Misplaced Inventory and Radio-Frequency Identiﬁcation (RFID) Technology: Information...

Misplaced Inventory and Radio-FrequencyIdentification (RFID) Technology Information and

Coordination

Almula Z CamdereliMcDonough School of Business Georgetown University Washington District of Columbia USA zac2georgetownedu

Jayashankar M SwaminathanKenan-Flagler Business School University of North Carolina Chapel Hill North Carolina USA msjuncedu

Misplaced inventory is a major operational problem in many supply chains Radio-frequency identification (RFID)technology has been publicized as a promising solution for the misplaced inventory Adoption of this technology has a

fixed cost and variable cost of implementation which can cause incentive issues in the supply chain In this paper weconsider a supply chain under misplacement of inventory subject to uncertain demand We study both centralized anddecentralized cases and identify the conditions to coordinate the supply chain under implementation of RFID We show thatthe incentives of the parties for investing in the technology are not perfectly aligned in the existence of the fixed cost ofinvestment Based on the relative payments of the parties for the fixed cost of investment the incentives to adopt RFID can becharacterized into regions where we observe only one party or two parties benefiting from the technology when the tag pricefalls in a region specified in the paper We further establish the effects of changes in mean and variance of a uniform demandon the incentives for investing in RFID and find that the incentives of the firms may indeed decrease as demand becomesmore variable

Key words RFID supply chain coordination incentives inventory misplacementHistory Received November 2006 Accepted March 2009 after 1 revision

1 IntroductionInventory misplacement is expensive and is prevalent inmany industries An empirical study by Raman et al(2001) shows that the inventory loss proportions canreach significant numbers in retail stores up to 16 insome cases When items are misplaced in the store theybecome unavailable to the customers until they arefound One of the ways to handle misplaced inven-tory is through radio-frequency identification (RFID) de-vices Through this technology it is possible to track anitem on which an RFID tag is attached RFID has be-come a major technology enabler for developinggreater visibility in supply chains (Swaminathan andTayur 2003) Implementation of RFID is beginning on alarge scale at the distribution level ie pallets are be-ing tagged This should reduce misplacement at thewarehouse level Firms started to perceive the RFIDtechnology as a development beyond being only anextension to bar coding when Walmart declared therequirement for her major suppliers to tag each palletwith an RFID tag It gained momentum with severalfirms including Unilever United Biscuits FluorowareInc Ford Motor Company and Toyota launching pilotprojects of RFID (Angeles 2005) Although pallet-level

RFID applications provide some visibility to firms theymay not deliver all the strategic benefits of RFID par-ticularly in the case of retailers As a result Marks ampSpencer Tesco and Metro Group three European re-tailers have already started testing RFID at the itemlevel (Sullivan 2005) The next level of implementationwill be at the store level where RFID should enableSKU level tracking and identification More recentlyAmerican Apparel has already started to place RFIDtags at item level (httpwwwinformationweekcomaccessed on April 16 2008)

RFID is not cheap enough to become as common atechnology as barcoding yet An empirical study byWhitaker Mithas and Krishnan (2007) shows thatfirms with larger information technology budgets aremore likely to adopt this technology In addition tovarious variable costs RFID adopters also have toconsider the upfront costs for deploying the newtechnology in the supply chain (Kambil and Brooks2002) For example a typical consumer packagedgoods manufacturer was estimated to spend betweenUS$13 million and US$23 million for shipping 50 mil-lion cases per year including various fixed costs andvariable costs (Asif and Mandviwalla 2005) of whichUS$8ndashUS$13 million was estimated to include upfront

1

PRODUCTION AND OPERATIONS MANAGEMENTVol 19 No 1 JanuaryndashFebruary 2010 pp 1ndash18ISSN 1059-1478|EISSN 1937-5956|10|1901|0001

POMSDOI 103401poms108001057

r 2009 Production and Operations Management Society

costs such as system integration changes to existingsupply chain applications and storage of the largevolumes of data According to a report by A T Kear-ney in addition to tagging expenses systemsintegration is estimated to cost US$35ndashUS$40 million(httpretailindustryaboutcom accessed on April15 2008) It has been pointed out by the practitionersthat a sharing of costs is necessary to see the benefitsof the technology (Thomas 2004 Kearney 2003)

As these big retailers (including Walmart) havepopularized RFID a common opinion has been thatthe main beneficiaries of RFID will be the downstreamplayers in the supply chain (Agarwal 2001 Kevan2004) In addition to being able to track the items theretailers are expected to benefit from store and ware-house labor reductions and reduced inventories Onthe other hand the benefits of RFID to manufacturershave been anticipated in improved demand planningstricter quality control reduced scrap waste andrework and more accurate inventory data (BearingPoint 2005) An Italian subsidiary of Honda Motor Cohas integrated RFID on one of its scooter lines andclaims to see benefits beyond return on investment(Selko 2008) However it appears that Samrsquos Club(operated by Walmart) has to push even stronger toget its suppliers to comply with the RFID require-ments by making them pay a fee per pallet otherwise(Weier 2008) According to research presented byGlobal Commerce Initiative retailers and consumergoods suppliers are still sceptical about the benefits ofRFID (Burnell 2008) In a recent paper Dutta et al(2007) point out the need to have a better understand-ing of how the benefits of the technology might bedistributed over supply chain partners Motivated bythe debate among the upstream and downstreamplayers about the adoption of the RFID technologyusing a stylized model we intend to gain insightsabout how and when their incentives are aligned andespecially misaligned in the existence of a fixed cost ofinvestment in addition to variable expenses

11 Related LiteratureStudies related to RFID in inventory management arerelatively new Lee and Ozer (2007) provide a reviewof the literature about the emerging technology RFIDby examining the papers under three main categoriesmisplacement of inventory shrinkage and transac-tion errors As indicated by Raman et al (2001) in-ventory inaccuracy and misplaced inventory aremajor operational inefficiencies Several researchershave developed models for inventory inaccuracy (seeAtali et al 2005 DeHoratius et al 2008 DeHoratiusand Raman 2008 Heese 2007 Iglehart and Morey1972 Kang and Gershwin 2005 Kok and Shang 2007)Models for inventory misplacement problem havealso been studied by researchers (see Camdereli and

Swaminathan 2005 Rekik et al 2008b) In the follow-ing passages we will relate our work to other researchthat has explicitly incorporated RFID in their analysisof inventory inefficiencies

There is some recent work on analysis of the effectsof improved visibility in RFID-enabled supply chainsFor example Gaukler et al (2008) characterize a com-pound replenishment (Q R) policy with the option ofemergency ordering for a retailer subject to stochasticorder lead times The authors assume that the retailerhas order progress information due to being able totrack items through technology In another paperKaraer and Lee (2007) model degree of visibility for acentralized manufacturer with product returnsthrough order progress information in the reversesupply chain and knowledge of statistical character-istics of the product return flow Contrary to thesepapers rather than focusing on the value of informa-tion in RFID-enabled systems we explicitly modelcosts of the technology adoption for parties in bothcentralized and decentralized supply chains toremove operational inefficiencies due to inventorymisplacement

Gaukler et al (2007) study item-level RFID wherethe retailer uses in-store sales to estimate demanddistribution The tagging expenses are assumed to beshared and no fixed cost of implementation is takeninto account They research the behavior of the opti-mal stocking quantity and the profits of the parties forchanges in the responsiveness level of the retailer andthe tag price As opposed to their model where RFIDimproves demand visibility in our model RFID im-proves supply visibility In this paper besides taggingexpenses we take the fixed cost of RFID implemen-tation into consideration and allow the parties toshare the fixed cost of adoption We study both sce-narios where the tagging expenses are covered byonly the manufacturer and only the retailer Addi-tionally we also characterize the incentives for theparties to invest in RFID in vertically integrated un-coordinated and coordinated environments

Rekik et al (2007) study supply chains subject tomisplacement under a wholesale price contract andfind a sufficient condition on the tag price to make theparties adopt RFID technology under normal demanddistribution when no fixed cost of investment isconsidered Further they numerically quantify thebenefits gained through RFID adoption vs coordina-tion of the supply chain In this paper we explicitlyconsider the fixed cost of technology investment andshow that the incentives of the parties to adopt thetechnology are completely characterized by a maxi-mum of three regions based on relative payments ofparties Additionally rather than searching for suffi-cient conditions for the parties to invest in the tech-nology we are particularly interested in analytically

Camdereli and Swaminathan Misplaced Inventory and RFID2 Production and Operations Management 19(1) pp 1ndash18 r 2009 Production and Operations Management Society

identifying those regions where only the retailer or themanufacturer benefits from the technology in additionto those where the incentives are aligned We furthercarry out this analysis in supply chains under quan-tity contracts In another paper Rekik et al (2008a)computationally study the benefits of using Auto-ID systems for the retailer to completely remove theinventory misplacement by comparing such systemswith those where the retailer is not aware of the mis-placement problem and where the retailer knows themisplacement problem and optimizes accordinglyOur work is distinguished from their model in that wealso consider gaming and coordination issues in asupply chain with a retailer and a manufacturer

Heese (2007) studies the effect of inventory inaccu-racy on supply chain performance as well as theimpact of double marginalization in a decentralizedsupply chain on the partiesrsquo incentives to adopt RFIDAssuming the fixed cost of investment is zero theauthor finds that the manufacturer who is the Stack-elberg leader is better off with RFID technology if andonly if the retailer is better off In comparison withthe above work we consider a misplaced inventoryproblem and assume sharing of fixed cost of imple-mentation We find that the incentives of the retailerand the manufacturer to adopt RFID are not alwaysaligned under inventory misplacement We also in-vestigate the changes in the incentives of the parties toadopt the technology as the mean and the variance ofthe demand distribution changes

Since RFID is a recent development in informationtechnology literature about adoption of ElectronicData Interchange (EDI) is also relevant to our researchDecisions concerning EDI adoption have been studiedin different settings Wang and Seidmann (1995)showed that while one supplierrsquos EDI adoption canincrease her own profit it may decrease the profits ofthe other suppliers and a supplierrsquos incentive in EDIadoption decreases in the number of suppliers adopt-ing EDI While assuming a direct benefit forthe buyer Wang and Seidmann show that suppliersinstalling EDI can indirectly benefit from it In thispaper we research the effects of RFID adoption on theparties Instead of assuming a direct benefit to anyparty we model the incentives as a result of solvingthe problem of inventory misplacement

Camdereli and Swaminathan (2005) is a closelyrelated paper to our work The main focus of theauthors is to characterize the optimal policy for a sin-gle product inventory problem under misplacedinventory They expand the analysis to the two-stagesupply chain in a single-period setting in that paperUsing uniform distribution for demand they showthat behavior of the optimal ordering quantity for anincrease in the availability level depends on the ex-isting availability level and attractiveness of the items

to stock in vertically integrated supply chains there-fore it does not monotonously increase or decrease inall cases Under the decentralized setting they ana-lyze uncoordinated supply chains as well as thosecoordinated by buyback and revenue sharing mech-anisms In their work they do not consider the costsand incentive issues arising as a result of implemen-tation of an information system such as RFID In thispaper we incorporate the cost of removing misplace-ment using RFID and focus on the incentives of theparties in the supply chain to adopt such a technology

12 Our Paper and ContributionsIn this paper we study the benefits of RFID imple-mentation on a two-stage supply chain experiencingmisplaced inventory at the retailer We consider bothfixed and variable costs for RFID implementation andassume that the fixed cost is shared between the twousing an arbitrary proportion while the variable costcould be charged to either the retailer or the manu-facturer We study three different settings (1) avertically integrated supply chain where the manufac-turer owns the retailer (2) a decentralized anduncoordinated supply chain with a wholesale contractand (3) a supply chain that is coordinated with a rev-enue sharing contract and a buyback contract In allcases the manufacturer is assumed to be the leader Wederive conditions under which it is beneficial to investin the RFID technology and establish a threshold onvariable tagging cost where the manufacturer or theretailer or both or neither benefit from such invest-ment Finally we establish the effect of changes inmean and variance of a uniform demand on the in-centives for investing in RFID We also show some ofthese results for normal demand distributions

The remainder of the paper is organized as followsIn Section 2 we study the vertically integrated supplychain Section 3 focuses on the decentralized supplychains where we study wholesale price contract andquantity contracts such as revenue sharing and buy-back We extend some of our results to generaldemand distributions in Section 4 Finally we pro-vide concluding remarks in Section 5

2 Centralized FirmIn this section we study a vertically integrated supplychain where the manufacturer owns the retailer Forconvenience we will refer to the centralized manu-facturerretailer as the centralized firm We consider asingle-seasonal product We assume that misplace-ment of inventory occurs immediately on deliveryHence as soon as the order is complete l (l 5 1 ao1)proportion of the order gets misplaced in the storeand only a proportion of the order is available to theend customers during the selling season Inventorycan be misplaced due to various reasons Customers

Camdereli and Swaminathan Misplaced Inventory and RFIDProduction and Operations Management 19(1) pp 1ndash18 r 2009 Production and Operations Management Society 3

or employees can misplace items on the shop floor oritems can be misplaced in storage areas In most real-life settings misplacement happens gradually overtime We assume instantaneous misplacement foranalytical tractability Therefore one can think of ourmodel as an approximation to a real-life setting wherethe costs can be perceived as an upper bound on thenegative effects of inventory misplacement Demandoccurs right after the misplacement

When the firm invests in RFID we assume that eachSKU is tagged with an RFID chip so the availabilityproportion becomes 100 (a 1) Since the imple-mentation of RFID in supply chains is relatively newthe efficiency rate of the readers can be below 100 insome instances This can also be incorporated into ourmodel easily by assuming that availability goes to ao1 instead of 1 The firm adopting RFID incurs afixed cost of K and a variable cost of t40 per unitwhen it implements RFID The centralized firm thatdoes not invest in RFID technology orders QC and thefirm investing in the technology orders QCRF Itemscost c per unit Each available unit is sold for p duringthe sales season and any leftover inventories aresalvaged at s per unit If the firm does not invest in thetechnology it always salvages the lost inventories(lQC) at the end of the season There may be moreleftover inventories if demand is less than theavailable inventories (aQC) Although we assume thatboth misplaced and leftover items are salvaged at thesame price s differentiation of the salvage valuebetween those items can easily be incorporated intoour model If demand is more than the available items(aQC when items are misplaced and QCRF when RFIDis implemented) the firm incurs gC per each unit ofexcess demand ie a penalty cost for stock out Wemake several assumptions on the cost parametersAssumption 1 holds for both centralized anddecentralized settings

ASSUMPTION 1 socopLet QN QC and QCRF denote the optimal

quantities The centralized firmrsquos expected profitwithout any misplaced inventory is EPCN(QN) 5

H(QN gC) cQN where H(x gC) is given by (1) andF() is the cumulative distribution function (cdf) of thedemand The firmrsquos profit under misplaced inventoryand after implementing RFID are formulated asEPC(QC) 5 H(aQC gC) cQC1slQC and EPCRF(QCRF) 5

H(QCRF gC) (c1t)QCRFK respectively

Hethx gTHORN frac14pethmthornZ 1

xethx xTHORNdFethxTHORNTHORN thorn s

Z x

0

ethx xTHORNdFethxTHORN

g

Z 1xethx xTHORNdFethxTHORN

eth1THORN

The profit under RFID is clearly a version of theclassical Newsvendor function where the marginalcost of production is adjusted by the tag price Herewe state the optimum order quantities without anyproof The profit function is concave in QCRF thus

QCRF frac14 F1 1 cthorntspthorngCs

and QCRF40 if and only if

top1gC s Because of the tag price it is clear thatthe optimal order under RFID is always smaller thanthe optimal order under no inventory misplacement

QN frac14 F1 1 cspthorngCs

As presented by Camdereli

and Swaminathan (2005) the optimum QC solves FethaQCTHORN frac14 1 ~a=a where ~a frac14 cs

pthorngCso1 and QC is positive

if and only if a4~aTo gain analytical insights through closed form so-

lutions we assume that demand is uniformlydistributed in [0 b] for this section We extend ourresults to general distributions in Section 4 The op-

timum expressions translate to QN frac14 b 1 cspthorngCs

QCRF frac14 b 1 cthorntspthorngCs

and QC frac14

ba eth1 ~a=aTHORN for uni-

formly distributed demand Unless otherwise statedall of the proofs are given in the SupportingInformation (available on request)

LEMMA 1

1 Given QCRF40 there exists a threshold value aominf1~a=eth1 ~aTHORNg such that QCRF4QC if and only ifaoa

2 (a) Given QCRFQC40 there exists a threshold value

tfrac12a frac14 1a2frac12c s aethpthorn gC sTHORN thorn a2ethpthorn gC cTHORN

such that QCRF4QC if and only if tot[a]

(b) t[a]40 if and only if aominf1~a=eth1 ~aTHORNg where~a frac14 ethc sTHORN=ethpthorn gC sTHORN

Lemma 1(1) states that as the inventory availabilityvaries the values of QC and QCRF become equivalent

at only one value of availability aoaominf1~a=eth1 ~aTHORNg Figure 1 gives two numerical examples tocompare QC with QCRF for the two cases where ~a frac143=16o05 and ~a frac14 9=16405 As also numerically il-lustrated by these examples QCRF crosses QC only at

one value of availability (a 0228 in the graph where~ao05 and a 0870 in the graph where ~a405) forwhich QC is always less than QN)

Although one may expect to order less under RFIDthan under inventory misplacement due to 100 in-ventory availability it may not be the case if the tagprice is sufficiently low In Lemma 1(2)(a) we providea threshold value (t[a]) on the tag price below whichit is always optimal to order more under RFID thanunder inventory misplacement for appropriate rangesof inventory availability The expression ~a is the prob-


ability of stocking out in a newsvendor problemwhere no misplacement occurs One may also inter-pret ~a as how unattractive products are to stockCeteris paribus as the unit cost of order increases ~aincreases or as the sales price of the product increases~a decreases When ~ao05 ie items are relativelyattractive to stock and ao~a=eth1 ~aTHORN t[a] is positiveHence the optimal order under RFID is indeed largerthan the optimal order under inventory misplacementif the tag price is less than t[a] For the same case of~ao05 when a4~a=eth1 ~aTHORN one always orders moreunder inventory misplacement than the classicalnewsvendor does (QC4QN) Thus QCRF is alwayssmaller than QC for this range of availability valuesObviously when items are not attractive to stock(~a 05) and the tag price is expensive (t4t[a]) thefirm stocks less under RFID

Next we study the centralized profit under RFID andthe incentives of the firm to invest in the technology

THEOREM 1

1 (a) For a given K EPCRFethQCRFTHORN EPCethQCTHORN40 ifand only if totC(b) For a given t EPCRF(QCRF)EPC(QC)40 if andonly if KoKC

2 If K 5 0 then tC 5 t13 KC40 if and only if tot1 given QC QCRF40

Where tC and KC are given in Appendix A andt1 frac14 eth1aTHORN

a ethc sTHORN40An investment in this technology always brings in

more profits if and only if the tag price is less than tCNote that tC can also be negative in which case it isnever optimal to invest in the technology For a giventag price the centralized firm benefits from an invest-ment in RFID if and only if the fixed cost of adoptionis less than KC A special case of our model is wherethere is no fixed cost of RFID adoption In such a casethe upper bound on the maximum tag price tC frac14 t1 frac14eth1 aTHORNethc sTHORN=a is always positive

Theorem 1 defines the incentive of a firm to adoptthe technology in absolute terms Another way toquantify the benefits of a technology is to study thepercentage change in the profits under misplacementas a result of adopting RFID Since the firmrsquos optimumprofit under the technology decreases in t and K toachieve an x improvement on the profits under in-ventory misplacement after RFID adoption thecorresponding threshold values will be lower thantC and KC See the Supporting Information (availableon request) for the closed-form expressions of thecorresponding threshold values using such relativecriterion

Next we study how the incentives of the central-ized firm change as the mean or the variance of thedemand increases We use a more general demanduniformly distributed in frac12b bwhere b is allowed to bepositive We will use 0 (prime) to denote the optimalvalues when b 0 We find the effects of changes inmean by shifting the range of the demand distributionwhile keeping the width of the range constant Tocapture the effects of changes in variance we changethe width of the range while keeping the mean con-stant In the below results we only consider the casewhere tot1 which is equivalent to saying that thefirm may invest in RFID

THEOREM 2 The following findings hold for uniformly dis-tributed demand in frac12b b if tot1

1 The incentive of a centralized firm under inventorymisplacement to adopt RFID decreases as inventoryavailability increases

2 Given the variance of demand is fixed as the expectedvalue of demand increases

(a) Q0C and Q0CRF increase(b) The incentive of a centralized firm under inventory

misplacement to adopt RFID increases

The findings of Theorem 2 are not restricted to uni-form demand distributions as they also go through for

1000

2000

3000

4000

5000

6000

QCRF

QCRF

QC

QC

500

1000

1500

2000

a~

a = 316lt5~ a = 916lt5~a a asymp 0228~ a asymp 0870

Figure 1 QCRF and QC with Changes in a


normally distributed demand with [ms2] where s isthe standard deviation The proofs of the findingsfor normally distributed demand can be found in theSupporting Information (available on request) Onewould expect to stock more when demand is expectedto be larger and our results follow this intuition Fur-ther the firm has more incentives to adopt the newtechnology as the mean of demand increases Hencethe greatest benefits from RFID accrue to firms underlow inventory availability and in expectation ofhigher demand (Figure 2)

THEOREM 3 For uniformly distributed demand in frac12b b iftot1 given the expected value of demand is fixed as thevariance of demand increases

1 Q0C decreases if ao2~a If a42~a it increases

2 Q0CRF decreases if t4t3 If tot3 it increases

3 If t2otot1 holds the incentive of a centralized firmunder inventory misplacement to adopt RFID de-creases Otherwise it increases Further t2ot1 if andonly if ao2~a

Where t2 frac14 pthorn gC c ethcsTHORNa and t3 frac14 etht1 thorn t2THORN=2

One may also anticipate the firm to order more asdemand becomes more variable However as shownin Theorem 3(1) the optimal order under misplacedinventory does decrease in demand variability if ao2~abecause the effective cost of acquiring an itembecomes too costly as variance increases For examplewhen the products are relatively unattractive to stock(~a 05) the cost of average is higher than the costof underage Similarly a tag price greater than t3

increases the average cost such that the firm underRFID decreases the order size with increasing vari-ance However unlike the case under uniformdemand distribution both of the optimum ordersincrease as s increases when demand is normallydistributed with [m s2]

As indicated by Theorem 3(3) if the firm is alreadyoperating under low inventory availability level ethao2~aTHORN and the tag price is sufficiently high (t4t2) RFID

becomes a more beneficial technology as demand liesin a smaller interval of values ie with a smallervariance However if a42~a then RFID is more ben-eficial for systems under higher demand variabilityThe effects of changes in the variance of demandon the incentives of the firm to adopt RFID portrayexactly the same behavior when demand is distrib-uted according to a normal demand distribution with[ms2]

3 Decentralized Supply ChainWe consider a supply chain consisting of one retailerand one manufacturer We assume that the manufac-turer acts as a Stackelberg leader and announces thewholesale price to the retailer The retailer orders tak-ing the wholesale price into consideration If thesupply chain adopts RFID technology there will be noloss of inventories Otherwise the retailer misplaces0ol 5 1 ao1 proportion of the items when the orderarrives Therefore as in the centralized firm settingonly a proportion of the order will be available to thecustomers during the selling season In both casesproducts are sold for p and the leftover inventories(remaining items after the selling season and also lostitems under inventory misplacement) are salvaged ats per unit by the retailer If demand is larger than theavailable items in the retail store both parties incur astock-out cost The stock-out cost incurred is sharedbetween the manufacturer and the retailer in thedecentralized settings The retailer incurs gR and themanufacturer incurs gM for each unit of excess de-mand where gR1gM 5 gC If the supply chain adoptsRFID technology each SKU will be tagged with oneRFID chip Each RFID chip costs t per unit For allcases we study both scenarios where either the re-tailer or the manufacturer pays for the taggingexpenses We also assume that there is a fixed costof K of the RFID adoption and it is shared betweenthe manufacturer and the retailer Thus the retailerpays yK and the manufacturer pays (1 y)K where0 y 1 We first study a supply chain under awholesale price contract Since the manufacturersets the wholesale price it should be greater than cotherwise the manufacturer would never make posi-tive profits Similarly it should be less than p sothat the retailer may make positive profits There-fore Assumption 1 is necessary but not sufficient forthe decentralized supply chain under a wholesaleprice contract and a buyback contract thereforewe make Assumption 2 for Section 31 and Sec-tion 322

ASSUMPTION 2 socowopNote that w (wholesale price) will be represented by

wD in Section 31 and wB in Section 322 under mis-

t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases

Figure 2 Changes in Q0C Q

0C RF and the Incentive of a Centralized Firm

under Inventory Misplacement to Adopt RFID Technology whenao2a and t240 as Variance of the Uniformly DistributedDemand Increases


placed inventory In the existence of RFID we willdenote the wholesale prices by wDRFi and wBRFi

where i stands for the party paying for the taggingexpenses (i 5 M if the manufacturer and i 5 R if theretailer pays for the tagging expenses) ThereforeAssumption 2 will be transformed to socowDwD

RFRwDRFMop in Section 31 and socowBwBRF

RwBRFMop in Section 322

31 Wholesale Price ContractIn this section we study a supply chain whereno mechanism exists for coordination and the man-ufacturer acts as a Stackelberg leader The man-ufacturer announces the wholesale price and theretailer orders QD under inventory misplacementand QDRFi under RFID We will denote the retailerrsquosand manufacturerrsquos profits under misplaced inven-tory in an uncoordinated supply chain by EPRD

and EPMD as given by the following equationsrespectively

EPRDethQDTHORN frac14 wDQD thornHethaQD gRTHORN thorn slQD eth2THORN

EPMDethwDTHORN frac14 ethwD cTHORNQD gM

Z 1aQD

ethx aQDTHORNdFethxTHORN

eth3THORN

The retailerrsquos and the manufacturerrsquos profits in anuncoordinated supply chain inclusive of the fixed costof adoption but exclusive of the tagging expenses un-der RFID are given by GD(QDRFiwDRFi) andLD(QDRFiwDRFi) where iAfR Mg

GDethx yTHORN frac14 yx yK thornHethx gRTHORN

LDethx yTHORN frac14ethy cTHORNx eth1 yTHORNK gM


We use (4) and (5) to represent the retailerrsquos profitand the manufacturerrsquos profit under RFID whereIR 5 1 if the retailer pays for the tagging expenses(i 5 R) and 0 otherwise

EPRDRFiethQDRFiTHORN frac14 GDethQDRFiwDRFiTHORN IRtQDRFR

eth4THORN

EPMDRFiethwDRFiTHORN frac14 LDethQDRFiwDRFiTHORN eth1 IRTHORNtQDRFM

eth5THORN

The retailerrsquos problem is to find QD frac14 arg maxQD

EPRD under inventory misplacement and QDRFi frac14arg max QDRFiEPRDRFi under RFID whereas the man-ufacturerrsquos problem is wD frac14 arg maxwD

EPMD andwDRFi frac14 arg maxwDRFi

EPMDRFi in the corresponding

settings Camdereli and Swaminathan (2005) showthat there exists a unique wholesale price whichoptimizes the manufacturerrsquos profit and an optimumorder quantity which optimizes the retailerrsquos profit

under inventory misplacement The expressions aregiven by (6) and (7) for uniformly distributed de-mand

wD frac141

4

frac122ethcthorn sTHORN 2aethpthorn gR sTHORN agM thorn gMfrac12agM 2ethc sTHORNfrac122ethpthorn gR sTHORN thorn gM

eth6THORN

QD frac14 keth1=aTHORNeth1 ~a=aTHORNb frac14 kQC where k

frac14 frac12ethpthorn gR sTHORN thorn gMfrac122ethpthorn gR sTHORN thorn gM

o1 eth7THORN

In a recent paper Heese (2007) considers inventoryinaccuracies where the number of physical items inthe store can be more than the system record and findsthat the optimal decentralized order under inventoryinaccuracy is at most 50 of the optimal order of avertically integrated supply chain under inventoryinaccuracy Note that k given by (7) is 12 Henceunlike the case of inventory inaccuracy the optimaldecentralized order under inventory misplacement isat least 50 of the order quantity of a verticallyintegrated supply chain Next we study the optimalwholesale price and the ordering quantity under theimplementation of RFID technology

THEOREM 4 EPRDRFi(QDRFi) and EPMDRFi(wDRFi) arestrictly concave in QDRFi and wDRFi respectively

1 The optimal wholesale prices in an uncoordi-nated supply chain in the existence of RFID are asfollows

wDRFR frac14 frac12ethgR thorn p sTHORNethgR thorn pthorn cTHORN thorn sgM

tethpthorn gC sTHORN=eth2ethgR thorn p sTHORN thorn gMTHORNeth8THORN

owD if and only if t4eth1 aTHORNethpthorn gR sTHORN2=ethpthorn gC sTHORN eth9THORN

wDRFM frac14 wDRFR thorn t4wD

2 The optimal ordering quantities in an uncoordi-nated supply chain in the existence of RFID are asfollows

QDRFR frac14QDRFM frac14ethpthorn gC t cTHORNbeth2ethpthorn gR sTHORN thorn gMTHORN

40 if and only if topthorn gC c

eth10THORN

In Theorem 4 we prove that when RFID improvessupply visibility the wholesale price under RFID isindeed smaller than the one with no RFID if theretailer covers for the tagging expenses and the tagprice is sufficiently high Gaukler et al (2007) showthat when RFID improves demand visibility the


optimum wholesale price under RFID is at least asmuch as the one with no RFID In Gaukler andcolleaguesrsquo model responsiveness has been modeledthrough scaling of the expected value and thevariance of the normal demand distribution by aconstant fraction The optimum wholesale prices intheir paper are found to be invariant of the firmrsquos levelof responsiveness which is reflected in the demanddistribution but not in the available number of itemsduring the selling season Hence in their model asa result of adopting item-level RFID tag price isthe only parameter that causes the wholesale pricebefore RFID to increase However in our model thewholesale price before RFID directly depends onthe inventory availability as well and this drives thedifference The condition given in (9) can also bestated as a condition on inventory availabilityetha4~aethtTHORNTHORN This would indicate that those retailerswho are already operating under high inventory levelwill be willing to pay only lower wholesale pricesunder RFID when they bear the tagging expenses

When the manufacturer pays for the taggingexpenses she can adjust the wholesale price by t ascompared with the wholesale price in the scenariowhere the retailer pays for them As a result the op-timal ordering quantity does not change whether themanufacturer or the retailer is charged for the taggingexpenses The next corollary follows from the fact thatwDRFM frac14 wDRFR thorn t and QDRFR frac14 QDRFM as givenby Theorem 4

COROLLARY 1 EPRDRFi(QDRFi) 5 EPRDRFj(Q

DRFj) and

EPMDRFi(wDRFi) 5 EPMDRFj(w

DRFj) where i jAR M

and i 6frac14jFollowing Corollary 1 the rest of the results related

to profits of the retailer or the manufacturer hold re-gardless of the party paying for the tagging expensesHence we drop the subscript that indicates the partycovering these variable costs wherever possible fornotational convenience

LEMMA 2 Let us call incDRethyTHORN frac14 EPRDRFethQDRFTHORN EPRD

ethQDTHORN and incDMethyTHORN frac14 EPMDRFethwDRFiTHORN EPMDethwDTHORNwhere iAfR Mg

1 incDiethyTHORN40 if and only if totDi for given values of0 y 1 and K

2 Provided that party i covers a positive portion of thefixed cost of investment K40 incDiethyTHORN40 if andonly if KoKDi for given values of t and appropriatevalues of y where tDi and KDi are explicitly given inAppendix A

Lemma 2 separately characterizes the incentives ofthe parties in the supply chain to adopt thetechnology in terms of the fixed and the variable

costs of the investment If the unit tag price is greaterthan tDi the technology will not be beneficial forparty i Similarly KDi is a threshold on the entire fixedcost of investment Party i benefits from the tech-nology as long as K is less than this threshold valueNote that the maximum fixed cost of investment that afirm can afford is equivalent to the incentive of thatfirm to adopt the technology in absence of any fixedcost of investment inflated by the portion of the fixed

cost that she pays (KDR 1yincDReth0THORN for y 6frac140 and KDM

11yincDMeth1THORN for y 6frac141)

LEMMA 3 incDReth0THORN40 if and only if tot1 and incDMeth1THORN40 if and only if tot1

In an extreme case where one party bears the entirefixed cost of the investment any threshold value onthe fixed cost is irrelevant to the other party for whomthe problem simplifies to identification of the maxi-mum tag price that can be afforded in order to takeadvantage of the technology We show in Lemma 3that tDR (and tDM) reduces to t1 when y5 0 (and

y5 1) As y5 0 (y5 1) is equivalent to having a fixedcost of zero for the retailer (the manufacturer) thisalso implies that in a special case where fixed cost ofinvestment is completely ignored (K 5 0) the maxi-mum tag price that any party can afford will be equalto t1 which is the same maximum tag price for thevertically integrated supply chains to benefit from thetechnology when K 5 0 (see Theorem 1) In otherwords if a centralized firm does not benefit fromRFID then decentralized and uncoordinated supplychains cannot either

Further since both of the threshold values reduce tothe same value (t1) when fixed cost of investment isignored the incentives of the retailer and the manu-facturer are perfectly aligned when K 5 0 This resultis similar to those derived by Gaukler et al (2007) andRekik et al (2007) where no fixed costs of investmenthave been taken into account Different than thosepapers rather than identifying a sufficient conditionfor the incentives to be aligned we focus on exploringthose areas where firms may have interests in theopposite directions

Having characterized the incentives of the partiesindependent from each other we next analyze thebenefits of RFID for one party relative to the otherrsquos

THEOREM 5 In an uncoordinated supply chain the follow-ing findings hold if QD40

1 tDR tDMot1

2

tDR is

otDM if y4yD4tDM if yoyDfrac14 tDM otherwise

8gtltgt


3 Given KDRKDM40

KDR is

oKDM if y4yD4KDM if yoyDfrac14 KDM otherwise

8gtltgt

4 (a) tDR=ao0 tDM=ao0 KDR=ao0 and

KDM=ao0

(b) (i) If y yD tDRotC KDRoKCetht

Ct

DRTHORN

a o0ethK

CKDRTHORNa o0

(ii) If yoyD tDMotC KDMoKCetht

Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0

Where yD frac14 ethpthorn gR sTHORN=frac123ethpthorn gR sTHORN thorn gM 1=3

Benefits of parties from making an investment inRFID technology in comparison with each otherdepend on the relative fixed cost of investment aswell as the tag prices One would expect thethresholds to be different due to the fixed cost ofinvestment As illustrated by Theorem 5 the relationbetween tDRand tDM depends on the value of y Whenthe retailer covers for exactly yDK these thresholds areequal to each other Therefore in such a case thereexist only two regions regarding the RFID adoptionwhere both parties benefit from the adoption for totDR frac14 tDM and where no party benefits Figure 3shows these regions

When y 6frac14 yD the incentives of the parties to adoptRFID are not always perfectly aligned If the tag priceis smaller than minftDR tDMg both parties benefit

from the investment If the tag price is greater thanmaxftDR tDMg no party benefits from the invest-ment An interesting situation arises when the tagprice is in between these two values because only oneparty benefits in that case If the retailer covers formore than yD 1=3 then tDR is less than tDM therebyonly the manufacturer benefits for tag prices falling inthe middle region ethtDRototDMTHORN However if theretailer covers for less than yD tDR is greater than tDMand thereby only the retailer benefits for the tag pricesfalling in the middle region ethtDMototDRTHORN

We know from Lemma 3 that t4t1 is a sufficientcondition for none of the parties to adopt RFID FurtherTheorem 5 shows that both threshold valuestDR and tDM are less than t1 Hence one can concludethat although a given tag price can induce both partiesto adopt RFID in the absence of fixed cost in reality itmay make only one party benefit from this investmentdepending on the relative payments of fixed cost Whenfixed cost of investment is considered the partiesrsquo RFID-adoption decisions are not perfectly aligned unless theretailer pays exactly yD of the fixed cost of investment

An interesting observation from Theorem 5 is thateven if the parties share the fixed cost as half and halfif the tag price falls into frac12tDR tDMTHORN contrary to pop-ular belief in press about retailers being the mainbeneficiaries of the RFID investment only the man-ufacturer benefits from this investment In fact wheny 5 12 being a leader the manufacturer can alwaysextract more benefits from the technology thereforeshe affords higher tag prices than the retailer doesFurther as the manufacturerrsquos goodwill cost (gM) in-creases yD decreases Thus as the manufacturer gets

tDR

tDR = tDM

tDM

Both partiesbenefit from

an investmentin RFID

Onlythe manufacturer

benefits froman investment

in RFID

No partybenefits froman investment

in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =

Figure 3 Investment in RFID Technology in an Uncoordinated Supply Chain for Positive Threshold Values


more concerned about the stockouts the retailer has tocover for even lower proportions of the fixed cost tobe the only beneficiary of this investment for certainvalues of tag prices As given by the relation betweenKDR and KDM a similar setting of regions exist forranges of fixed cost as well

As illustrated in Theorem 5(4)(a) the maximum tagprice that a firm can afford to benefit from RFID doesnot generate benefits for another firm where inventorymisplacement is less of a problem An improvementin the availability level will increase both partiesrsquo pro-fits under misplacement As a result the profits underRFID should be even higher to yield the same amountof benefits as before which is only possible with alower tag price everything else being constant Sim-ilar effects on the threshold values of the fixed cost ofinvestment take place as a result of changes in the tagprice availability level and the sharing of fixed cost

We further compare the maximum RFID costs thatuncoordinated supply chains can afford to those ofthe vertically integrated supply chains in Theorem5(4)(b) We assume that the maximum tag price (or thefixed cost) that an uncoordinated supply chain canafford is equal to the threshold value that makes bothparties adopt this technology which depends on thevalue of y We show that the centralized firms canafford higher tag prices as well as a higher fixed costof investment than the uncoordinated supply chainsAs inventory availability increases the correspondingincrease in the profit of the centralized firm is alwayshigher than that in either partyrsquos profits in a decen-tralized supply chain As a result the maximum tagprice that an integrated supply chain can afford dropseven faster than that of a partyrsquos maximum affordabletag price in an uncoordinated supply chain Hencethe gap between the thresholds of the decentralizedand the centralized supply chains shrinks as inven-tory availability improves

THEOREM 6 The following findings hold for uniformlydistributed demand in frac12b b if tot1

1 Regardless of the party paying for the taggingexpenses the incentives of the retailer and the man-

ufacturer under inventory misplacement to adoptRFID decreases as inventory availability increases

2 The following results hold for each party as the ex-pected value of demand changes given the variance isfixed or vice versa regardless of the party paying forthe tagging expenses

(a) The results given in Theorem 2 and Theorem 3 forQ0C and Q0CRF are exactly valid for Q0D and Q0DRFrespectively

(b) The results given in Theorem 2 and Theorem 3 re-garding the incentives of a centralized firm underinventory misplacement to adopt RFID are exactlyvalid for both the retailer and the manufacturer un-der inventory misplacement to adopt RFID

In the above results we only consider cases wheretot1 since each firm may invest in RFID for such tagprices Theorem 6 shows how the changes in the ex-pected value or the variance of demand affectstocking decisions and the incentives of the firms inan uncoordinated supply chain to adopt RFID Cor-ollary 1 holds (see Section 4) therefore we also dropindex i when referring to values under RFID whereverpossible Since both Q0D and Q0DRF can be expressedas Q0D frac14 kQ0C and Q0DRF frac14 kQ0CRF where ko1 theresults that are given by Theorem 2 and Theo-rem 3 related to corresponding order quantities ofa centralized firm apply to those in the uncoordi-nated supply chain Furthermore we show that theincentive of each party to adopt RFID changes inthe same manner Thus both firmsrsquo incentives toadopt the technology decreases with variance of de-mand if the existing inventory availability level ofthe retailer is low and the value of tag price is highFigure 4 shows a numerical example where the in-centives of the firms decrease as variance of demandincreases

32 Coordination Through Quantity ContractsVertically integrated supply chains benefit morefrom a costless improvement in availability thanuncoordinated supply chains do (see Camdereli andSwaminathan 2005) However the total benefit to acoordinated supply chain due to improvements in

Figure 4 Changes in the Incentives of the Parties in an Uncoordinated Supply Chain under Inventory Misplacement to Adopt RFID Technology as Variance ofUniformly Distributed Demand Increases when t4t2 (Variance Increases as d Increases)


inventory availability would be equivalent to that of acentralized firm in the absence of any investmentto accomplish the improvements Motivated by thisfact we study supply chains under two widely stud-ied contracts in the next two sections and analyze eachpartyrsquos incentive to adopt RFID to remove inventorymisplacement at variable and fixed costs of invest-ment

321 Revenue Sharing Sometimes supply chainsare coordinated through a revenue sharing mech-anism (see Cachon 2003 Cachon and Lariviere 2005)which are particularly prevalent in franchiseoperations Such mechanisms are also common invideo rental industries which are prone tooperational inefficiencies of our interest In thissection we study the implications of RFIDimplementation in such situations The sequence ofevents is the same as in Section 31 except for therevenue sharing contract the retailer takes g of thepositive earnings (sales and salvage value earnings)and the manufacturer takes 1 g of them where0ogo1 As in the previous decentralized setting ifthe supply chain is subject to inventory misplacement0ol 5 1 ao1 proportion of the order released to themanufacturer is misplaced in the retail store We willuse QRS and wRS to denote the ordering quantity andthe wholesale price under misplaced inventoryrespectively The retailerrsquos and the manufacturerrsquosprofits under inventory misplacement are given by(11) and (12) in that order

EPRRSethQRSTHORN frac14 wRSQRS thorn g pethmthornZ 1

aQRS

ethaQRS xTHORNdFethxTHORNTHORN

thornsethlQRS thornZ aQRS

0


gR

Z 1aQRS

ethx aQRSTHORNdFethxTHORN

eth11THORN

EPMRSethwRSTHORN frac14 ethwRS cTHORNQRS thorn eth1 gTHORN

pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN

These partiesrsquo profits under a revenue sharingcontract in the existence of RFID are given byEPRRSRFi and EPMRSRFi where iAfR Mg Theexpressions GRS(QRSRFi wRSRFi) and LRS(QRSRFi

wRSRFi) where QRSRFi is the order and wRSRFi

is the wholesale price show the retailerrsquos and themanufacturerrsquos profits exclusive of the taggingexpenses under a revenue sharing contract respec-tively

GRSethx yTHORN frac14 yx yK thorn gfrac12pethmthornZ 1

xethx xTHORNdFethxTHORNTHORN

thorn s

Z x

0

ethx xTHORNdFethxTHORN gR


LRSethx yTHORN frac14 ethy cTHORNx eth1 yTHORNK thorn eth1 gTHORN

pethmthornZ 1


Z x

0

ethx xTHORNdFethxTHORNTHORN

gM


We use (13) and (14) to represent the retailerrsquos profitand the manufacturerrsquos profit under RFID where IR

is given in Section 31

EPRRSRFiethQRSRFiTHORN frac14 GRSethQRSRFiwRSRFiTHORN IRtQRSRFi eth13THORN

EPMRSRFiethwRSRFiTHORN frac14 LRSethQRSRFiwRSRFiTHORN eth1 IRTHORNtQRSRFi eth14THORN

To coordinate a supply chain the manufacturersets the wholesale price such that the retailer ordersthe centralized optimum order thereby making thetotal supply chain profits equal to that of a verticallyintegrated supply chain We assume that g is set suchthat the partiesrsquo profits are at least as much as thosebefore the coordination

THEOREM 7 The supply chain is coordinated by a revenuesharing contract in the existence of RFID where the re-tailer takes 0ogo1 of the earnings as follows

1 When the retailer pays for the tagging expenses thecoordination is achieved by

wRSRFR frac14ethcthorn t sTHORNfrac12gethp sTHORN thorn gR

pthorn gC s tthorn gsowRS eth15THORN

2 When the manufacturer pays for the taggingexpenses the coordination is achieved by

wRSRFM frac14 wRSRFR thorn t4wRS eth16THORN

3 Given QRSRFi40 where i 2 fRMg the followingfindings hold(a) wRSRFRis always less than c

(b) wRSRFM4c if and only if t4cethgMthorneth1gTHORNethpsTHORNTHORNthornsethgRggCTHORN

gRthorngethpsTHORN 40

Under revenue sharing contracts it is common forthe coordination wholesale prices to be lower than


the marginal cost of production (see Cachon andLariviere 2005) which is also the case under inven-tory misplacement (Camdereli and Swaminathan2005) However unlike the traditional models thecoordination wholesale price is always higher thanthe marginal cost of production if the tag price is

expensive t4 cethgMthorneth1gTHORNethpsTHORNTHORNthornsethgRggCTHORNgRthorngethpsTHORN

and the man-

ufacturer pays for the expensesThe manufacturer makes the retailer pay for

the tag price through the wholesale price whenshe is charged for the tagging expenses Furtherthe two ordering quantities are equal to each otherdue to coordination Thus similar to Corollary 1the profit of each party under RFID is the same aswell as the benefits accrued to the same party frominvesting in RFID whoever covers for the taggingexpenses

We can further show the following results for asupply chain under a revenue sharing contract (referto Lemma 8 through Theorem 9 in Appendix A forthe mathematical representation of the followingresults)

1 RFID benefits the retailer (manufacturer) in asupply chain coordinated by a revenue sharingcontract under misplaced inventory as long asthe tag price is less than tRSRethtRSMTHORN for a givenfixed cost and as long as the fixed cost is less thanKRSRethKRSMTHORN for a given tag price (see Lemma 8for the closed-form expression) The correspond-ing threshold values are lower for supply chainsthat expect to have an x improvement on theprofits under inventory misplacement as a resultof adopting RFID

2 When one party covers for the entire fixed costthe other party has an incentive to invest in thetechnology if and only if the tag price is lowerthan t1 Thus one can conclude that when thefixed cost of investment is ignored each party inthe supply chain therefore the supply chain un-der a revenue sharing contract has an incentiveto adopt the technology if and only if the tagprice is less than t1 With respect to incentives toadopt the RFID technology the supply chain un-der a revenue sharing contract behaves as acentralized firm under no fixed cost due to thecoordination

3 We prove the counterpart of Theorem 5 for thesupply chain under a revenue sharing contractwhere yRS frac14 frac12gR thorn gethp sTHORN=ethpthorn gC sTHORNo1 (referto Theorem 8)

4 When the total supply chain profits undercoordination is concerned the maximum tagprice that the supply chain can afford (in order tohave an increase in the total profits as a result of

adopting RFID) is equal to that of the centralizedfirmrsquos ethtCTHORN However minftRSR t

RSMg is always

smaller than tC therefore such a tag price willalways leave one of the parties at loss after RFIDThe same holds for the fixed costs of investmentas well Hence when the fixed cost of investmentis considered it is interesting that even coordi-nated supply chains cannot make as highinvestments in the technology as centralizedfirms can since the incentives of the parties arenot perfectly aligned However the gap betweenthe two thresholds gets smaller as inventoryavailability increases

5 When the tag price is sufficiently small (lowerthan t1) the retailerrsquos incentive to invest in thetechnology increases in g The manufacturerrsquosincentive changes in the opposite direction bythe same magnitude because the summation ofthe incentives of parties in the coordinatedsupply chain is always equal to that of acentralized firm

6 The optimum order quantity in a coordinatedsupply chain is equal to that of a centralized firmHence it is obvious that optimal stockingdecisions in a coordinated supply chain react tochanging mean or variance of demand in theexact same way as in the centralized firms Wefurther prove that the incentives of each firm in acoordinated supply chain are affected in thesame way as the centralized firm is by such achange (refer to Theorem 9) Further theseresults also hold for normally distributeddemand

322 Buyback Contract Another commonly usedcontracting mechanism in supply chains is a buybackcontract where the retailer returns leftover items backto the manufacturer for a credit Here we analyze abuyback contract where the manufacturer buysremaining items back from the retailer for a price ofb per unit and she salvages these items for s per unitIn order to prevent the retailer from salvaging theleftovers himself following the model by Pasternack(1985) we assume that b4s Under this contract theretailerrsquos and the manufacturerrsquos profit functionsare as follows under inventory misplacement andunder RFID where iAfR Mg In fact the profitfunctions under RFID are equivalent to Pasternackrsquoswith the exception that either the wholesale priceor the marginal cost of production is inflated by thetag price and the fixed cost of RFID adoption isadded Further we assume bop holds so that theretailer has an incentive to sell the items to customersfirst and then return the leftovers to the manu-facturer


HBethx g yTHORN frac14pethmthornZ 1

xethx xTHORNdFethxTHORNTHORN thorn y

Z x

0


g


eth17THORN

EPRBethQTHORN frac14 HBethaQ gR bTHORN thorn beth1 aTHORNQ eth18THORN

EPMBethwTHORN frac14 HBethaQ gM s bTHORN wQ ethb sTHORNeth1 aTHORNQeth19THORN

EPRBRFiethQTHORN frac14 HBethQ gR bTHORN IRtQ yK eth20THORN

EPMBRFiethwBRFiTHORN frac14HBethQ gM s bTHORN wBRFiQ

eth1 IRTHORNtQ eth1 yTHORNKeth21THORN

We study cases where the buyback credit is strictlysmaller than the wholesale price and show that onecan find a coordinating wholesale price under RFID(see Lemma 9 in Appendix A) We can also showthat incentives of the parties to adopt the technologyrelative to each other also depends on the value of yand these incentives can be completely characterizedby three regions as in Figure 3 (see Theorem 11 inAppendix A)

4 General Demand DistributionIn this section we discuss how some of our earlierresults can be extended to general continuous de-mand distributions with a finite mean and a cdf ofF(0) 5 0

Centralized firm

LEMMA 4 The following findings hold for a general con-tinuous demand distribution

(i) tC=Ko0 and KC=to0 (ii) Given QC40 tC=ao0 and KC=ao0

Obviously the incentive of the centralized firm toadopt RFID decreases in the fixed cost of investmentOne can also show that the incentive decreases in thetag price (see the proof of Lemma 4) Thus there existsa threshold value of tC and KC over which theinvestment in the technology does not bring moreprofits to the firm As the fixed costs of the RFIDbecome less expensive the firms can afford higher tagprices and vice versa If K (or t) increases beyondsome value tC(or KC) can no longer be positive Thefirmrsquos profit always benefits from reductions in theinventory misplacement at no cost Accordingly asLemma 4 shows the firms already operating underhigh inventory availability levels become less willingto pay for the technology This is similar to the result

by Gaukler et al (2007) who found that the thresholdvalue of the tag price for the firm to benefit from thetechnology also decreases with the value of respon-siveness of the firm under a normal demanddistribution when RFID improves demand visibility

A comparison of Ffrac12aQC to Ffrac12QCRF both of which

are o1 yields that aQC QCRF if and only if t t1

However Theorem 1(3) also holds for a generalcontinuous demand distribution (see the proof ofLemma 4) and makes KCo0 for t t1 Hence the firmwill never adopt RFID technology in that caseThereby RFID technology will enable the firms tohave more available items during the selling season

Wholesale price contract Lariviere and Porteus (2001)show that in a classical newsvendor Stackelberggame a unique optimum wholesale price and anoptimum order quantity exist when demand distribu-tion has an increasing generalized failure rate (IGFR)Lemma 5 gives the corresponding expressions for theoptimum values in a supply chain under RFID Asmany commonly used distributions such as uniformnormal exponential are IGFR the result above is notrestrictive Camdereli and Swaminathan (2005) givethe expressions for the corresponding optimumvariables under inventory misplacement under IGFRdemand distributions We assume that F() is IGFR forthe rest of this section to ensure that the manufac-turerrsquos profit function is unimodal

LEMMA 5 If demand distribution is IGFR the optimumorder QDRFi and wholesale price wDRFi solve the following

where iAfR Mg FethTHORN frac14 1 FethTHORN and gfrac12x frac14 xfethxTHORNFethxTHORN

wDRFM frac14ethpthorn gR sTHORNFethQDRFMTHORN thorn s

frac14wDRFR thorn teth22THORN

FethQDRFiTHORNpthorn gc s

pthorn gR s gfrac12QDRFi

frac14 c sthorn t

pthorn gR s eth23THORN

QDRFR frac14 QDRFM eth24THORN

We observe that leading manufacturers always ad-just the wholesale price by t depending on the partypaying for the tagging expenses Additionally theoptimum order quantities are equally independent ofthe party paying for the tagging expenses HenceCorollary 1 holds for a general IGFR demand distri-bution

LEMMA 6 In an uncoordinated supply chain the follow-ing findings hold given QDRFi40 and yK 6frac14 0 whereiAfR Mg

(i) tDi=Ko0 and KDi=to0

(ii) tDR=yo0 KDR=yo0 and tDM=y40

KDM=y40


Both partiesrsquo optimum profits under RFID decreasein t and K for IGFR demand distributions and so arethe incentives to adopt RFID Thus a threshold typeof a condition exists for firms in an uncoordinatedsupply chain to adopt the technology (tDR and KDRfor the retailer and tDM and KDM for the manufac-

turer) As the fixed cost of investment or theproportion of the fixed cost that a party is chargedincreases the new technology becomes so costly thatthe maximum amount of tag price a firm can afforddecreases Similar effects on the threshold values ofthe fixed cost of investment take place as a result ofchanges in the tag price and the sharing of fixed cost

Although we are not able to prove the counterpartof Theorem 5 for a general demand distribution weprovide two numerical examples in Figure 5 for nor-mally and exponentially distributed demand toillustrate the regions of incentives Figures 5(a) and(b) portray the changes in the incentives of the partiesas y and t change We have [t y 0] for any value oft and y at Incentive 5 0 plane Figures 5(c) and (d) giveus the top views of the graphs in (a) and (b) Inter-mittent lines indicate the intersection of the cor-responding partyrsquos incentives with the Incentive 5 0

plane Projections of these lines onto the t axes give usthe maximum tag price the corresponding party canafford to benefit from RFID When y is equal to athreshold value (y frac14 yD1 under normal demand dis-tribution and y frac14 yD2 under exponential demanddistribution) incentives of the retailer and the man-ufacturer are perfectly aligned such that themaximum tag price that they can afford is the sameHowever if y is smaller than this threshold value theretailer can always afford higher tag prices than themanufacturer and vice versa if y is greater

Revenue Sharing Theorem 7 exactly holds for a gen-eral demand distribution as the coordinating whole-sale prices turn out to be independent of the demanddistribution (see Theorem 10 in Appendix A)

LEMMA 7 In a supply chain coordinated by a revenuesharing contract the following findings hold given QRSRF

frac14 QCRF40 and yK 6frac140 where iAR M

(i) tRSi=Ko0 and KRSi=to0(ii) tRSi=ao0 and KRSi=ao0

(iii) tRSR=yo0 KRSR=yo0 and tRSM=y40

KRSM=y40

Incentive = 0

Manufacturerrsquosincentivefunction

Retailerrsquosincentivefunction

θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)

Demand is Normal [ 2] K = 6 times 105

Incentive = 0 Manufacturerrsquosincentivefunction

Retailerrsquos incentivefunction θ

t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)

Demand is Exponential [] K = 106

03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ

tDR gt tDMtDR lt tDMtDR gt tDMtDR lt tDM

D2θ

(d)

Exponential []

Figure 5 Incentives of Parties to Invest in RFID Technology as t and h Change for Normally and Exponentially Distributed Demand (l = 106 r = 4105k = 10 6 p = 25 c = 5 gR = 1 gM = 3 s = 2 a = 07)


(iv) If tot1 tRSR=g40 KRSR=g40 and

tRSM=go0 KRSM=go0

Similar to the previous settings there exists athreshold value (of t or K) beyond which RFID is notbeneficial for a firm We further perform comparativestatistics for the thresholds on the tag prices and thefixed cost of investment in Lemma 7 Maximum tagprices and fixed costs that each party can afford tobenefit from the technology portray parallel behaviorto their counterparts in an uncoordinated supply chainwith changes in tag price availability level fixed costand sharing of fixed cost Additionally in the areawhere the parties may have incentives to adopt RFID(tot1) the retailer taking more of the supply chainearnings puts tighter bounds on the threshold valuesrelated to the manufacturer and vice versa

One can also find numerical examples similar toFigure 5 where we can observe the thresholds of theparties with respect to each other when demand isnormally and exponentially distributed

Buyback contract We can prove that a tBi and a KBiexist where iAR M under buyback contracting Wecan also show the counterpart of the results reportedin Lemma 7(i)ndash(iii) (see Supporting Information(available on request))

Here we note that the entire analysis of the paperwould go through had we assumed that parties in thedecentralized supply chains also shared the variablecosts of RFID adoption according to a constantfraction 0oAo1 In that case the optimum orderswould be equal to the ones reported in this paperHowever the wholesale prices would be adjustedsuch that the optimum profit of the retailer and themanufacturer are equal to EPRDRF and EPM

DRFrespectively under the wholesale pricing contract andto EPRRSRF and EPM

RSRF under the revenue sharingcontract and to EPRBRF and EPM

BRF under thebuyback contract Hence sharing of the variable costsof the technology does not create any difference in theincentives of the companies unlike the sharing of thefixed costs of investment

5 ConclusionWe study incentives of players in supply chains toinvest in RFID to remove inefficiencies of misplacedinventory in this paper We consider both fixed andvariable costs of adoption of RFID in verticallyintegrated and bilaterally decentralized supplychains for which we study uncoordinated andcoordinated environments by revenue sharing buy-back contracts We analyze scenarios where the fixedcost of adoption is shared and study both cases whereonly the retailer or only the manufacturer pays for thevariable costs of adoption ie tagging expenses

We find that in all of the decentralized settingswhen the manufacturer pays for the tagging expensesshe inflates the wholesale price by the tag price ascompared with the wholesale price in the scenariowhere the retailer pays for the tagging expensesHence the incentive of a party to adopt RFID is thesame regardless of the one paying for the taggingexpenses Further we show that the manufacturercharges a higher wholesale price under RFID than shewould under no RFID if she covers for the taggingexpenses However we also prove that the wholesaleprice under RFID is unconditionally smaller than theone under inventory misplacement in coordinatedsupply chains and can indeed be smaller than that inuncoordinated environments for high tag prices if theretailer pays for the tagging expenses

One common result in all of our settings supportsthe current reactions of the supply chains to the RFIDtechnology and show that unless the fixed cost ofRFID is sufficiently low and the tag prices are cheapenough no party would benefit from an investment inthis technology However our findings regarding theincentives of the parties in the decentralized settingscounter the common opinion that the main bene-ficiaries of RFID will be the retailers We show that fora given fixed cost of investment (or a tag price of anRFID chip) the characterization of incentives dependson relative investments of fixed cost and the tag price(or the fixed cost of investment) If the retailer coversfor yj K (j 5 D in an uncoordinated supply chainj 5 RS in a coordinated supply chain by a revenuesharing contract and j 5 B in a coordinated supplychain by a buyback contract) the incentives of theparties are perfectly aligned such that both partieswill benefit from the investment if and only if the tagprice is smaller than a threshold value Otherwise noparty will benefit from such an investment If theretailer pays for an amount other than yj K theincentives of the parties are characterized by twothreshold values of tag prices (or fixed cost ofinvestment) for a given fixed cost of investment (ora given tag price) Given that these threshold valuesare positive no party benefits from this investment ifthe tag price is higher than the maximum of the twoand both parties benefit if the tag price is smaller thanthe minimum of the two An interesting situationarises when the tag price is in between these twovalues and only one party benefits from theinvestment If the retailer pays for more than yj Kthe manufacturer is indeed the only party benefitingfrom this investment for such tag prices Although ouranalytical results are proven for uniform demanddistributions our numerical examples with truncatednormal and exponential demand distributions lendsupport to our analytical findings regarding thethreshold behavior of the incentives of the parties


We show that greatest incentives to adopt thetechnology occur for lower values of availability Westudy the effects of changes in the mean and thevariance of demand independent from each other onthe incentives of the centralized firm and parties inuncoordinated and coordinated decentralized supplychains Our findings regarding the effects of changes inthe mean of the distribution for fixed variance complywith intuition The more the expected value of demandis the more beneficial the RFID technology becomes foreach firm However we find an interesting resultregarding the effects of a change in the variance ofthe distribution We show that the firmsrsquo incentives inthe aforementioned supply chains can indeed decreasewith increasing variance of demand if the existingavailability level is less than a threshold value and thetag price is sufficiently high Furthermore thosethreshold values happen to be identical for each firmand all types of supply chains studied in this paper

We study incentives of parties to adopt RFID tomitigate the negative effects of inventory misplace-ment in this paper However shrinkages due to theftcan easily be incorporated into our existing model byformulating a generalized cleanup process where xof the products are misplaced and retrieved at the endof the selling season while (100 x) is lost andcannot be retrieved In our decentralized settings weassume that RFID adoption is an exogenous decisionIt is interesting to study contracts where thetechnology adoption is also endogenized as a decisionvariable and we intend to study this in the futureClearly the retailer in a two-player supply chain maynot be willing to participate if she bears all of the RFIDcosts However if there is competition retailers maybe forced to participate when some customers whoare not able to find a product in one retail store searchfor it at another retailer (Camdereli et al 2006) Finallyit would be interesting to study the problem oftechnology adoption in multiple sales periods in-corporating price markdowns between periods Whileabove studies are geared toward the theoreticalunderstanding of benefits of RFID there is amplescope for future studies on benefits of RFID takinginto behavioral aspect of decision making (like Lurieand Swaminathan 2009) as well as empiricallystudying the benefits using primary data

Appendix A

THEOREM 1

tC frac14ethpthorn gC cTHORN ffiffiffiffiffidC

pwhere

dC frac142a2Kethpthorn gC sTHORN thorn ethaethpthorn gC sTHORN ethc sTHORNTHORN2b

a2b40

KC frac14u1u2b

2a2ethpthorn gC sTHORN where u1 frac14 frac12eth1 aTHORNethc sTHORN at and

u2 frac14frac12aeth2ethpthorn gCTHORN ethcthorn sTHORNTHORN ethc sTHORN at

LEMMA 2

KDR frac14ethpthorn gR sTHORNu1u2b

2a2frac122ethpthorn gR sTHORN thorn gM2yand

KDM frac14u1u2b

2a2frac122ethpthorn gR sTHORN thorn gMeth1 yTHORN

where n1 and n2 are given by Theorem 1

tDR frac14ethpthorn gC cTHORN dDR1

ffiffiffiffiffiffiffiffiffiffiffidDR2

p

tDM frac14ethpthorn gC cTHORN ffiffiffiffiffiffiffiffiffiffidDM

p

where dDR1 5 [4(p1gC s)1gM2(p1gR s)]40 and

dDR2 frac14frac12ethaethpthorn gC sTHORN ethc sTHORNTHORNethpthorn gR sTHORN2thorn2a2Kfrac122ethpthorngRsTHORNthorngM2yethpthorngRsTHORN

b =frac12a2frac122ethpthorn gR sTHORN thorn gM440

and dDMfrac14frac12ethaethpthorn gCsTHORNethcsTHORNTHORN2thorn2a2Kfrac122ethpthorngRsTHORNthorngMeth1yTHORNb

=a240

LEMMA 8 In a coordinated supply chain by a revenuesharing contract where QRSRF and QRS40 findings ofLemma 2 hold where the thresholds are modified as follows

tRSR frac14ethpthorn gC cTHORN eth1=aTHORNffiffiffiffiffiffiffiffiffiffidRSR

pand

tRSM frac14ethpthorn gC cTHORN eth1=aTHORNffiffiffiffiffiffiffiffiffiffiffidRSM

pwhere

dRSR frac14ethaethpthorn gC sTHORN ethc sTHORNTHORN2 thorn 2a2Kethpthorn gC sTHORN2ybethgR thorn gethp sTHORNTHORN 40

dRSM frac14ethaethpthorn gC sTHORN ethc sTHORNTHORN2 thorn 2a2Kethpthorn gC sTHORN2eth1 yTHORNbethgM thorn eth1 gTHORNethp sTHORNTHORN 40

KRSR frac14ethgethp sTHORN thorn gRTHORNfrac12eth1 aTHORNethc sTHORN atfrac12aeth2ethpthorn gCTHORN ethcthorn sTHORNTHORN ethc sTHORN atb

2a2ethpthorn gC sTHORN2y

KRSM frac14frac12etheth1 gTHORNethp sTHORN thorn gMTHORNfrac12eth1 aTHORNethc sTHORN atfrac12aeth2ethpthorn gCTHORN ethcthorn sTHORNTHORN ethc sTHORN atb

2a2ethpthorn gC sTHORN2eth1 yTHORN

THEOREM 8 The results of Theorem 5 go through for a sup-ply chain under a revenue sharing contract where wholesaleprices are set according to Theorem 7 and QD tDi KDiand yD are replaced by QRS tRSi KRSi and yRS 5 [gR1g(p s)](p1gC s)o1 in that order for iAR M

THEOREM 9 In a supply chain coordinated by a revenuesharing contract the following findings hold for uniformlydistributed demand in frac12b bif tot1

1 Regardless of the party paying for the taggingexpenses the incentives of the retailer and the


manufacturer under inventory misplacement to adoptRFID decreases as inventory availability increases

2 The results given in Theorem 2 and Theorem 3 re-garding the incentives of a centralized firm underinventory misplacement to adopt RFID are exactlyvalid for both the retailer and the manufacturer underinventory misplacement in a coordinated supply chainby revenue sharing to adopt RFID

THEOREM 10 Theorem 7 stated for a uniform demand dis-tributed in [0 b] exactly goes through for a generalcontinuous demand distribution with a finite mean

LEMMA 9 A supply chain under RFID can be coordinatedby a buyback contract with unlimited returns and partialcredit when demand is distributed continuously with afinite mean The coordinating wholesale prices are as givenbelow where iAR M and IR 5 1 if i 5 R and 0 otherwise

wBRFi frac14ethcthorn t sTHORNethpthorn gR bTHORN

pthorn gC s IRtthorn b

wBRFM frac14 wBRFR thorn t

THEOREM 11 The results of Theorem 8 go through for asupply chain under a buyback contract where wholesaleprices are set according to Lemma 9 and tRSi KRSi andyRSy are replaced by tBi KBi and yB in that order foriAR M

tBi frac14 ethpthorn gC cTHORN ffiffiffiffiffiffiffidBi

pwhere i 2 fR Mg eth25THORN

KBR frac14u1u2ethpthorn gR bTHORNb2a2ethpthorn gC sTHORN2y

KBM frac14u1u2ethb sthorn gMTHORNb

2a2ethpthorn gC sTHORN2eth1 yTHORNand

yB frac14pthorn gR b

pthorn gC s

eth26THORN

where

dBR frac14 frac12aethpthorn gC sTHORN ethc sTHORN2=a2 thorn 2KethpthorngCsTHORN2ybethpthorngRbTHORN 40

dBM frac14 frac12aethpthorn gC sTHORN ethc sTHORN2=a2 thorn 2KethpthorngCsTHORN2eth1yTHORNbethbsthorngMTHORN 40

and n1 and n2 are given by Theorem 1

Supporting Information ElectronicCompanionAn electronic companion to this paper is available onrequest

AcknowledgmentsWe are grateful to three anonymous referees and the asso-ciate editor whose comments significantly improved boththe clarity and the quality of the paper We also thank RobinDillon-Merrill seminar participants at Cornell UniversityPurdue University the Ohio State University George-town University and conference participants at INFORMS-

Pittsburgh in 2006 POMS-Boston in 2006 and INFORMS-Seattle in 2007

References

Aboutcom Retail industry Available at httpretailindustryaboutcomcsit_rfidabl_atk111003htm (accessed on April15 2008)

Agarwal V 2001 Assessing the benefits of Auto-ID technology in theconsumer goods industry White Paper Auto-ID Center MIT

Angeles R 2005 RFID technologies Supply chain applications andimplementation issues Inf Syst Manage 22(1) 51ndash65

Asif Z M Mandviwalla 2005 Integrating the supply chain withRFID A technical and business analysis Commun Assoc InfSyst 15 393ndash426

Atali A H L Lee O Ozer 2005 If the inventory manager knewmdashRFID in retail and distribution MSOM Conference 2005Proceedings Chicago IL

Bearing Point 2005 Beyond compliance The future promise ofRFID White Paper

Burnell J 2008 DSD study finds skepticism about RFID value RFIDupdate 809

Cachon G 2003 Supply chain coordination with contracts GravesS T Kok eds Handbooks in OR amp MS Supply Chain Manage-ment Amsterdam Elsevier Publishers 231ndash239

Cachon G P M A Lariviere 2005 Supply chain coordination withrevenue-sharing contracts Strengths and limitations ManageSci 51(1) 30ndash44

Camdereli A Z E Kemahlioglu-Ziya J M Swaminathan 2006Inventory management under shrinkage and customer-drivensearch Working Paper Kenan-Flagler Business School Univer-sity of North Carolina at Chapel Hill NC

Camdereli A Z J M Swaminathan 2005 Coordination of a sup-ply chain under misplaced inventory Working Paper Kenan-Flagler Business School University of North Carolina at ChapelHill NC

DeHoratius N A Mersereau L Schrage 2008 Retail inventorymanagement when records are inaccurate Manuf Serv OperManage 10(2) 257ndash277

DeHoratius N A Raman 2008 Inventory record inaccuracy Anempirical analysis Manage Sci 54(4) 627ndash641

Dutta A H L Lee S Whang 2007 RFID and operations man-agement Technology value and incentives Prod Oper Manag16(5) 646ndash655

Gaukler G M O Ozer W H Hausman 2008 Order progressinformation Improved dynamic emergency ordering policiesProd Oper Manag 17(6) 599ndash613

Gaukler G M R W Seifert W H Hausman 2007 Item-level RFIDin the retail supply chain Prod Oper Manag 16(1) 65ndash76

Heese S 2007 Inventory record inaccuracy double marginalizationand RFID adoption Prod Oper Manag 16(5) 542ndash553

Iglehart D L R C Morey 1972 Inventory systems with imperfectasset information Manage Sci 18(8) B388ndashB394

Informationweekcom American apparel taking wireless inventorywith RFID Available at httpwwwinformationweekcomnewsmobilityRFIDshowArticlejhtmlarticleID=207200508(accessed on April 16 2008)

Kambil A J D Brooks 2002 Auto-ID across the value chain Fromdramatic potential to greater efficiency amp profit White PaperCambridge MIT Auto-ID Center amp Accenture

Kang Y S B Gershwin 2005 Information inaccuracy in inventorysystems IIE Trans 37(9) 843ndash859

Karaer O H L Lee 2007 Managing the reverse channel withRFID-enabled negative demand information Prod Oper Manag16(5) 625ndash645


Kearney A T 2003 Meeting the retail RFID mandate A discussionof the issues facing CPG companies White Paper

Kevan T 2004 Calculating RFIDrsquos benefits Frontline Solutions 5(1)16ndash20

Kok G K H Shang 2007 Inspection and replenishment policiesfor systems with inventory record inaccuracy Manuf Serv OperManage 9(2) 185ndash205

Lariviere M A E L Porteus 2001 Selling to the newsvendor ananalysis of price-only contracts Manuf Serv Oper Manage 3(4)293ndash305

Lee H L O Ozer 2007 Unclocking the value of RFID Prod OperManag 16(1) 185ndash205

Lurie N H J M Swaminathan 2009 Is timely information alwaysbetter The effect of feedback frequency on decision makingOrgan Behav Hum Decis Process 108(2) 315ndash329

Pasternack B A 1985 Optimal pricing and return policies for per-ishable commodities Mark Sci 4(2) 166ndash176

Raman A N DeHoratius Z Ton 2001 Execution The missing linkin retail operations Calif Manage Rev 46(3) 136ndash152

Rekik Y Z Jemai E Sahin Y Dallery 2007 Improving the perfor-mance of retail stores subject to execution errors Coordinationversus RFID technology OR Spectrum 29(4) 597ndash626

Rekik Y E Sahin Y Dallery 2008a Analysis of the impact of theRFID technology on reducing product misplacement errors atretail stores Int J Prod Econ 112 264ndash278

Rekik Y E Sahin Z Jemai Y Dallery 2008b Execution errors inretail supply chains Analysis of the case of misplaced productsInt J Syst Sci 39(7) 727ndash740

Selko A 2008 RFID amp auto manufacturing Available at httpwwwindustryweekcom (accessed on February 25 2008)

Sullivan Laurie 2005 Europe tries on RFID Information WeekMarch 7 (1029) 36ndash42

Swaminathan J M S R Tayur 2003 Models for supply chains inE-business Manage Sci 49(10) 1387ndash1406

Thomas D 2004 High cost of RFID slows progress Available athttpvnunetcom (accessed April 10 2008)

Wang E T G A Seidmann 1995 Electronic data interchangeCompetitive externalities and strategic implementation poli-cies Manage Sci 41(3) 401ndash418

Weier M H 2008 Wal-Mart gets tough on RFID Information Week26 1169

Whitaker J S Mithas M S Krishnan 2007 A field study of RFIDdeployment and return expectations Prod Oper Manage 16(5)599ndash612


costs such as system integration changes to existingsupply chain applications and storage of the largevolumes of data According to a report by A T Kear-ney in addition to tagging expenses systemsintegration is estimated to cost US$35ndashUS$40 million(httpretailindustryaboutcom accessed on April15 2008) It has been pointed out by the practitionersthat a sharing of costs is necessary to see the benefitsof the technology (Thomas 2004 Kearney 2003)

As these big retailers (including Walmart) havepopularized RFID a common opinion has been thatthe main beneficiaries of RFID will be the downstreamplayers in the supply chain (Agarwal 2001 Kevan2004) In addition to being able to track the items theretailers are expected to benefit from store and ware-house labor reductions and reduced inventories Onthe other hand the benefits of RFID to manufacturershave been anticipated in improved demand planningstricter quality control reduced scrap waste andrework and more accurate inventory data (BearingPoint 2005) An Italian subsidiary of Honda Motor Cohas integrated RFID on one of its scooter lines andclaims to see benefits beyond return on investment(Selko 2008) However it appears that Samrsquos Club(operated by Walmart) has to push even stronger toget its suppliers to comply with the RFID require-ments by making them pay a fee per pallet otherwise(Weier 2008) According to research presented byGlobal Commerce Initiative retailers and consumergoods suppliers are still sceptical about the benefits ofRFID (Burnell 2008) In a recent paper Dutta et al(2007) point out the need to have a better understand-ing of how the benefits of the technology might bedistributed over supply chain partners Motivated bythe debate among the upstream and downstreamplayers about the adoption of the RFID technologyusing a stylized model we intend to gain insightsabout how and when their incentives are aligned andespecially misaligned in the existence of a fixed cost ofinvestment in addition to variable expenses

11 Related LiteratureStudies related to RFID in inventory management arerelatively new Lee and Ozer (2007) provide a reviewof the literature about the emerging technology RFIDby examining the papers under three main categoriesmisplacement of inventory shrinkage and transac-tion errors As indicated by Raman et al (2001) in-ventory inaccuracy and misplaced inventory aremajor operational inefficiencies Several researchershave developed models for inventory inaccuracy (seeAtali et al 2005 DeHoratius et al 2008 DeHoratiusand Raman 2008 Heese 2007 Iglehart and Morey1972 Kang and Gershwin 2005 Kok and Shang 2007)Models for inventory misplacement problem havealso been studied by researchers (see Camdereli and

Swaminathan 2005 Rekik et al 2008b) In the follow-ing passages we will relate our work to other researchthat has explicitly incorporated RFID in their analysisof inventory inefficiencies

There is some recent work on analysis of the effectsof improved visibility in RFID-enabled supply chainsFor example Gaukler et al (2008) characterize a com-pound replenishment (Q R) policy with the option ofemergency ordering for a retailer subject to stochasticorder lead times The authors assume that the retailerhas order progress information due to being able totrack items through technology In another paperKaraer and Lee (2007) model degree of visibility for acentralized manufacturer with product returnsthrough order progress information in the reversesupply chain and knowledge of statistical character-istics of the product return flow Contrary to thesepapers rather than focusing on the value of informa-tion in RFID-enabled systems we explicitly modelcosts of the technology adoption for parties in bothcentralized and decentralized supply chains toremove operational inefficiencies due to inventorymisplacement

Gaukler et al (2007) study item-level RFID wherethe retailer uses in-store sales to estimate demanddistribution The tagging expenses are assumed to beshared and no fixed cost of implementation is takeninto account They research the behavior of the opti-mal stocking quantity and the profits of the parties forchanges in the responsiveness level of the retailer andthe tag price As opposed to their model where RFIDimproves demand visibility in our model RFID im-proves supply visibility In this paper besides taggingexpenses we take the fixed cost of RFID implemen-tation into consideration and allow the parties toshare the fixed cost of adoption We study both sce-narios where the tagging expenses are covered byonly the manufacturer and only the retailer Addi-tionally we also characterize the incentives for theparties to invest in RFID in vertically integrated un-coordinated and coordinated environments

Rekik et al (2007) study supply chains subject tomisplacement under a wholesale price contract andfind a sufficient condition on the tag price to make theparties adopt RFID technology under normal demanddistribution when no fixed cost of investment isconsidered Further they numerically quantify thebenefits gained through RFID adoption vs coordina-tion of the supply chain In this paper we explicitlyconsider the fixed cost of technology investment andshow that the incentives of the parties to adopt thetechnology are completely characterized by a maxi-mum of three regions based on relative payments ofparties Additionally rather than searching for suffi-cient conditions for the parties to invest in the tech-nology we are particularly interested in analytically



















Z x

0


g


eth1THORN













and QC frac14



LEMMA 1













THEOREM 1














1000

2000

3000

4000

5000

6000

QCRF

QCRF

QC

QC

500

1000

1500

2000

a~

















t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases













Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References




























































Z x

0


g


eth1THORN













and QC frac14



LEMMA 1













THEOREM 1














1000

2000

3000

4000

5000

6000

QCRF

QCRF

QC

QC

500

1000

1500

2000

a~

















t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases













Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References



















































Z x

0


g


eth1THORN













and QC frac14



LEMMA 1













THEOREM 1














1000

2000

3000

4000

5000

6000

QCRF

QCRF

QC

QC

500

1000

1500

2000

a~

















t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases













Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References













































THEOREM 1














1000

2000

3000

4000

5000

6000

QCRF

QCRF

QC

QC

500

1000

1500

2000

a~

















t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases













Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References
























































t0 t2 t3 t1

decreasesQC

QCRF

Incentive

decreases

decreases

increases

increases













Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References



















































Z 1aQD


eth3THORN







eth4THORN


eth5THORN







wD frac141

4


eth6THORN



o1 eth7THORN











eth10THORN






DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References














































DRFj) and


DRFj) where i jAR M

















1 tDR tDMot1

2

tDR is


8gtltgt


3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References











































3 Given KDRKDM40

KDR is


8gtltgt


KDM=ao0


Ct

DRTHORN

a o0ethK

CKDRTHORNa o0


Ct

DMTHORN

a

o0ethK

CKDMTHORNa o0







tDR

tDR = tDM

tDM





in RFID


in RFID

t0

Dθθ gt

tDRtDM



Onlythe retailer


in RFID


in RFID

t0

Dθθ lt




in RFID

t0

Dθθ =



















aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References



























































aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References














































aQRS



0


gR

Z 1aQRS


eth11THORN


pethmthornZ 1

aQRS



0


gM

Z 1aQRS


eth12THORN






thorn s

Z x

0




pethmthornZ 1


Z x

0


gM




















and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References













































and the man-









RSMg is always








Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References













































Z x

0


g


eth17THORN








Centralized firm















frac14 c sthorn t







KDM=y40











KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References




















































KRSM=y40

Incentive = 0



θ

t

03

025

02015

01

minus250000

500000

0

250000

1

07505

0250

(a)




t

03

025

02

01501

minus500000

500000

0

1075

05025

0(b)


03

10

t

D1θ

0 1θ

(c)

Normal [ 2]

03

01

t

0 1θ


D2θ

(d)

Exponential []




tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References












































tRSM=go0 KRSM=go0














Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References













































Appendix A

THEOREM 1


pwhere


a2b40

KC frac14u1u2b



LEMMA 2



KDM frac14u1u2b





p


p





=a240



pand


pwhere

























pthorn gC s

eth26THORN

where







References

























































pthorn gC s

eth26THORN

where







References






























































Date post:	08-Mar-2018
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Misplaced Inventory and Radio-Frequency Identiﬁcation (RFID) Technology: Information...

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