remanufacturing and the component commonality decision

18
Remanufacturing and the Component Commonality Decision Ravi Subramanian College of Management, Georgia Institute of Technology, 800 West Peachtree St. NW, Atlanta, Georgia 30332, USA, [email protected] Mark E. Ferguson Moore School of Business, University of South Carolina, 1705 College Street, Columbia, South Carolina 29208, USA, [email protected] L. Beril Toktay College of Management, Georgia Institute of Technology, 800 West Peachtree St. NW, Atlanta, Georgia 30332, USA, [email protected] F irms often determine whether or not to make components common across products by focusing on the manufacturing and sales of new products only. However, component commonality decisions that ignore remanufacturing can adversely affect the profitability of the firm. In this article we analyze how remanufacturing could reverse the OEM’s com- monality decision that is based on the manufacturing and sales of new products only. Specifically, we determine the con- ditions under which the OEM’s optimal decision on commonality may be reversed and illustrate how her profit can be significantly higher if remanufacturing is taken into account ex ante. We illustrate the implementation of our model for two products in the Apple iPad TM family. Key words: component commonality; remanufacturing; competition; closed loop supply chains History: Received: July 2008; Accepted: January 2012 by Luk van Wassenhove, after 3 revisions. 1. Introduction Product line proliferation, where the variety of prod- ucts offered increases (to sell to a broader customer base) but the sales volume of each product variant typically decreases (Swaminathan 2001), presents a major challenge for many firms today. Component commonality or standardization has been widely regarded as a mechanism for firms to mitigate the negative effects of product line proliferation. The ben- efits from making components common across differ- ent products include a reduction in unit production costs due to economies of scale, and savings in inven- tory carrying or shortage costs due to risk pooling. However, component commonality may also result in negative effects. For example, the production cost of a lower performance product may increase if a common component has to also meet the requirements of a higher performance product. Also, consumer percep- tion of the high-end product may deteriorate if the high- and low-end products share common compo- nents. Thus, the typical decision as to whether a com- ponent should be made common or not involves considering both the cost and revenue-related effects, and evaluating if the decision results in an overall increase in the firm’s profit (see Labro 2004 for a review of the costs and benefits of commonality iden- tified in the related literature). Indeed, in many ways the component commonality decision represents a classic supply chain problem for the Operations Management field. Thus, it is not sur- prising that it has been well studied (Ramdas 2003, Swaminathan and Tayur 1998). Missing, however, from the traditional component commonality strategy literature is the consideration of remanufacturing operations. Remanufacturinga $53 billion dollar industry in the United States alone (Hauser and Lund 2003)refers to the process of collecting, inspecting, disassembling, and refurbishing used products to their original or improved performance specifications. Examples of products that are commonly remanufac- tured include machine tools; consumer electronics, computers, and peripherals; furniture; and tires. Some of these products are primarily remanufactured by their original manufacturers, but the majority are remanufactured by third parties. Caterpillar is an often-cited example of an OEM that actively and profitably remanufactures its own 1 Vol. 0, No. 0, xxxx–xxxx 2012, pp. 1–18 DOI 10.1111/j.1937-5956.2012.01350.x ISSN 1059-1478|EISSN 1937-5956|12|0|0001 © 2012 Production and Operations Management Society

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Page 1: Remanufacturing and the Component Commonality Decision

Remanufacturing and the Component CommonalityDecision

Ravi SubramanianCollege of Management, Georgia Institute of Technology, 800 West Peachtree St. NW, Atlanta, Georgia 30332, USA,

[email protected]

Mark E. FergusonMoore School of Business, University of South Carolina, 1705 College Street, Columbia, South Carolina 29208, USA,

[email protected]

L. Beril ToktayCollege of Management, Georgia Institute of Technology, 800 West Peachtree St. NW, Atlanta, Georgia 30332, USA,

[email protected]

F irms often determine whether or not to make components common across products by focusing on the manufacturingand sales of new products only. However, component commonality decisions that ignore remanufacturing can

adversely affect the profitability of the firm. In this article we analyze how remanufacturing could reverse the OEM’s com-monality decision that is based on the manufacturing and sales of new products only. Specifically, we determine the con-ditions under which the OEM’s optimal decision on commonality may be reversed and illustrate how her profit can besignificantly higher if remanufacturing is taken into account ex ante. We illustrate the implementation of our model fortwo products in the Apple iPadTM family.

Key words: component commonality; remanufacturing; competition; closed loop supply chainsHistory: Received: July 2008; Accepted: January 2012 by Luk van Wassenhove, after 3 revisions.

1. Introduction

Product line proliferation, where the variety of prod-ucts offered increases (to sell to a broader customerbase) but the sales volume of each product varianttypically decreases (Swaminathan 2001), presents amajor challenge for many firms today. Componentcommonality or standardization has been widelyregarded as a mechanism for firms to mitigate thenegative effects of product line proliferation. The ben-efits from making components common across differ-ent products include a reduction in unit productioncosts due to economies of scale, and savings in inven-tory carrying or shortage costs due to risk pooling.However, component commonality may also result innegative effects. For example, the production cost of alower performance product may increase if a commoncomponent has to also meet the requirements of ahigher performance product. Also, consumer percep-tion of the high-end product may deteriorate if thehigh- and low-end products share common compo-nents. Thus, the typical decision as to whether a com-ponent should be made common or not involvesconsidering both the cost and revenue-related effects,

and evaluating if the decision results in an overallincrease in the firm’s profit (see Labro 2004 for areview of the costs and benefits of commonality iden-tified in the related literature).Indeed, in many ways the component commonality

decision represents a classic supply chain problem forthe Operations Management field. Thus, it is not sur-prising that it has been well studied (Ramdas 2003,Swaminathan and Tayur 1998). Missing, however,from the traditional component commonality strategyliterature is the consideration of remanufacturingoperations. Remanufacturing—a $53 billion dollarindustry in the United States alone (Hauser and Lund2003)—refers to the process of collecting, inspecting,disassembling, and refurbishing used products totheir original or improved performance specifications.Examples of products that are commonly remanufac-tured include machine tools; consumer electronics,computers, and peripherals; furniture; and tires.Some of these products are primarily remanufacturedby their original manufacturers, but the majority areremanufactured by third parties.Caterpillar is an often-cited example of an OEM

that actively and profitably remanufactures its own

1

Vol. 0, No. 0, xxxx–xxxx 2012, pp. 1–18 DOI 10.1111/j.1937-5956.2012.01350.xISSN 1059-1478|EISSN 1937-5956|12|0|0001 © 2012 Production and Operations Management Society

Page 2: Remanufacturing and the Component Commonality Decision

products. In fact, Caterpillar has been shifting itsstrategy from solely manufacturing and selling con-struction equipment to one that has embraced reman-ufacturing (Gutowski et al. 2001). Building on thisearly success, Caterpillar established a remanufactur-ing division which had over $2 billion in sales in 2007and was the fastest growing among all of Caterpillar’sdivisions. Caterpillar also actively implements andpromotes its use of component commonality. Forexample, Caterpillar’s 2008 press release for the 785DMining Truck states that “… improvements also focuson component commonality to keep parts stockingand maintenance simple…” (Caterpillar 2008).Although the quote addresses the benefits of compo-nent commonality to the customer, one can expectthat Caterpillar itself benefits from managing andstocking fewer stock keeping units (SKUs), both forits manufacturing and remanufacturing operations.Given the prevalence of third-party remanufactur-

ing (Hauser and Lund 2003), an interesting questionis whether or not component commonality would alsomake it more economical for third parties to remanu-facture the product. HP provides an interesting casein point. HP is well known for its approach to manag-ing product line proliferation, for which it wasrecently awarded the Edelman prize (Horner 2009).For example, HP advertises that its server designs use“the highest degree of component commonality in theindustry” through its “universal design” approach.At the same time, HP adopts a contrasting strategyfor its “business inkjet” printers (HP’s business inkjetprinters are feature-rich and substantially moreexpensive than its other inkjet printers, making themattractive to third-party remanufacturers). HP usesdifferent print heads (which, in turn, require differentfixed ink cartridges) across different models. Since theprint heads are fairly consistent in their functionality,customers are not likely to emphasize a specific printhead as a differentiating factor in their purchase deci-sion, relative to other printer features. Therefore,these print heads would appear to be prime candi-dates for commonality. However, making the printheads common will likely lower the costs of remanu-facturing, leading third parties to be more competitivenot only in the market for printers, but also in themarket for replacement parts and supplies. Unlikeprinters, although, HP servers require special soft-ware to run, and the high relicensing fees charged byHP for this software limits the influence of third-partyremanufacturers, regardless of HP’s commonalitystrategy. Thus, strategic considerations regardingremanufacturing competition and the different meansavailable to HP for different products may explainHP’s divergent component commonality strategies.This article aims to uncover under what conditions

and to what extent secondary market factors influence

an OEM’s component commonality strategy. Ourfocus is OEM or third-party remanufacturing of end-products belonging to the same product line. Specifi-cally, we aim to answer the following questions:

(i) How does consideration of end-product remanufac-turing affect the OEM’s component commonalitydecision? Under what circumstances would a deci-sion that is based only on manufacturing consider-ations be reversed when remanufacturing is alsotaken into account?

(ii) If the OEM makes the component commonalitydecision without taking into account end-productremanufacturing, what is the economic significanceof this omission? Under what circumstances is itmost important to take remanufacturing consider-ations into account ex ante?

To answer these questions, we analyze how theOEM’s optimal component commonality decision ischanged when the effects of end-product remanufac-turing by either the OEM or a third party are includedin the decision criteria. As is typical in the related litera-ture, we do not model the firm’s original product linedesign decision, but rather the decision as to whether toimplement component commonality across an existingproduct line with given quality levels. We determinethe conditions underwhich theOEM’s optimal decisionon commonality may be reversed and illustrate howher profit can be substantially higher if end-productremanufacturing is taken into account ex ante. We findthat this profit impact is higher if a third-party firm con-ducts the remanufacturing as opposed to the OEM.Relative to the prior literature where the manufac-

turing and sales of new products alone are consideredin determining the OEM’s commonality strategy, wefind that the cost reduction and cannibalization effectsof commonality may lead to a different strategy whenremanufacturing is also considered. Specifically, withthird-party remanufacturing, commonality may handa cost reduction (from economies of scale or inventoryrisk pooling) to not only the OEM but also the thirdparty. Thus, commonality may not be preferred bythe OEM if the remanufacturing cost reduction is sub-stantial. This is in contrast to the prior literaturewhere the economies of scale and inventory risk pool-ing benefits always favor commonality because theyaccrue only to the OEM (see e.g., Kim and Chhajed2000, Labro 2004). In addition, counter to the priorliterature where a greater cannibalization effect ofcommonality is always detrimental to the OEM (againsee e.g., Kim and Chhajed 2000, Labro 2004), we findthat under third-party remanufacturing, the OEMmay benefit from a greater cannibalization effectbecause its low-end product becomes more competi-tive relative to the third party’s remanufactured prod-uct. Thus, the consideration of remanufacturing may

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality2 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

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lead to a different commonality decision than predictedby the prior literature that focuses only on new products.The remainder of this article is organized as

follows. In section 2, we position our work in relationto the extant literature. In section 3, we introduce ourmodel and its key assumptions. In section 4, wederive the optimal results (prices and segment sizes)for the no remanufacturing, OEM remanufacturing,and third-party remanufacturing scenarios. In section5, we first numerically investigate the likelihood ofcommonality decision reversals and associated profitimpacts if remanufacturing is taken into account, andcontrast the same when the OEM does the remanufac-turing vs. when a third party does the remanufactur-ing. We then analytically derive conditions underwhich component commonality decisions couldchange with the consideration of remanufacturing.We discuss the implementation of our model for theexample of iPadsTM in section 6. Section 7 discussesextensions of our model and section 8 concludes thearticle. Proofs of all results are included in AppendixA and tables pertaining to our numerical analysis arepresented in Appendix B.

2. Relation to the Literature

In practice, managerial decisions are often made with-out consideration of the remanufacturing potential ofthe product. Possible reasons include: (i) remanufactur-ing operations are often developed after the fact, (ii)remanufacturing is not viewed as the firm’s core busi-ness, and (iii) the threat from third-party remanufactur-ers is not sufficiently appreciated. Thus, even at OEMsthat do remanufacture, remanufacturing and remarket-ing operations are often handled separately from themanufacturing and marketing operations of new prod-ucts, and are mostly managed as cost centers (Guideet al. 2006, Subramanian et al. 2010). The academicliterature on closed-loop supply chains, however,demonstrates that firms that ignore remanufacturingoperations in their decision making do so at their owndetriment; the literature advocates an integratedapproach to designing and managing forward andreverse supply chains: Fleischmann et al. (2001)address the question of designing the distribution net-work with considerations for collecting used products;Toktay et al. (2000) demonstrate the value of new com-ponent sourcing policies that take into account futureproduct returns; Debo et al. (2005), Ferguson andToktay (2006), and Ferrer and Swaminathan (2006)demonstrate that product pricing for new and remanu-factured products should be undertaken jointly; Toktayand Wei (2011) develop cost allocation mechanisms tocoordinate the production volumes of new and reman-ufactured products; Debo et al. (2006) address inte-grated capacity management under the joint diffusion

of new and remanufactured products; and Savaskanet al. (2004) and Atasu et al. (2010) analyze the manu-facturer-retailer relationship under product collection.We contribute to this stream of literature by incorporat-ing remanufacturing considerations into the classiccomponent commonality decision, noting that therecent engineering-focused literature on design forremanufacturing also proposes component commonal-ity and platform-based approaches to product design(Bras 2007, King and Burgess 2005). Furthermore, wediscuss and contrast the possible economic impacts ofthe omission of remanufacturing considerations in aproduct design decision when either the OEM or athird-party firm conducts the remanufacturing.There is a rich body of literature that studies the

trade-offs involved in commonality decisions in thecontext of new articles’ manufacture and sales (seeRamdas [2003] and Labro [2004]) for reviews of thisliterature). Seminal articles identifying the benefits ofcomponent commonality include Rutenberg (1969)that recognizes the economies of scale in productionfrom using a common product module for multipleproducts, Baker et al. (1986) that recognizes the reduc-tion in inventory costs due to the pooling effect underdemand uncertainty, and Cooper (1994) and Pisanoand Rossi (1994) that recognize the reduction in over-all investments in production equipment. Lee andBillington (1994) discuss how higher component vari-ety leads to higher forecast errors; excessive invento-ries for some parts and shortages for others; higheroverhead and administrative costs; and higher manu-facturing costs due to more specialized processes,materials, changeovers, and quality assurance meth-ods. On the other hand, the literature also identifiesthe costs of component commonality to include therequired over-design of components and demand can-nibalization across differentiated products (Desaiet al. 2001, Kim and Chhajed 2000, Krishnan andGupta 2001, Robertson and Ulrich 1998, Ulrich andTung 1991). However, the context of remanufacturingby either the OEM or a third-party firm has not beenanalytically studied in prior research. Also, whereasthe above articles have addressed important dimen-sions of the component commonality decision, we inte-grate each of the key parameters into a single modeland numerically test which ones have the most signifi-cant influence on the OEM’s commonality decisionand resulting profit. Thus, we contribute to this litera-ture by developing an understanding of how remanu-facturingwould affect the commonality decision.

3. Model

In the base scenario, the OEM produces two verti-cally differentiated products that do not share anycomponents. Similar to the established marketing

Subramanian, Ferguson, and Toktay: Remanufacturing and CommonalityProduction and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society 3

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literature, we assume that each consumer’s valuationis a linear function of the product’s quality q as per-ceived by the consumer (Moorthy 1984, 1988, Mussaand Rosen 1978). In particular, consumer type h,where h is uniformly distributed on [0,1], obtainsutility hq � p from a product of quality q sold atprice p. The high-end and low-end products aredenoted by the subscripts h and l, respectively. Asmentioned earlier, we do not model the originalproduct quality choices but rather the OEM’s deci-sion of whether to implement component commonal-ity in an existing product line. Thus, the originalproduct qualities qh and ql are exogenous and satisfyqh [ ql. The OEM determines the product prices phand pl. Although the product quality levels are exog-enous, the resulting segment sizes, denoted by nhand nl, are endogenous and are determined by theOEM’s pricing decisions. We normalize the marketsize to 1 without loss of generality. The unit costs toproduce the two products are ch and cl, respectively.

3.1. Component CommonalityIf the products share common components, consum-ers may perceive a change in quality due to the simi-larity between the products, resulting in a lowerwillingness to pay for the high-end product and ahigher willingness to pay for the low-end product(Desai et al. 2001, Kim and Chhajed 2000). To capturethis phenomenon, we denote consumers’ perceivedqualities of the two products by q0h :¼ qh � D, andq0l :¼ ql þ D, respectively, where D � 0. Note thatalthough different changes in perceived qualities ofthe high- and low-end products, say, Dh and Dl, canbe considered in our model, we assume Dh ¼ Dl ¼ Dfor simplicity. Consumer type h has willingness topay hq0h and hq0l, respectively, for the high- and thelow-end products that share common components.Component commonality affects costs in two ways:

An increase in the production cost of the low-endproduct (since the common components must at leastmeet the functionality required by the high-end prod-uct) and operational cost savings due to economies ofscale or inventory risk pooling. For tractability of ourstrategic-level analysis, rather than explicitly model-ing the latter operational effects, we propose tocapture them in the unit production cost. In particu-lar, we assume that the unit production costs of thetwo products with component commonality arec0h :¼ ch � s and c0l :¼ gcl � s, where s > 0 and g > 1.Although the total savings could potentially be con-vex in the number of units due to inventory risk pool-ing and economies of scale, the additive per-unitsavings s allows us to capture a first-order approxi-mation of these benefits while maintaining tractabil-ity. The multiplier increase in the per-unit cost ofproducing the lower quality product, g, reflects the

fact that components often have to be overdesigned toimplement commonality; g > 1 captures the increasein the cost of the low-end product since the commoncomponents must at least meet the functionalityrequired by the high-end product.In practice, there may be a fixed cost associated

with redesigning the products to allow the use ofcommon components. However, this fixed cost doesnot influence market segmentation decisions andaffects our results in the expected direction: Com-monality becomes less profitable as the fixed costincreases. Therefore, for exposition, we assume fixedcosts to be zero and do not include them in ouranalysis.

3.2. RemanufacturingTo clearly compare the commonality-related trade-offs under OEM remanufacturing and under third-party remanufacturing, and to ensure tractability, weassume that either the OEM or a third party does theremanufacturing, but not both. This is observed inpractice as well, because when the OEM remanufac-tures herself, she typically structures the sales process(using product leases or trade-in rebates) to ensurethat the majority of the used products come back toher and not to a third party. Examples of industrieswhere the OEM typically dominates the remanufac-tured product market include business and industrialequipment (e.g., commercial power tools, commercialcopiers, and machine tools), cameras and photo-graphic equipment, and home and garden products(e.g., vacuum cleaners); see, for example, Subramani-an and Subramanyam (2012) and the remanufacturingindustry profiles in Ferguson et al. (2010). On theother hand, when third-party firms are well estab-lished, the OEMs are typically hesitant to participatein the remanufactured product market either due tomanagerial and cost hurdles, or so as to not legitimizethis market. Products that are observed to be mostlyremanufactured by third parties include cellphonesand personal digital assistants (PDAs), computers andnetworking equipment (e.g., routers and switches),and video game consoles (Subramanian and Sub-ramanyam 2012).We also assume that when either the OEM or the

third party remanufactures, they use the high-endproduct for this purpose. This assumption is basedon the observation from practice (e.g., laptop com-puters and power tools) that remanufactured ver-sions are typically offered for OEMs’ higher-endproducts, since the lower willingness to pay for theremanufactured version of a product makes thelow-end products less profitable to remanufacture.To capture possible constraints on collection and/oryields on collected product cores, we include aconstraint on the size of remanufactured product

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality4 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

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segment, nr � qnh, where ρ ∈ (0,1]. For simplicity, weanalyze a base scenario where the third party’s andthe OEM’s remanufacturing cost structures are thesame; if the remanufacturing cost or access to prod-uct cores is less favorable for the third party, thiswould reduce the OEM’s profit impact from a com-monality decision that ignores remanufacturing.Guide and Li (2010) and Subramanian and Subr-

amanyam (2012) offer empirical evidence of the lowervaluation of remanufactured products by consumers.To model this, we assume that a consumer’s valuationper unit of quality for the remanufactured product is afraction k ∈ (0,1) of its valuation for the high-end newproduct. For simplicity, we assume the same relativevaluation of the remanufactured product with andwithout commonality. Thus, qr :¼ kqh (base scenario)and q0r :¼ kðqh � DÞ (with component commonality),with the valuation of the remanufactured productassumed to be located between the valuations of thehigh-end and low-end products (i.e., ql \ qr \ qh, and

q0l \ q0r \ q0h, implying that we assume k[ qlþDqh�D).

Although we focus on the scenario where only thehigh-end product is remanufactured and the per-ceived quality of the remanufactured product isbetween the perceived qualities of the low- and high-end products, we recognize that other scenarios arepossible. Although the steps in the analysis are gener-alizable, we caution the reader that our findings arelimited to the aforementioned scenario (in section 8,we qualitatively discuss the implications of extendingthe model to allow for the low-end product beingremanufactured). The model can also be extended toinclude a fraction of consumers who would not con-sider the remanufactured product at any price, but ourqualitative results do not change with this generaliza-tion (please see section 7 for a discussion). The unitcost to remanufacture is cr for the base scenario andacr, on average, with component commonality (a < 1).This captures the fact that sharing components acrossproducts should reduce the cost to remanufacturethem because of improved access to components,reduced safety stocks, and a reduced effect of uncer-tainty in remanufacturing yields. A lower a reflects asetting for which such benefits are higher. For ease ofreference, we summarize our notation in Table 1.

4. Analysis

Our objective is to understand how the OEM’s choiceof whether to implement component commonality ornot is affected by secondary market considerations,namely remanufacturing by the OEM or by a third-party remanufacturer. Sections 4.1, 4.2, and 4.3,respectively, analyze the benchmark scenario withmanufacturing only, the scenario with OEM remanu-

facturing, and the scenario with third-party remanu-facturing. The optimal commonality decisions underthese scenarios are contrasted in section 5. To avoidend-of-horizon effects from affecting our insights, wedevelop a model of a representative period whereboth manufacturing and remanufacturing occur, as in

Table 1 Notation

Symbol Description

Subscriptsh, l, r high-end, low-end, remanufactured productM,T Manufacturer (OEM), Third-PartySuperscripts ScenarioFN Forward Chain (No Remanufacturing), No

CommonalityFC Forward Chain (No Remanufacturing), with

CommonalityMN OEM Remanufacturing, No CommonalityMC OEM Remanufacturing, with CommonalityTN Third-Party Remanufacturing, No CommonalityTC Third-Party Remanufacturing, with Commonalityqj Perceived quality of product j with no

commonality; j ∈ {h,l}D Effect of commonality on perceived product

qualityq0h ¼ qh � D Perceived quality of the high-end product under

commonalityq0l ¼ ql þ D Perceived quality of the low-end product under

commonalityk ∈ (0,1) Valuation of the remanufactured product relative

to the high-end productqr ¼ kqh Perceived quality of the remanufactured product

with no commonalityq0r ¼ kq0h Perceived quality of the remanufactured product

under commonalitycj Unit production cost of product j; j ∈ {h,l,r}s > 0 Savings (on average) in unit production costs

from commonalityg > 1 Effect of commonality on the unit production

cost of the low-end productc 0h ¼ ch � s Unit production cost of the high-end product

under commonalityc 0l ¼ gcl � s Unit production cost of the low-end product

under commonalitya ∈ (0,1) Effect of commonality (on average) on the unit

remanufacturing costc 0r ¼ acr Unit remanufacturing cost under commonalitypj (p

0j ) Price of product j without (with) commonality;

j ∈ {h,l,r}nj (n

0j ) Segment size for product j without (with)

commonality; j ∈ {h,l,r}ρ ∈ (0,1] Fraction of high-end product sales that can

be remanufacturedPi

k Profit of entity k under scenario i ;k ∈ {M,T}, i ∈ {FN,FC,MN,MC,TN,TC}

PFDM ¼ PFC

M � PFNM Benefit of commonality to the OEM under no

remanufacturingPMD

M ¼ PMCM � PMN

M Benefit of commonality to the OEM under OEMremanufacturing

PTDM ¼ PTC

M � PTNM Benefit of commonality to the OEM under

third-party remanufacturing½��ij Optimal/Equilibrium value of [·] for product

j and scenario i ;j ∈ {h,l,r}, i ∈ {FN,FC,MN,MC,TN,TC}

Subramanian, Ferguson, and Toktay: Remanufacturing and CommonalityProduction and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society 5

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Savaskan et al. (2004). Since the No Commonality sce-nario is a special case of the Commonality scenariowith D = 0, g = 1, s = 0, and a = 1, we only presentthe results for the Commonality scenario. All the ana-lytical and numerical results are presented for param-eter settings where the optimal/equilibrium segmentsizes are positive (nh [ 0, nr [ 0 if applicable, andnl [ 0) and nr \ qnh holds such that these first-orderconditions can be independently solved to obtainunconstrained optimal (or equilibrium) solutions. Weomit the associated explicit parameter conditions forbrevity. We also analyze the case where nr ¼ qnh holdsat optimality (or in equilibrium), and discuss the differ-ences relative to the unconstrained case in section 7.

4.1. Manufacturing Only (Forward Chain)This is the base scenario where the OEM only pro-duces two vertically differentiated products. Recallthat the perceived qualities of the high- and low-endproducts are given by q0h ¼ qh � D and q0l ¼ ql þ D,and prices (decisions) are denoted by ph and pl,respectively. The net utilities that consumer type hobtains from these products are uhðhÞ ¼ hq0h � ph andulðhÞ ¼ hq0l � pl, respectively, from which the seg-ment sizes nh and nl can be derived for given prices.Unit production costs are c0h ¼ ch � s andc0l ¼ gcl � s. The OEM’s profit is:

PM ¼ nhðph � c0hÞ þ nlðpl � c0lÞ: ð1Þ

LEMMA 1. The optimal prices and segment sizes in the

manufacturing-only scenario are: ph ¼ 12 ðq0h þ c0hÞ,

pl ¼ 12 ðq0l þ c0lÞ, and nh ¼ 1

2

ðq0h�q0

lÞ�ðc0

h�c0

ðqh�qlÞ , nl ¼ 12

ðq0lc0h�q0

hc0lÞ

q0lðq0

h�q0

lÞ .

4.2. OEM RemanufacturingIn this scenario, the OEM produces two new products(high- and low-end) and a remanufactured version of

the high-end product. The perceived quality of theremanufactured product is q0r :¼ kq0h, whereq0h [ q0r [ q0l. Prices (decisions) are ph, pr, and pl, andthe resulting segment sizes are nh, nr, and nl. Net utili-ties from the products are uhðhÞ ¼ hq0h � ph,urðhÞ ¼ hq0r � pr, and ulðhÞ ¼ hq0l � pl. Unit produc-tion costs are c0h, c

0r ¼ acr, and c0l, where a ∈ (0,1)

captures the reduction in remanufacturing costs fromcommonality (i.e., a lower a implies a greater reduc-tion in the unit remanufacturing cost from commonal-ity). The OEM’s profit is:

PM ¼ nhðph � c0hÞ þ nrðpr � c0rÞ þ nlðpl � c0lÞ: ð2Þ

LEMMA 2. The optimal prices and segment sizes in the

OEM remanufacturing scenario are: ph ¼ 12 ðq0h þ c0hÞ,

pr ¼ 12 ðq0r þ c0rÞ, pl ¼ 1

2 ðq0l þ c0lÞ, and nh ¼ 12

ðq0h�q0rÞ�ðc0

h�c0rÞ

ðq0h�q0rÞ ,

nr ¼ 12

q0rðc0h�c0lÞ�q0

hðc0r�c0

l�q0

lðc0

h�c0rÞ

ðq0h�q0rÞðq0r�q0

lÞ , nl ¼ 1

2

ðq0lc0r�q0rc

0lÞ

q0lðq0r�q0

lÞ .

4.3. Third-Party RemanufacturingFor this scenario, we assume that the OEM is the Stac-kelberg leader who chooses prices ph and pl for hernew products. The third-party remanufacturerchooses price pr for the remanufactured high-endproduct as a best response. We solve for the equilib-rium prices and segment sizes by backward induc-tion. The OEM’s profit is:

PM ¼ nhðph � c0hÞ þ nlðpl � c0lÞ: ð3Þ

And the third-party remanufacturer’s profit is:

PT ¼ nrðpr � c0rÞ: ð4Þ

LEMMA 3. The optimal prices and segment sizes in thethird-party remanufacturing scenario are:

ph ¼ 1

2

2q0rq0lq

0h þ q0lc

0hq

0h þ 2q0lq

0rc

0r � 3q0r

2q0l þ 3q0rq0lc0h þ q0lq

0h2 � q0rc

0lq

0h þ q0r

2c0lq0r

2 � 4q0rq0h þ 2q0rq

0l þ q0lq

0h

þ 1

2

4q0r2q0h � 4q0rc

0hq

0h � 2q0rq

0hc

0r � 4q0rq

0h2

q0r2 � 4q0rq

0h þ 2q0rq

0l þ q0lq

0h

;

pr ¼q0r q0lq

0h � q0rq

0l þ 2q0lc

0r þ q0lc

0h � q0rc

0h þ q0r

2 � c0lq0h þ q0rc

0l � 2q0hc

0r � q0rq

0h

� �

q0r2 � 4q0rq

0h þ 2q0rq

0l þ q0lq

0h

;

pl ¼ 1

2

q0l2q0h � 4q0rc

0lq

0h � q0rq

0lq

0h þ q0r

2q0l � 2q0lq0hc

0r � q0rq

0lc0h þ 3q0rc

0lq

0l þ 2q0l

2c0r þ q0r2c0l þ q0l

2c0h � q0l2q0r

q0r2 � 4q0rq

0h þ 2q0rq

0l þ q0lq

0h

; and

nh ¼ 1

2

2q0rq0lq

0h � q0rq

0lc0h � q0lc

0hq

0h � q0rc

0lq

0h þ 2q0lq

0rc

0r þ 4q0rc

0hq

0h � 2q0rq

0hc

0r þ q0lq

0h2 � 3q0r

2q0l þ q0r2c0l

ðq0r2 � 4q0rq0h þ 2q0rq

0l þ q0lq

0hÞðq0h � q0rÞ

þ 1

2

4q0r2q0h � 4q0rq

0h2 � 2q0r

2c0hðq0r2 � 4q0rq

0h þ 2q0rq

0l þ q0lq

0hÞðq0h � q0rÞ

;

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality6 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

Page 7: Remanufacturing and the Component Commonality Decision

5. Investigating Reversals in theCommonality Strategy

Define PFDM :¼ PFC

M � PFNM as the increase in the

OEM’s profit from commonality when there is noremanufacturing. When this value is positive, theOEM benefits from component commonality in themanufacturing-only scenario. Similarly, definePMD

M :¼ PMCM � PMN

M as the OEM’s profit increasefrom commonality when the OEM undertakes theremanufacturing of her high-end product. When thisvalue is positive, the OEM benefits from componentcommonality in the OEM remanufacturing scenario.Finally, define PTD

M :¼ PTCM � PTN

M as the increase inthe OEM’s profit from commonality when the reman-ufacturing of her high-end product is conducted by athird-party remanufacturer. When this quantity ispositive, the OEM benefits from investing in com-monality despite the fact that the secondary market isexploited by a third party.We focus on the cases where the OEM’s preferred

commonality strategy differs with and withoutremanufacturing. In particular, identifying whetherthe signs of PFD

M and PMDM are reversed helps us

answer the following question: Will the OEM’s com-monality strategy be different if she takes into account thatshe will engage in remanufacturing? Similarly, weinvestigate sign reversals between PFD

M and PTDM to

answer the following question: Will the OEM’s com-monality strategy be different if she takes into account thata third party will engage in remanufacturing? For easeof exposition, we summarize the reversals of interestin Table 2.We measure the profit impact or opportunity cost

of a commonality decision that is made without con-sideration of remanufacturing, as:

First, in section 5.1, we present a detailed numericalstudy that illustrates the likelihood of commonalitydecision reversals and the magnitude of associated

profit impacts. The numerical study also identifies theparameters that most significantly explain decisionreversals and profit impacts. We then analytically char-acterize the effects of parameters that capture the costeffects of commonality—namely, a, s, and g—on thesereversals in section 5.2. We numerically illustrate theeffect of the market-related parameter D because ana-lytical results cannot be obtained for it. Where possible,we relate the findings to specific types of products thatare remanufactured in practice, drawing from Subra-manian and Subramanyam’s (2012) data on remanu-factured products purchased on eBay across differentproduct categories that include Business and Indus-trial, Cameras and Photo, Cellphones and PDAs, Com-puters and Networking, Consumer Electronics, Homeand Garden, Musical Instruments, and Video Games.Finally, we present the analysis of a specific product(iPadsTM) in section 6.

5.1. Numerical StudyWe illustrate the likelihood of commonality decisionreversals and the magnitude of associated profitimpacts through a broad numerical study. Table 3summarizes the parameter ranges used in the numeri-cal study. We choose these parameter ranges to berepresentative of a broad range of industries whereremanufacturing is conducted, and, where available,base them on previous research studies. To examine arange of separation between the perceived qualities ofthe high- and low-end products, we set ql ¼ 10 andvary qh between 15 and 40. To examine the cannibal-ization effect, we vary D such that at its highest value,D brings the low- and high-end products close enoughyet preserves the ordering of perceived qualities. Toconsider a range of margins from the products, we varycj between 0:3qj and 0:9qj, ∀j ∈ {h,l,r}. With respect to

the other parameters, we vary a between 0.5 and 0.9so that commonality reduces the cost of remanufac-turing by up to 50%; we vary k between 0.5 and 0.9

nr ¼ q0hq0l2c0r � q0rc

0lq

0h2 � q0lq

0h2c0r þ 2q0rq

0h2c0r � q0rq

0l2q0h � q0rq

0l2c0h þ q0r

2q0lc0h � q0r

2q0lc0l þ q0lq

0rq

0h2 � q0r

3q0lðq0r2 � 4q0rq

0h þ 2q0rq

0l þ q0lq

0hÞðq0h � q0rÞðq0r � q0lÞ

þ q0r2q0l

2 þ q0r3q0h � q0r

2q0h2 � 2q0rq

0lq

0hc

0r þ q0rq

0lc0lq

0h þ q0lq

0rc

0hq

0h þ q0lq

0r2c0r þ q0r

2c0lq0h � q0r

2c0hq0h � q0r

2q0hc0r

ðq0r2 � 4q0rq0h þ 2q0rq

0l þ q0lq

0hÞðq0h � q0rÞðq0r � q0lÞ

;

nl ¼ 1

2

q0r q0l2q0h � q0l

2q0r þ 2q0l2c0r þ q0l

2c0h � q0rq0lc0h � 2q0lc

0lq

0h � q0rc

0lq

0l

� �

ðq0r2 � 4q0rq0h þ 2q0rq

0l þ q0lq

0hÞðq0r � q0lÞq0l

þ 1

2

q0r q0r2q0l � 2q0lq

0hc

0r � q0rq

0lq

0h þ 4q0rc

0lq

0h � q0r

2c0l� �

ðq0r2 � 4q0rq0h þ 2q0rq

0l þ q0lq

0hÞðq0r � q0lÞq0l

:

Profit from decision that considers remanufacturing�Profit from decision that ignores remanufacturing

Profit from decision that ignores remanufacturing� 100

Subramanian, Ferguson, and Toktay: Remanufacturing and CommonalityProduction and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society 7

Page 8: Remanufacturing and the Component Commonality Decision

(as observed in Subramanian and Subramanyam2012) provided the ordering of perceived qualities ismaintained; we vary g such that commonalityincreases the cost of the low-end product by 10% to amaximum of 90%; and, we vary s from 0:1cl to a maxi-mum of 0:5cl so that the savings in unit productioncosts from commonality is up to half the cost of thelow-end product.We vary the parameters from their minimum to

their maximum values in equispaced increments in afull-factorial fashion and omit those parameter combi-nations that violate any one of the conditionsnh; nr; nl; qnh � nr [ 0 at the solution of the first-orderconditions. This yields a set of 5,939 parameter combi-nations. Analyzing these instances with respect to theprevalence of different types of reversals and theirprofit impacts, we develop the following managerialguidelines:1. It is much more important to take remanufactur-

ing into account when it is a third party that reman-ufactures: The component commonality decisionchanged in 34.7% of the numerical instances in our setwith third-party remanufacturing, whereas this per-centage was only 2% with OEM remanufacturing.Further, the median opportunity cost of ignoringremanufacturing was 18.20% with third-party reman-ufacturing but only 0.33% under OEM remanufactur-ing.This is an intriguing finding in that the impact of

component commonality is dramatically differentbetween the OEM-remanufacturing and third-party-remanufacturing scenarios: If the OEM anticipatesthat she will be able to monopolize the remanufac-

tured product market, then she can afford to ignoreremanufacturing in determining the commonalitydecision (the optimal commonality decision for themanufacturing-only scenario continues to be optimalwith OEM remanufacturing in 98% of the numericalinstances). However, if she expects third parties todominate, component commonality should be ele-vated to a more strategic level, and the effect of third-party remanufacturing should be taken into accountat the outset (the optimal commonality decision forthe manufacturing-only scenario continues to be opti-mal with third-party remanufacturing in only 65.3%of the numerical instances; also, the opportunity costsof ignoring remanufacturing are rather significant, asdiscussed in point 3 below). Products that areobserved to be largely remanufactured by OEMsinclude business and industrial equipment (e.g., com-mercial power tools), cameras and photographicequipment, and home and garden products (e.g., vac-uum cleaners), whereas products that are observed tobe mostly remanufactured by third parties includecellphones and PDAs, computers and networkingequipment (e.g., routers and switches), and videogame consoles: Subramanian and Subramanyam(2012) find that more than 65% of the products in theformer categories are remanufactured by OEMs,whereas more than 65% of the products in the lattercategories are remanufactured by third parties. Thus,OEM attention for the design of the latter types ofproducts should be focused on the eventuality ofthird-party remanufacturing at the outset.2. If the OEM anticipates third-party remanufac-

turing, it is much more important to review an“Implement Commonality” decision than a “Do NotImplement Commonality” decision: In our numeri-cal set, 88% of all reversals (or, 30.5% of all parametercombinations) were of the C ? NC type under third-party remanufacturing. Although the extent of thisdominance may not have been anticipated, it can beexplained by considering who reaps the benefits ofcommonality (if any) at the remanufacturing stage:When it is a third party, commonality becomes lessattractive to the OEM because some of the benefitsaccrue to the third party.The larger implication of this result is that not

investing in component commonality can be used as

Table 2. Types of Reversals in the Commonality Decision When Remanufacturing Is Taken into Account

Remanufacturing by Reversal type OEM preference if reman ignored OEM preference if reman considered

OEM PFDM [ 0 but PMD

M \ 0 Commonality No Commonality

PFDM \ 0 but PMD

M [ 0 No Commonality Commonality

Third party PFDM [ 0 but PTD

M \ 0 Commonality No Commonality

PFDM \ 0 but PTD

M [ 0 No Commonality Commonality

Table 3. Parameter Ranges for the Numerical Study

Parameter Min Increment Max

g 1.1 0.2 1.9k 0.5 0.1 0.9ql 10 0 10qh 15 5 40D 0 qh�ql

15qh�ql

3

cl 0.3ql 0.15ql 0.9 qlcr 0.3qr 0.15qr 0.9 qrch 0.3qh 0.15qh 0.9 qha 0.5 0.1 0.9s 0.1cl cl 0.5 cl

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality8 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

Page 9: Remanufacturing and the Component Commonality Decision

an entry deterrent strategy (see Ferguson and Toktay[2006] for other such strategies). Indeed, an examina-tion of our numerical data reveals cases where theequilibrium size of the remanufactured product seg-ment is 0 if the OEM does not choose commonality,but the segment is in fact served by the third party ifthe OEM chooses commonality. Our numerical analy-sis suggests that such preemption (where it is optimalfor the OEM to not choose commonality, whichcauses the third party to be forced out of the market)is facilitated if the savings in unit production costs sfrom commonality is relatively small but the benefitof commonality to the third party is high (i.e., a islow). The same effect is seen if D is low, which makesthe low-end product of the OEM less competitivecompared to the remanufactured product if common-ality is chosen. In contrast, as the remanufacturedproduct becomes more competitive (i.e., as the rela-tive willingness to pay k increases), the prospect ofpreemption of the third party by not choosing com-monality diminishes.3. The profit improvement obtained from opti-

mally adopting commonality in the absence ofthird-party competition is dominated by the oppor-tunity cost of this strategy being sub-optimal shouldthird-party remanufacturing emerge: In our numeri-cal study, this occurs for 71.9% of the instances wherecommonality is the optimal strategy in the absence ofremanufacturing. In these instances, the averageprofit improvement from adopting commonality inthe absence of remanufacturing is 10.45%, whereasthe average opportunity cost of this decision ceasingto be optimal if third-party remanufacturing emergesis 24.62%.The reason for this strong effect is the following:

When there is no remanufacturing, commonality hasa cost-reduction benefit for only the OEM’s new prod-ucts. In contrast, under third-party remanufacturing,commonality also reduces the cost of remanufactur-ing for the third party, allowing him to price theremanufactured product more aggressively, puttingdownward pressure on new product prices and/orhelping the third party obtain greater market share.The negative competitive effects dominate the posi-tive cost effect, resulting in a large opportunity costfor the OEM from having chosen commonality.

5.2. Comparative Statics for Third-PartyRemanufacturingGiven their prevalance and significant profit impacts,we further investigate commonality decision reversalsunder third-party remanufacturing. Table 4 summa-rizes how the commonality-related parameters in ourmodel may influence the competitiveness of theOEM’s products under third-party remanufacturing.To assess the relative significance of these parameters

in explaining the likelihood of commonality decisionreversals or the magnitude of profit impact, we usethe regression approach in Global Sensitivity Analysis(GSA; Souza et al. 2004, Wagner 1995). GSA involvesrunning a regression of the metric of interest (i.e.,dependent variable such as indicator of change in thecommonality decision or profit impact) on the mod-el’s parameters (i.e., independent variables) to iden-tify the parameters that have the most significanteffects. Results of these regressions are summarizedin Table 5. Tables B1–B4 in Appendix B present theregression coefficients and t-statistics for the fourregressions.An examination of Table 5 yields the following rec-

ommendations for OEMs facing third-party remanu-facturing:

1. It is important to review the “Implement Common-ality” decision for products that promise largersavings from commonality to the third-partyremanufacturer (a low) or whose production costsavings to the OEM from commonality are low (slow). The associated profit impacts of ignoringremanufacturing, too, are significantly influencedby these cost factors.

This observation is further supported by Proposi-tion 1, which indicates that if commonality is prefera-ble under no remanufacturing, but is not preferableunder third-party remanufacturing, this happensbelow a threshold value of a or s. The intuition is thatas a decreases, the cost of remanufacturing decreases.

Table 4. Anticipated Competitive Effects of Commonality-RelatedParameters Under Third-Party Remanufacturing

Parameter Effect of a larger value of the parameter

g A larger g makes the OEM’s low-end product lesscompetitive compared to the third-party’sremanufactured product.

D A larger D makes the OEM’s low-end product morecompetitive but the high-end product less competitivecompared to the third-party’s remanufactured product.

a A larger a makes the third-party’s remanufactured productless competitive compared to the OEM’s products.

s A larger s makes the OEM’s products more competitivecompared to the third-party’s remanufactured product.

Table 5 Three Most Significant Parameters (in Decreasing Order ofSignificance) that Explain Commonality Decision Reversalsand Profit Impacts Under Third-Party Remanufacturing

Type ofdecisionreversal

Parameters thatexplain decision

reversal

Parameters thatexplain profit impact

given decisionreversal occurs

C ? NC ↓a, ↑g, ↓s ↓a, ↓s, ↑gNC ? C ↑D, ↓g ↑a ↑D, ↓g, ↑s

A downward ↓ (upward ↑) arrow in front of a parameter means that asthat parameter decreases (increases), the metric of interest increases

Subramanian, Ferguson, and Toktay: Remanufacturing and CommonalityProduction and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society 9

Page 10: Remanufacturing and the Component Commonality Decision

Thus, under third-party remanufacturing, low valuesof a enhance third-party competition and, in turn,hurt the OEM. Also, as s decreases, the OEM faces thedisadvantage of a lower reduction in the manufactur-ing cost from commonality.

PROPOSITION 1. All else being equal, the case where com-monality is preferred in the manufacturing-only scenariobut is not preferred in the third-party remanufacturingscenario (i.e., PFD

M [ 0 but PTDM \ 0, or a C ? NC

reversal) can exist: (i) below a threshold value of a (i.e.,the effect of commonality on the unit remanufacturingcost), or (ii) below a threshold value of s (i.e., the savingsin unit production costs from commonality). Further, (iii)the manufacturing savings threshold �sðaÞ below which aC ? NC reversal takes place decreases as a increases.

Figure 1 illustrates this proposition and providesinsight on interaction effects not captured by the GSAapproach, namely, that �sðaÞ decreases in a. The ratio-nale is the following: As a decreases, remanufacturingbenefits more from commonality. Since the third partybecomes more competitive, the OEM chooses to notimplement component commonality over a largerrange of manufacturing savings s that accrue to herself.Ferrer and Whybark (2003) discuss how product

complexity may affect the economics of remanufac-turing. The number of components across differentproduct modules—including the casing, the functionalmodule, functional connectors, and structural connectors—affect product complexity. Since remanufacturing istypically labor intensive, product lines with greatercomplexity and component diversity entail greaterworker skills and training and, thus, higher costs ofremanufacturing. Such products, in turn, affordgreater savings in remanufacturing from commonal-ity (i.e., low a). A similar level of savings from

commonality may not be derived in manufacturing(i.e., s is low) if flexible automation or delayed differ-entiation is employed.

2. It is important to review the “Do Not ImplementCommonality” decision if, with commonality, thelow-end product’s contribution margin and com-petitiveness vis-a-vis the remanufactured productare high, i.e, g is low and D (or, equivalently, q0l)is high.

This is an interesting result that underlines thepotential for commonality to provide a competitiveadvantage vis-a-vis the third party. The low-endproduct’s market position is elevated through com-monality such that it cannibalizes the third party’sremanufactured product. If the production costincrease of the low-end product is low enough, a com-monality strategy is beneficial to the OEM despite theremanufacturing cost advantage it confers on thethird party. Proposition 2 provides support for thisresult with respect to g; however, the effect of D canonly be characterized numerically.

PROPOSITION 2. All else being equal, (i) the case wherecommonality is not preferred in the manufacturing-onlyscenario but is preferred in the third-party remanufacturingscenario (i.e., PFD

M \ 0 but PTDM [ 0, or an NC ? C

reversal) can exist below a threshold value of g (i.e., theeffect of commonality on the unit production cost of thelow-end product). Further, (ii) the threshold �gðaÞ belowwhich an NC ? C reversal takes place increases as aincreases.

Figure 2 illustrates the above results and highlightsinteraction effects with a. Under third-party remanu-facturing, as a increases (giving a smaller cost advan-tage to the third party), commonality is preferable forthe OEM for a larger range of increase in the low-endproduct’s cost, that is, �gðaÞ increases in a (Figure 2a).In other words, the OEM has a greater opportunity touse the low-end product to compete with the thirdparty when the third party’s gain from commonalityis low. On the other hand, as a increases, the thresholdfor D above which the OEM would switch to com-monality decreases, that is, �DðaÞ decreases in a (Figure2b). This is because a higher degree of cannibalizationof the remanufactured product by the low-end prod-uct and a higher remanufacturing cost are substitutes;they both reduce the threat from the third-partyremanufacturer.An example to the situation discussed herein is any

product family that uses common product casings.Product casings are typically the least expensive tomake common (i.e., g low) yet may significantlyimpact perceived value (i.e., D high) because of imme-diate visibility. Common casings for low- and

Figure 1 Parameter Regions Depicting C ? NC Reversals in the s � a

Space (Parameter Values: qh = 20, ql = 10, k = 0.7, D = 1,ch ¼ 7, cl ¼ 3, cr ¼ 5, g = 1.2)

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality10 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

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high-end models are employed in several OEM prod-ucts, including computers and networking equip-ment, consumer electronics, cellphones and PDAs,and cameras. Many news articles and discussion for-ums show up in a simple Internet search with “samechassis” as the search phrase; the discussions evi-dence the potentially high cannibalization effectbetween the low- and high-end products (e.g., Tom’sHardware 2007); the cannibalization effect betweenthe low- and remanufactured high-end productswould be even more pronounced.Tying the findings in this section back to Table 4,

we observe that all of them can be explained by thecompetitive implications of commonality choice. Thedirectional effects of the most significant parameterson C ? NC (NC ? C) decision reversals and theassociated profit impacts are consistent with the OEMbecoming less (more) competitive as compared to thethird party by choosing commonality. In the C ? NCcase, cost-related parameters have the most significantcompetitive implications, whereas in the NC ? C case,we find that the effect of commonality on perceived

quality assumes a large importance. This is becauseNC ? C reversals occur when the low-end productcan compete strongly with the remanufactured prod-uct, which is enabled by the changes in perceivedquality from commonality. Table 6 adds the inter-action effects discussed above to update the findingssummarized in Table 5.

6. Numerical Illustration: Example ofiPads

In this section, we discuss the implementation of ourmodel using the example of iPadsTM. We use iPads asan example because: (i) iPads had a � 90% marketshare of the tablet market in 2010 (Business Insider2011), (ii) cost estimates for different iPad models areavailable through product teardowns by marketresearch firms such as iSuppli Corporation (Crothers2010, see Table 7), (iii) the teardowns reveal a signifi-cant extent of commonality across the different iPadmodels, and (iv) iPads are sold to end customers onlyas complete units (i.e., parts are not available sepa-rately).Although the choice of iPads as an example may

not be a perfect match with our model assumptions(e.g., both high- and low-end iPad models are nowremanufactured by Appler as well as third parties),

(a)

(b)

Figure 2 Parameter Regions Depicting NC ? C Reversals in theg � a and D � a spaces (Parameter Values: qh ¼ 20,ql ¼ 10, k = 0.8, ch ¼ 7, cl ¼ 3, cr ¼ 5, s = 1)

Table 7 iPadTM Bill of Materials, Cost Breakdown, and Retail Prices

Components 16GB 64GB

Core componentsDisplay and touchscreen $80.00 $80.00Electromechanical and mechanical $35.30 $35.30Battery $17.50 $17.50

MPU and memoryA4 processor $17.00 $17.00Supporting DRAM $11.90 $11.90

WLAN n + BT + FM $8.05 $8.05User interface components $10.20 $10.20Other power management components $2.40 $2.40Configuration-dependent componentsNAND flash $29.50 $118.00

Other costsBox contents $7.50 $7.50

TotalsTotal materials cost $219.35 $307.85Total manufacturing cost $10.00 $10.00

Grand total $229.35 $317.85Retail price $499.00 $699.00

Source: iSuppli Corporation (Crothers 2010)

Table 6 Significant Parameters that Explain Commonality DecisionReversals, and Selected Interaction Effects

Type ofdecision reversal

Parameters thatexplain decisionreversal Interaction effects

C ? NC ↓a, ↑g, ↓s �sðaÞ # in aNC ? C ↑D, ↓g ↑a �gðaÞ " in a; �DðaÞ # in a

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Page 12: Remanufacturing and the Component Commonality Decision

the publicly available component breakdown and costdata for iPads allows us to demonstrate how ourmodel can be used in practice and affords insightsinto the opportunity cost of ignoring remanufacturingwith realistic (albeit approximate) data.For our illustration, we consider the 16GB version

of the iPad as the low-end product and the 64GB ver-sion as the high-end product. To validate the rele-vance of our research questions, we interviewed apractitioner familiar with the remanufacturing ofApple’s products (Mr. Brian Gventer, former Director,ATC Logistics & Electronics). From these interviews,we learned that (i) third-party remanufacturers facegreater costs for parts than Apple does in manufactur-ing, in some cases up to 10 times as much (e.g., theLCD screen). Further, “the cost for getting at the parts[from product cores] is very low since a relativelyunskilled temp can take the unit apart once shownhow.” Thus, component commonality can signifi-cantly benefit third parties since their remanufactur-ing yields increase due to access to greater volumes ofcomponents; and (ii) certain steps of the remanufac-turing process, such as diagnosing what it would taketo fix the device and performing board-level work,are complex, requiring skilled technicians with a lowthroughput rate. Apart from the NAND flash mem-ory difference, the 16GB and 64GB models are essen-tially identical. The high degree of componentcommonality can be expected to reduce the overallcomplexity of problem diagnosis across the productmodels. At the same time, the ability to salvage agreater number of usable parts (including entireboards) from product cores would decrease replace-ment parts costs and/or increase the remanufacturingprocess throughput.

6.1. Calibrating the Model to Known Parameters/DecisionsWe assume that the prices of the 16GB and 64GBiPads at the time of product release (April 2010) corre-spond to the prices in our “manufacturing only” sce-nario or the forward chain (section 4.1). Further, theproduct teardowns reveal that many components areshared across the 16GB and 64GB models, includingthe display and touchscreen; electromechanical andmechanical components; battery; processor, and sup-porting DRAM (memory); wireless LAN, bluetooth,and FM circuitry; user interface components; andpower management components (see Table 7). Wetherefore assume that the OEM (Apple) has made anoptimal decision to choose Commonality for the for-ward chain. Thus, Lemma 1 is the relevant analyticalresult for calibration purposes.iSuppli’s total materials and manufacturing cost

estimate for the 16GB model is $229.35 and that forthe 64GB model is $317.85 (Crothers 2010). However,

these cost estimates do not include potential savingsfrom inventory pooling and economies of scale fromhaving common components (i.e., the value of s inc0h ¼ ch � s and c0l ¼ gcl � s is not accounted forby iSuppli). Therefore, we set ch ¼ 317:85 andgcl ¼ 229:35. Due to the high level of commonalitybetween the 16GB and 64GB models, we assume thatthe benefit of inventory pooling and economies ofscale is 15–30% of product cost (i.e., s ranges from 40to 50). With regard to the cannibalization effect D, weobserve that most comments in Apple’s discussionforums cite the memory difference as being an impor-tant differentiating factor; in other words, that common-ality in the other components is not a significant reasonfor consumers to move away from the 64GB model.Therefore, we assume moderate values for D (50–70,which works out post facto to a 4–9% effect of common-ality on perceived qualities). The prices of the 16GB and64GB models at product release were $499 and $699,respectively. If we assume that Apple priced the prod-ucts optimally for the forward chain, we havepFCl ¼ 499 and pFCh ¼ 699. Using the expressions forpFCl and pFCh from Lemma 1, we can solve for qh and ql.

6.2. Implications of Ignoring Third-PartyRemanufacturingWith a third-party remanufacturer in the fray, ourpurpose is to compare the OEM’s profit with com-monality against that in the hypothetical situationwhere the OEM did not choose commonality in thefirst place. To fully specify our model, we need to pro-vide base values for the parameters k, cr, g, and a,noting to the best of our experience that OEMs andthird-party remanufacturers do not always track theseparameters. Using eBay data from late 2010, we foundthat the purchase prices of remanufactured iPadswere, on average, about 85% of corresponding newiPad prices (average over 10 transactions = 84.47%,standard deviation = 6.94%). We therefore set thebase value of k to be 0.85. As mentioned earlier, thecosts of replacement parts can be quite high for thirdparties that remanufacture Apple’s products. Conse-quently, we set the base value of cr for the third partyto be 0:85ch. Due to the high level of commonalitybetween the 16GB and 64GB models, we assume thefollowing base values: (i) g = 1.5, that is, a 50%increase in the cost of the low-end product whenmoving from the hypothetical No Commonality sce-nario to the observed Commonality scenario, and (ii)a = 0.85, that is, a 15% reduction in the cost of reman-ufacturing attributable to commonality.Using the specified parameter values and the

derived qh and ql values, we obtain the equilibriumprofits for the third-party remanufacturing scenariounder Commonality and under No Commonality. Wevary the parameters locally from their base values to

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understand under what circumstances and to whatextent commonality would be sub-optimal whenthird-party remanufacturers have access to usedproduct cores and their common components. Forease of exposition, we change a, cr, g, and k from theirbase values (by 5%) in the direction that benefits thethird-party remanufacturer.In all cases considered, commonality is optimal in

the manufacturing only scenario (i.e., cF ¼ PFCM �PFN

M

PFNM

is

always >0). This is consistent with Apple’s choice toadopt commonality. However, commonality ceases tobe optimal when competition from a third-party

remanufacturer is also considered (i.e., cR ¼ PTNM �PTC

M

PTCM

is

always >0). Consistent with the third managerialinsight presented in section 5.1, we see that the profitimprovement (cF) obtained from adopting commonal-ity but without considering third-party remanufactur-ing, is dominated by the opportunity cost (cR) of thisdecision not being optimal should third-party reman-ufacturing emerge. This is a first-order effect that ispresent for all the parameters considered and that isillustrated in Table 8 for s = 50 and D = 50. Asexplained previously, the reason is that the negativecompetitive effects (i.e., benefits to third-party reman-ufacturing) from component commonality dominatethe positive manufacturing effects. In this illustration,the opportunity cost is most sensitive to a followed byk and g. The high sensitivity to a and g was also docu-mented in Table 5, which was based on a broadnumerical set, whereas the high sensitivity to k is spe-cific to the illustration considered herein (with s = 50,D = 50). We additionally observe that as s (D)decreases (increases) then cF decreases and cRincreases, implying a more severe opportunity cost ofignoring remanufacturing. Of course, if s is largeenough (J 57 in this case), we have cF [ 0 andcR \ 0: A C ? NC decision reversal ceases to occurand commonality is preferred under third-partyremanufacturing as well because the magnitude ofthe economies of scale effect is the dominating factor.

In concluding this illustration, we would like tonote some caveats. First, since many parameters hadto be estimated or assumed, the numbers in Table 8would change with more accurate data. However, thefirst-order effects recorded in the cR column and therelative sensitivities to the different parameters areexpected to hold. Second, since ours is a representa-tive-period model, the profit impacts (of ignoringremanufacturing) estimated by our model may beregarded as an upper bound on the actual profitimpact over the life-cycle of the product because therewould be a period of time when product returnswould be sporadic (barring warranty or “grace-period”returns) and before enough cores become available for athird-party remanufacturer. However, component com-monality could speed the third-party remanufacturer’sentry into the market because of access to greater vol-umes of components for remanufacturing. Third, theillustration assumed full access to cores for the third-party remanufacturer and no remanufacturing byApple; the opportunity cost of ignoring remanufactur-ing can be expected to be lower when these conditionsare relaxed. Nevertheless, the illustration demonstrateshow our modeling approach can be utilized for inform-ing an OEM’s commonality decision in the face ofpotential remanufacturing competition.

7. Discussion of Model Extensions

We briefly discuss certain extensions to our mainmodel. First, we examine the situation where a portionof the market would never consider buying a remanufac-tured product—a phenomenon discussed in Guide andLi (2010). By modeling a fraction ξ ∈ (0,1] of the mar-ket that would only consider new products, with theremaining fraction 1 � ξ considering remanufacturedproducts as well, we obtain optimal (or equilibrium)segment sizes and prices in closed form and observethe following: (i) under both OEM and third-partyremanufacturing, the likelihood and profit impacts ofcommonality decision reversals decrease as ξincreases because of the shrinking remanufacturedproduct segment, (ii) over the entire range of ξ values,the profit impact under third-party remanufacturingis substantially higher than that under OEM remanu-facturing, and (iii) under third-party remanufactur-ing, as ξ increases, the OEM prefers commonality fora greater benefit to remanufacturing (e.g., lower a forthe same s) or a lower benefit to manufacturing (e.g.,lower s for the same a).Second, to see how our results are affected if the

consumer type h is non-uniformly distributed, we use adistribution of the form FðhÞ ¼ 1� ð1 � hÞk as inDebo et al. (2005). With this specification, as kincreases, the mass of customers shifts towards lowerconsumer types. We obtain optimal (or equilibrium)

Table 8. Profit Impact of Ignoring Remanufacturing: Illustration Usingthe Example of iPads (s = 50, D = 50)

Parameterchange (by 5%)

Profit improvementfrom commonalityfor manufacturingonly

cF ¼ PFCM�PFN

M

PFNM

� 100

Profit impactof ignoringremanufacturing(C ? NC reversal)

cR ¼ PTNM �PTC

M

PTCM

� 100

None (base values) 2.79% 6.88%a; from 0.85 to 0.8075 2.79% 20.65%cr ; from 0:85chto 0:8925ch

2.79% 8.24%

g; from 1.5 to 1.575 2.29% 9.40%k; from 0.85 to 0.8075 2.79% 9.74%

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segment sizes and prices in closed form for the OEMremanufacturing scenario but have to resort tonumerical insights for the third-party remanufactur-ing scenario due to intractability. We observe thefollowing: (i) as k increases, the OEM generally findscommonality more attractive. This is due to the com-plementary effects of commonality increasing the per-ceived quality of the low-end product and the larger kshifting the mass of customers toward the low-endproduct, (ii) over the entire range of k values, theprofit impact of commonality decision reversalsunder third-party remanufacturing is substantiallyhigher than that under OEM remanufacturing, and(iii) the profit impact of ignoring remanufacturingincreases as k increases. This is because as k increases,the total number of products sold to the marketdecreases, resulting in a greater sensitivity of profit to acommonality decision that ignores remanufacturing.Third, our main analysis focused on settings where

at optimality (or in equilibrium), remanufacturedproduct sales are not constrained by supply (i.e.,nr \ qnh holds). The analysis of the case when remanu-facturing is constrained by supply is similar except thatat optimality (or in equilibrium), the prices are cou-pled via the supply constraint nr ¼ qnh. In the OEMremanufacturing scenario, we solve for pr as a func-tion of ph and pl using the equality nr ¼ qnh. In thethird-party remanufacturing scenario, the thirdparty’s best response under the supply constraint is toprice so as to use all available supply, that is, tochoose pr such that nr ¼ qnh given the OEM’s choiceof ph and pl. We obtain optimal (or equilibrium)segment sizes and prices in closed form. We find thefollowing: (i) the profit impact of ignoring remanufac-turing decreases in ρ, but the observation of signifi-cantly higher profit impact under third-partyremanufacturing still holds, (ii) the level of a is notrelevant to the third-party remanufacturer’s pricingdecision and does not come into play in the OEM-third party equilibrium, (iii) as supply becomes moreconstrained (ρ decreases), the third-party remanufac-turer becomes a weaker competitor and the OEM’sprofit increases, and (iv) at the same time, the OEM’sbenefit from a reduction in ρ is lower with commonal-ity than without because of savings in the remanufac-turing cost (i.e., a) that accrue to the third party fromcommonality. Thus, for a given s, g, or D, as ρdecreases, the profit increase to the OEM under nocommonality is greater than the profit increase undercommonality, leading to a C ? NC type reversalbelow a threshold level of ρ.

8. Conclusion

In this article, we extend the classic component com-monality decision to consider end-product remanufac-

turing by either the OEM or a third-party firm. Ourbenchmark is anOEM that bases her commonality deci-sion on the manufacturing and sales of new productsalone. Our analysis determines the conditions—interms of the savings in unit production costs from com-monality, the effect of commonality on the productioncost of the low-end product, the effect of commonalityon perceived product quality, and the effect of com-monality on the unit remanufacturing cost—underwhich the commonality decision may be reversed ifremanufacturing is taken into account. Our analyticaland numerical results provide guidance on the existence,prevalence, and profit impacts (i.e., opportunity costs ofignoring remanufacturing) of different types of reversalsof the commonality strategy, that is, commonality inthe manufacturing-only scenario to no commonalityin the remanufacturing scenario, or vice versa. We alsoidentify the parameters that are the most influential indriving reversals of the commonality decision.Relative to when the manufacturing and sales of

new products alone are considered in determiningthe OEM’s commonality strategy, we find that thecost reduction and cannibalization effects of common-ality may lead to a different strategy when remanu-facturing is also considered. With third-partyremanufacturing, commonality may result in a costreduction for not only the OEM but also the thirdparty. Thus, commonality may not be preferred bythe OEM if the remanufacturing cost reduction is sub-stantial. Also, in the presence of third-party remanu-facturing, the cannibalization effect of commonality(which is always detrimental to the OEM if remanu-facturing is ignored) may instead be beneficial to theOEM because its low-end product becomes morecompetitive relative to the third-party’s remanufac-tured product. Thus, the consideration of remanufac-turing may lead to a different commonality decisionthan predicted by the prior literature that focuses onlyon new products.Our analysis yields a number of interesting mana-

gerial insights pertaining to the research questionsposed in the Introduction. First and foremost, it mat-ters significantly as to who does the remanufacturing.In our broad numerical study, not only was the likeli-hood of a commonality decision reversal greaterunder third-party remanufacturing, but also the med-ian profit impact was 18.20% as compared to 0.33%under OEM remanufacturing. Although this differ-ence is less dramatic when the supply of productcores for remanufacturing is limited, we can clearlyconclude that an OEM should pay special attention toincorporating remanufacturing considerations in hercommonality strategy if her products are remanufac-tured by third parties. Second, when third-partyremanufacturing is prevalent, it is particularly impor-tant to review an “Implement Commonality” decision

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality14 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

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if it was made without consideration of remanufactur-ing: Since commonality benefits the third party at theremanufacturing stage, we observe the majority ofcommonality decision reversals to be from common-ality to no commonality when third-party remanufac-turing is taken into account.Certain product types are more prone to commonal-

ity decision reversals and significant profit impacts ofignoring remanufacturing: Under third-party remanu-facturing: (i) the decision to implement commonalityis important to review for products that promise largersavings from commonality (i.e., lower a) to the third-party remanufacturer or whose production costsavings to the OEM from commonality are low (i.e.,low s). In such a situation, the OEM has much to losefrom handing a cost advantage to the third party and itis therefore desirable for her to not implement com-monality; conversely, and (ii) the decision to notimplement commonality is important to review if thelow-end product’s cost does not increase significantlywith commonality (i.e, g is low) but its perceived qual-ity and therefore, competitiveness vis-a-vis the reman-ufactured product, does (i.e., D is high).Recall that we focused on the scenario where only

the high-end product is remanufactured and the per-ceived quality of the remanufactured high-end prod-uct is between the perceived qualities of the low- andhigh-end products. For the finding (a) above (low a, lows), if both the high- and low-end products are remanu-factured by the third party, we expect that the decisionto implement commonality should receive increasedscrutiny because of the significant cost savings thatwould accrue to the third-party remanufacturer. Onthe other hand, if the perceived quality of the remanu-factured high-end product is below that of the OEM’slow-end product, we expect a diminished importanceof reviewing the decision to implement commonalitybecause although the remanufactured high-endproduct becomes a stronger competitor for the OEM’slow-end product, the OEM exclusively caters to thehigher-end customers. For the finding (b) above (low g,high D), if both the high- and low-end products areremanufactured by the third party, we expect a dimin-ished importance of reviewing the decision to notimplement commonality because although common-ality would make the OEM’s low-end product morecompetitive relative to the remanufactured high-endproduct, the remanufactured low-end product wouldbecome more competitive as well. We also expect adiminished importance of reviewing the decision tonot implement commonality if the perceived quality ofthe remanufactured high-end product is below that ofthe OEM’s low-end product, because the OEM’s low-and high-end products end up cannibalizing eachother whereas the remanufactured high-end productexclusively serves the lower-end customers.

We now turn to the limitations of our work. First,for tractability, we abstracted from the costs of collect-ing end-of-life products and did not explicitly modeluncertainties in the qualities and quantities of return-ing products. We expect that component commonal-ity would be favored with increasing collection costsand uncertainties in returns. Second, for tractabilityand clarity, we did not analyze the situation whereboth the OEM and a third party are active in theremanufactured product market (e.g., Atasu et al.2008). Based on our findings for the two separate sce-narios, we anticipate that as the third party’s share ofthe remanufactured product market increases, theopportunity costs of ignoring remanufacturing wouldincrease. Third, we did not consider the possibility ofa market for individual product modules. Intuitively,we expect that the likelihood and profit impacts ofcommonality decision reversals would increase as themarket for individual modules becomes more size-able. Fourth, we did not consider potential intricaciesrelated to pricing and demand. For example,Ovchinnikov (2011) provides some evidence thathigh-end customers may view pricing as a signal ofproduct quality and may prefer to not switch from anew product to the remanufactured version if theprice difference between them is too large. Althoughthe specific relationship of the relative willingness topay for remanufactured and new products as a func-tion of this price difference is currently an openresearch question, it will be worthwhile to revisit ourmodeling assumptions and analysis as additionalresearch in this area becomes available.We conclude by noting that the importance of pro-

actively considering remanufacturing holds true forseveral strategic decisions other than component com-monality. An increasing number of firms conductreverse supply chain activities in addition to those inthe traditional forward supply chain. We thereforebelieve that it would be useful to extend other seminaloperations and marketing models to account for thedifferent cost and market effects of remanufacturing.

Acknowledgments

We sincerely thank the anonymous reviewers, the SeniorEditor, and the Department Editor for their excellent sug-gestions. We also thank participants at various INFORMSand POMS meetings for the feedback provided. Thisresearch was partly supported by NSF DMI Grant No.0522557.

Appendix A. Proofs

PROOF OF LEMMA 1. Given the net utilities for theproducts, the segment sizes (when they are positive)

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Page 16: Remanufacturing and the Component Commonality Decision

are derived as follows: Let h00 :¼ hjuhðhÞ¼ulðhÞ and

h0 :¼ hjulðhÞ¼0. Then, nh ¼ 1 � h00 and nl ¼ h00 � h0,

or, nh ¼ ðq0h�phÞ�ðq0

l�plÞ

q0h�q0

land nl ¼ q0

lph�q0

hpl

q0lðq0

h�q0

lÞ. Substituting

these segment sizes into Equation (1), we have:

@2PM

@p2h¼ � 2

q0h � q0l\0;

@2PM

@p2l¼ � 2q0h

q0lðq0h � q0lÞ\0;

and the determinant of the Hessian matrix of PM w.

r.t. ph and pl is 4q0lðq0

h�q0

lÞ [ 0, implying that PM is

jointly concave in prices ph and pl. Equating thefirst-order derivatives of PM w.r.t. ph and pl to 0and solving simultaneously, yields the result. h

PROOF OF LEMMA 2. Given the net utilities for theproducts, the segment sizes (when they are positive)

are derived as follows: Let ~h000 :¼ hjuhðhÞ¼urðhÞ,~h00 :¼

hjurðhÞ¼ulðhÞ, and ~h0 :¼ hjulðhÞ¼ 0. Then, nh ¼ 1 � ~h000,

nr ¼ ~h000 � ~h00, and nl ¼ ~h00 � ~h0, or, nh ¼ðq0

h�phÞ�ðq0r�prÞ

q0h�q0r

, nr ¼ q0rðph�plÞ�q0hðpr�plÞ�q0

lðph�prÞ

ðq0h�q0rÞðq0r�q0

lÞ , and nl ¼

q0lpr�q0rpl

q0lðq0r�q0

lÞ. Substituting the segment sizes into Equation

(2), we have:

@2PM

@p2h¼ � 2

q0h � q0r\0;

@2PM

@p2r¼ � 2ðq0h � q0lÞ

ðq0h � q0rÞðq0r � q0lÞ\0; and

@2PM

@p2l¼ � 2q0r

q0lðq0r � q0lÞ\0:

The determinant of the principal minor (2 9 2) ofthe Hessian matrix of PM w.r.t. ph, pr, and pl is

4kð1�kÞq0

lðq0r�q0

lÞ [ 0, while the determinant of the Hes-

sian matrix itself (3 9 3) is � 8q0lðq0

h�q0rÞðq0r�q0

lÞ \ 0. The

alternating signs imply that PM is jointly concave inprices ph, pr, and pl. Equating the first-order deriva-tives of PM w.r.t. ph, pr, and pl to 0 and solvingsimultaneously, yields the result. h

PROOF OF LEMMA 3. We solve for the equilibriumvalues by backward induction. Given net utilities forthe products, the segment sizes (when they are posi-

tive) are as derived in Lemma 2; that is,

nh ¼ ðq0h�phÞ�ðq0r�prÞ

q0h�q0r

, nr ¼ q0rðph�plÞ�q0hðpr�plÞ�q0

lðph�prÞ

ðq0h�q0rÞðq0r�q0

lÞ , and

nl ¼ q0lpr�q0rpl

q0lðq0r�q0

lÞ. Substituting for nr in Equation (4), we

have:

@2PT

@p2r¼ � 2 q0h � q0l

� �

q0h � q0r� �

q0r � q0l� �\0;

implying that the third-party remanufacturer’s profitis concave in price pr. Equating the first-order deriv-ative of PT w.r.t. pr to 0 gives us:

prðph; plÞ ¼phðq0r � q0lÞ þ crðq0h � q0lÞ þ plðq0h � q0rÞ

2ðq0h � q0lÞðA1Þ

Also, we have:

@2PM

@p2h¼ � 2

q0h � q0r\0;

@2PM

@p2l¼ � 2q0r

q0lðq0r � q0lÞ\0;

and the determinant of the Hessian matrix of PM

w.r.t. ph and pl ¼ 4q0rq0lðq0

h�q0rÞðq0r�q0

lÞ [ 0. Thus, the OEM’s

profit PM is jointly concave in prices ph and pl.Equating the first-order derivatives of PM w.r.t. phand pl, respectively, to 0 and solving simultaneouslyfor ph, pr, and pl using (A1), yields the result. h

PROOF OF PROPOSITION 1. (i) We know PFDM is inde-

pendent of a. Using the envelope theorem, we have

Under our assumption that the ordering of the per-ceived qualities is maintained, we havekq0h � q0l [ 0. At optimality, the OEM would price

above cost, therefore pTCl � c0l [ 0 and pTCh �c0h [ 0. Consequently, PTD

M increases in a. When

PFDM is positive and PTD

M crosses zero in the feasiblerange of the parameter space, a C ? NC reversaloccurs below this crossover point. Figure 1 numeri-cally shows the existence of such reversals.(ii) Using the envelope theorem and the positivity of

segment sizes, we have@PFD

M

@s ¼ nFCh þ nFCl [ 0 6¼@PTD

M

@s ¼ nTCh þ nTCl [ 0. Thus, these functions

@PTDM

@a¼ 2kcrðq0h � q0lÞ½ð1� kÞq0hðpTCl � c0lÞ þ ðkq0h � q0lÞðpTCh � c0hÞ�

ð1� kÞq0hðkq0h � q0lÞ½ðkq0h � q0lÞ þ 2kðq0h � q0lÞ þ kð1� kÞq0h�:

Subramanian, Ferguson, and Toktay: Remanufacturing and Commonality16 Production and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society

Page 17: Remanufacturing and the Component Commonality Decision

increase monotonically. Let sFD be the solution, if

any, to PFDM ðsÞ ¼ 0, and sTD be the solution, if any,

to PTDM ðsÞ ¼ 0. If sFD \ sTD, the case PFD

M [ 0 but

PTDM \ 0, or a C ? NC reversal, occurs below sTD.

Figure 1 numerically shows the existence of suchreversals.

(iii) Solving for sTD using PTDM ðsÞ ¼ 0, and taking

the first derivative with respect to a, we obtain@sTD

@a ¼ � kqhcrð1�kÞþcrðkqh�qlÞkðqh�qlÞ \ 0. h

PROOF OF PROPOSITION 2. (i) Using the envelope theo-rem and the non-negativity of segment sizes, we

have@PFD

M

@g ¼ �clnFCl \ 0 6¼ @PTD

M

@g ¼ �clnTCl \ 0. Thus,

these functions decrease monotonically. Let gFD be

the solution, if any, to PFDM ðgÞ ¼ 0, and gTD be the

solution, if any, to PTDM ðgÞ ¼ 0. If gFD \ gTD, the case

PFDM \ 0 but PTD

M [ 0, or an NC ? C reversal,

occurs below gTD. Figure (2a) numerically shows the

existence of such reversals.(ii) Solving for gTD using

PTDM ðgÞ ¼ 0, and taking the first derivative with

respect to a, we obtain @gTD

@a ¼ kqhcrð1�kÞþcrðkqh�qlÞkqhclð1�kÞ [ 0.h

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Table B1. Parameters that Explain Indicator of C ? NC Reversals

Coefficient Standard error t-statistic

Intercept 117.5776 7.1553 16.4323g 41.0847 1.3512 30.4062k 28.9637 7.8067 3.7101qh �0.4346 0.0999 �4.3492D �3.2474 0.2311 �14.0543cl 4.3045 0.5279 8.1541cr 1.0303 0.3882 2.6539ch 0.6645 0.2958 2.2467a �204.8514 5.0178 �40.8247s �20.8246 0.7008 �29.7168

Table B2. Parameters that Explain Profit Impacts of C ? NC Reversals

Coefficient Standard error t-statistic

Intercept 162.7454 11.3047 14.3962g 59.1946 2.6246 22.5541k 35.4172 12.7167 2.7851qh �1.4977 0.1527 �9.8058D �1.8123 0.4531 �4.0002cl 7.7182 0.8807 8.7639cr 3.5904 0.6740 5.3270ch 0.7888 0.4933 1.5992a �284.8346 9.3317 �30.5235s �34.1948 1.4602 �23.4179

Table B3. Parameters that Explain Indicator of NC ? C Reversals

Coefficient Standard error t-statistic

Intercept �24.4995 6.8199 �3.5923g �12.4570 1.1209 �11.1134k 16.0163 7.6756 2.0866qh �0.3809 0.0953 �3.9963D 3.1937 0.1927 16.5757cl �3.7632 0.5345 �7.0407cr 0.0174 0.4139 0.0420ch 0.5032 0.2977 1.6900a 44.6797 4.6522 9.6040s 5.4720 0.6257 8.7458

Table B4. Parameters that Explain Profit Impacts of NC ? CReversals

Coefficient Standard error t-statistic

Intercept �499.4145 66.5704 �7.5020g �104.5896 7.8291 �13.3591k 370.1503 57.5510 6.4317qh �7.7009 0.7654 �10.0612D 24.2022 1.3955 17.3427cl �28.9978 3.7594 �7.7133cr �14.0434 3.0504 �4.6037ch 19.1346 2.5930 7.3794a 497.1949 54.0905 9.1919s 49.1705 4.0841 12.0394

Subramanian, Ferguson, and Toktay: Remanufacturing and CommonalityProduction and Operations Management 0(0), pp. 1–18, © 2012 Production and Operations Management Society 17

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