for different levels ofcapacity. Let F denote a capacity factor level such that N¼ F � λ andhence capacity N is a function of the mean returns rate λ. Weexplore values of F∈f1:05;1:20;1:50;1:75;2:00g. We also comparethese results with those of the uncapacitated case (F ¼1). Wesummarize our sensitivity analysis in Table 4, which providesaverage values across all experiments with the fixed parametervalue identified by the row header and the capacity factor Findicated by the column header. For example, the average VOI

across experiments where λ¼ 20 and F¼1.05 is 12.4%.In general, we observe that for moderate to low levels of

capacity (F≤1:5), the VOI is increasing as the level of capacitydecreases. Clearly, however, the relationship is more complexsince for values of F≥1:5, there is no clear relationship between Fand the VOI. To better understand, it is helpful to look at theunderlying cost components for the static and dynamic cases.

In Table 5 we report the average cost values across experimentsfor the static and dynamic cases at each capacity factor level F.Several observations emerge from Table 5. First, not only is theaverage total cost for the dynamic case less than the static case ateach level of capacity, both cost components are also lower(shipping cost and asset value loss). Hence, information is valuableat all levels of capacity. Second, we can observe that the costcomponents are strictly increasing as capacity decreases in thestatic case, with the costs associated with asset value lossincreasing at an increasing rate. Shipping cost, though increasing,is relatively flat. The queuing effects at play here are abundantly

1.20 1.50 1.75 2.00 1

58.8 46.8 43.9 42.2 37.831.4 29.2 29.0 28.1 23.827.4 17.7 14.9 14.0 14.0

53.3 43.2 40.4 38.7 35.128.9 28.5 27.7 27.0 23.424.4 14.7 12.7 11.7 11.7

8.5% 7.8% 8.3% 8.6% 7.4%

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–63 61

clear. As the arrival rate of returns approaches the service rate ofthe processing center, an inventory of returns accumulates at theprocessing center and the value of those assets diminishesappreciably. That is, as waiting lines for processing increase, assetvalue loss increases. Moreover, as capacity becomes scarce, itbecomes increasingly more important not to waste it by beingidle. Hence, as capacity decreases, there is downward pressure toreduce Tn to avoid idle periods.

In the dynamic case the cost relationships are less clear.Certainly as capacity decreases, total cost is increasing and so toois the cost associated with asset value loss. The shipping cost,however, demonstrates a concave relationship with respect tocapacity. Notice that average per period shipping cost is greatest atintermediate values of F. When capacity is limited, the processingcenter is working constantly so that if there are enough returnsalready at the center, no collection needs to take place in thecurrent period. Hence, when capacity is limited, the principalbenefit from information is delaying collection and thereforetransportation cost will be minimized. At intermediate levels ofcapacity, there is an opportunity to avoid wasting capacity byexpediting the collection process (going earlier and more often).Hence more transportation will occur at intermediate levels ofcapacity. At high levels of capacity, capacity itself is not thatvaluable so letting some go wasted is preferred to the excess costof shipping. Therefore, at high levels of capacity, transportationcosts will be lower. Note too that just as our model enables anassessment on the VOI, it also facilitates rationalizing capacitydecisions at the processing center.

5. Extending the model to the retail inspection case

Consider the following extension of the basic static model.Suppose that products are first returned to a retailer, which does afirst inspection to sort the products that can be directly re-shelvedfrom those that need to undergo further recovery operations (thatis repackaging and/or refurbishment). Further suppose that theexpected fraction of products that need recovery is p ð0op≤1);this fraction is sent to the collection center for consolidation.There, a collection interval T is determined and a fixed transporta-tion cost K applies, just like in the original model. To provide theretailer with incentive to do the inspection activities we payhim/her a premium of g per unit (that is, the difference betweenthe collection cost at the retailer and at the collection center is g).Although in the original model the product decay cost at therecovery facility was not explicitly modeled as it did not influencethe optimal decisions, now we need to do so to be able to comparethe cost performance of the two situations. Hence, if z is theaverage delay at the recovery center, then the period decay costdue to this delay is αλz. Fig. 3 contrasts the original model againstthe model extension.

Fig. 3. Original model (1) versus the extended model (2).

The research question we now address is howmuch premium gshould the recovery center maximally offer to the retailer toinspect and sort the product returns.

The dynamics of this extended model are the same as that ofthe basic model, since only the inflow to the collection center isreduced (pλ instead of λ). Hence, we can simply adapt the modelthat was developed in Section 3. The two cost functions are

π1 Tð Þ ¼ KTþ αλ T�1ð Þ=2þ αλz

π2 Tð Þ ¼ KTþ αpλ T�1ð Þ=2þ αpλz þ gλ

Since T1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2K=ðαλÞ

pis the optimal collection period of the

original model, we can write the optimal collection period of theextended model as T2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2K=ðαpλÞ

p¼ T1=

ffiffiffip

p. Note that T2≥T1. The

difference in optimal costs then is given by

π1 T1ð Þ�π2 T2ð Þ ¼ KT1

þ αλ T1�1ð Þ=2

þ αλz� Kffiffiffip

pT1

þ αpλ T1=ffiffiffiffiffiffiðpÞ

p�1

� �=2þ αpλz þ gλ

� �

which can be rewritten as

π1 T1ð Þ�π2 T2ð Þ ¼ 1� ffiffiffip

p� � KT1

þ αλ T1�1ð Þ=2� �

þð1�pÞαλz þ ðp� ffiffiffip

p Þλα=2�gλ

¼ ð1� ffiffiffip

p Þðffiffiffiffiffiffiffiffiffiffiffi2αλK

p�αλ=2Þ

þð1�pÞαλz þ ðp� ffiffiffip

p Þλα=2�gλ

Equating to zero and solving for g gives us the maximumwillingness to pay (gn) for the retailer's inspection efforts

gn ¼ 1� ffiffiffip

p� � ffiffiffiffiffiffiffiffiffi2αKλ

r�α=2

!þ 1�pð Þαz� ffiffiffi

pp �p� �

α=2

Here, the first term represents the per unit collection andproduct decay costs at the collection point (decreasing with thesquare root of p). The second term represents the per unit decaycosts at the recovery center (linearly decreasing in p). The thirdterm is a remainder that is typically very small as

ffiffiffip

p �p≤1=4.Hence, so long as gn is positive and gogn, it will be moreprofitable for the manufacturer to have the retailer inspect andsort returns. Note that the willingness to pay is a decreasingfunction of the return rate λ, an increasing function of fixedcollection cost K, and, if we ignore the remainder term, a decreas-ing function of p.

Unfortunately, the complexity of the dynamic case prevents asimilar analysis to that provided for the static case. Instead, weproceed with a numerical study to assess how the recovery center'smaximum willingness to pay the retailer for inspection and sortingbehaves in the dynamic case as well as when it operates under acapacity constraint. We also address the sensitivity of g with respectto a capacity constraint on the recovery center.

We consider the same factorial design of parameter values forour numerical study here as we used in Section 3.3. In addition, wereplicate the design for parameter p∈f0:2;0:4;0:8g and capacityfactor F∈f1:1;1:2;1:5;2:0;1g for a total of 1215 experiments. Wereport the maximum willingness to pay for the static case inTable 6 and for the dynamic case in Table 7. In both tables themaximum willingness to pay is reported as an average across allexperiments for the capacity factor F indicated by the columnheader and the parameter and value indicated by the row header.

The numerical results for the static case follow our analyticalresults. In addition we also see that g increases with respect to thevariability of the return rate (CV) and as capacity becomes morerestricted (F decreases). In both the instances, as the system

Table 6Maximum willingness to pay in the static case.

Parameter Value Capacity factor level (F) Average

1.10 1.20 1.50 2.00 1

λ 10 4.70 3.46 2.70 2.38 2.03 3.0515 3.59 2.99 2.23 1.99 1.73 2.5120 3.91 2.72 2.01 1.76 1.56 2.39

CV 0.35 2.73 2.40 2.14 1.97 1.77 2.200.50 3.39 2.70 2.19 2.00 1.76 2.410.85 6.05 4.05 2.60 2.16 1.78 3.33

K 25 3.43 2.42 1.72 1.52 1.37 2.0950 4.00 2.99 2.24 1.96 1.71 2.58100 4.76 3.74 2.97 2.64 2.23 3.27

α 1.0 3.05 2.37 1.85 1.64 1.39 2.061.5 4.07 3.07 2.33 2.05 1.78 2.662.0 5.06 3.72 2.75 2.43 2.13 3.22

p 0.2 4.94 3.91 3.12 2.81 2.50 3.450.4 4.04 3.02 2.28 2.00 1.72 2.610.8 3.21 2.22 1.53 1.31 1.09 1.87

Average 4.06 3.05 2.31 2.04 1.77 2.65

Table 7Maximum willingness to pay in the dynamic case.

Parameter Value Capacity factor level (F) Average

1.10 1.20 1.50 2.00 1

λ 10 4.12 3.17 2.56 2.27 1.95 2.8115 3.23 2.75 2.12 1.87 1.65 2.3220 3.49 2.53 1.92 1.66 1.49 2.22

CV 0.35 2.65 2.40 2.12 1.94 1.76 2.170.50 3.04 2.55 2.13 1.91 1.71 2.270.85 5.14 3.49 2.34 1.95 1.62 2.91

K 25 3.13 2.27 1.64 1.42 1.31 1.9550 3.53 2.74 2.12 1.84 1.64 2.37100 4.17 3.43 2.83 2.53 2.13 3.02

α 1.0 2.67 2.16 1.75 1.56 1.33 1.901.5 3.61 2.82 2.21 1.94 1.70 2.462.0 4.54 3.45 2.63 2.30 2.05 2.99

p 0.2 4.44 3.62 2.96 2.65 2.40 3.210.4 3.59 2.79 2.16 1.89 1.65 2.410.8 2.80 2.02 1.46 1.24 1.04 1.71

Average 3.61 2.81 2.20 1.93 1.70 2.45

R. Ruiz-Benítez et al. / Omega 43 (2014) 54–6362

becomes more congested, the value of reducing work in processinventory by having the retailer inspect returns increases. Theresults for the dynamic case demonstrate the same relationshipsas shown in Table 7. Note, however, that g in the static case isgreater than or equal to g in the dynamic case for all numericalcases. In the dynamic case, it is clear that the additional informa-tion on returns provides a much more efficient system (as we haveseen with regard to the VOI) so that the recovery center will be lesswilling to pay the retailer for inspection than in the static case.

6. Conclusion

Our research addresses a consumer returns process where theoperational decision of interest is the frequency in which returnsare picked up from a collection point and then processed at acentralized location. We derive optimal control policies for twoinformation cases: static and dynamic. In the static case, we findthat a stationary collection cycle of Tn periods is optimal. In the

dynamic case, we demonstrate that a dispose-down policy isoptimal and that the length of the collection cycle may vary overtime. At times, information may lead to expedited pickup ofreturns while at other times, information may lead to a delay incollection. Key assumptions of our model include stochastic,stationary returns and a constant asset value decay rate.

We also address the VOI for collecting returns. We find that theVOI is quite sensitive to parametric settings ranging upwards toover 20% with a median value of 5.0%. The highest value isgenerated in conditions that favor short collection cycles in thestatic case. We find that the VOI increases with respect to the assetvalue decay rate and the rate of returns, while it decreases withrespect to the shipping cost. We further show that the VOI increaseswith respect to the frequency of collections and that this relation-ship becomes strong as the coefficient of variation in the returnsprocess increases.

We also explore two model extensions. First, we extend ouranalysis into the impact of a capacity constraint on the returnsprocessing center. We find that as capacity becomes more restric-tive, the VOI generally increases, but the relationship is not strictlymonotonic. A second extension concerns the case in which theretailer is enlisted to inspect and sort returns on behalf of therecovery center. By doing so, costly time delays and transportationmay be avoided. We derive the recovery center's maximum will-ingness to pay in this scenario.

While we address a model of a single collection point, it isanalogous to the case of multiple collection points on a single route.From this perspective, the single collection point is simply anaggregation of multiple collection points where both the returnsdistribution and associated costs are combined for one point.

There are several avenues for future research. The mostpromising, we believe, is to address other functional forms ofthe asset value decay rate. In our study we assume a constant orlinear decay rate. While this assumption may be appropriate forcomputers and other electronics, other high clock speed industriesmay require a different form (e.g. exponential). Another avenue ofresearch is to consider the question of whether, and if so, underwhat conditions, it makes sense to integrate the reverse logisticsprocess with forward logistics.

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