Unversty of Massachusetts Boston ScholarWorks at UMass Boston Management Scence and Informaton Systems Faculty Publcaton Seres Management Scence and Informaton Systems January 2015 as Theory Suggests? An Emprcal Evaluaton Ehsan Elah UMASS Boston, ehsan.elah@umb.edu Roger Blake UMASS Boston, roger.blake@umb.edu Follow ths and addtonal works at: http://scholarworks.umb.edu/mss_faculty_pubs Part of the Management Scences and Quanttatve Methods Commons, and the Operatons and Supply Chan Management Commons Recommended Ctaton Elah, Ehsan and Blake, Roger, " as Theory Suggests? An Emprcal Evaluaton" (2015). Management Scence and Informaton Systems Faculty Publcaton Seres. Paper 52. http://scholarworks.umb.edu/mss_faculty_pubs/52 Ths Artcle s brought to you for free and open access by the Management Scence and Informaton Systems at ScholarWorks at UMass Boston. It has been accepted for ncluson n Management Scence and Informaton Systems Faculty Publcaton Seres by an authorzed admnstrator of ScholarWorks at UMass Boston. For more nformaton, please contact lbrary.uasc@umb.edu.
as Theory Suggests? An Emprcal Evaluaton Ehsan Elah Unversty of Massachusetts Boston ehsan.elah@umb.edu Roger Blake Unversty of Massachusetts Boston roger.blake@umb.edu ABSTRACT Ths research compares results from laboratory experments wth predctons from theory for decsons made by competng supplers. We consder a supply chan n whch a sngle buyer outsources the manufacture of a commodty product to supplers not on the bass of prce, but rather on servce. Three dfferent crtera on whch supplers compete are evaluated: 1) a guaranteed specfc nventory fll-rate, 2) guaranteed level of base-stock, and 3) a parameter optmzng the supply chan n the buyer s favor. Our results show that n most cases, supplers decsons are sgnfcantly dfferent than the ash equlbrum, meanng that they do not maxmze proft. We examne loss averson as an nfluence that mght offer an explanaton for ths behavor KEYWORDS: Behavoral Operatons Management, Servce Operatons; Supply Chan Contracts and Incentves, Outsourcng, Cognton and Reasonng, Laboratory experments ITRODUCTIO The mportance of outsourcng s wdely accepted both n academa and by practtoners. Outsourcng, among other benefts, lets companes focus on ther core competences and be more flexble n an ncreasngly compettve and volatle busness world. What s stll debatable among the experts s how outsourcng can be done most effectvely. The tradtonal approach s to negotate the contract terms wth the supplers. Some buyers then add ncentves such as revenue sharng, or monetary rewards and penaltes, based on the qualty of servce they receve. Another approach, whch can reduce negotaton efforts, s to let supplers compete for the buyer s busness. Many researchers have studed these forms of outsourcng confguratons. However, although wdely studed, exstng models and theoretcal results have rarely been subjected to emprcal verfcaton, and to our knowledge has never been done for the outsourcng model we consder. In ths research, we use laboratory experments to nvestgate whether decsons made by subjects playng the role of competng supplers wll match theoretcal predctons. The theoretcal bass on whch ths comparson s based from work by Elah (2013), who provdes results for dfferent types of competton for outsourcng setups. The model from that study utlzed a stylzed queung model to analyze decsons of make-to-stock supplers competng for demand share from a buyer usng several dfferent performance measures (crtera) to allocate demand. Our study s based on a smlar model, and we also evaluate dfferent crtera for demand allocaton.
We consder cases wth three dfferent crtera used by the buyer to allocate demand. In the frst, the buyer allocates demand to each suppler proportonally a servce level, as measured by nventory fll rate, the suppler guarantees wth respect to other supplers. We term ths type of competton a servce competton. Each suppler can ncrease the demand share they wll receve by provdng a hgher servce level than the competng supplers. Dependng on the decsons other supplers make, a suppler offerng a hgher servce level wll a larger share of the buyer s busness, but at the same tme also ncur hgher costs. In the second crtera the buyer allocates demand proportonally to the base-stock level a suppler guarantees to mantan on hand. Ths s termed an nventory competton, and the dynamcs of demand allocaton and suppler costs are smlar to a servce competton. In the thrd type of competton, the buyer allocates demand usng a parameter desgned to ntensfy the competton to a level at whch each suppler wll be nduced to offer the hghest feasble level of servce, even to the pont where the suppler has no profts. Because ths crtera optmzes the supply chan n favor of the buyer, we term ths an optmal competton. The parameter on whch an optmal competton s based s a combnaton of servce level, nventory level, and the supplers cost functons. Although ths parameter s more complcated than the crtera for servce or nventory compettons, ths type of competton can produce the best results for the buyer and can have mportant mplcatons n practce. Our analyss uses data gathered from experments to determne whether subjects decsons converge at predcted ash equlbrum n the three above mentoned types of competton. To ncrease the robustness of our study, scenaros n whch supplers have dssmlar cost structures the expermental desgn also part of the expermental desgn. Our results show that subjects decsons do not necessarly converge to the ash equlbrum. Wth two of the three types of competton, servce and nventory compettons, subjects decsons are usually hgher than the ash equlbrum. Under the thrd, the optmal competton, subjects decsons are usually lower than the ash equlbrum. Although, subjects cannot generally capture the theoretcal ash equlbrum, expermental results show that as theory predcts, subjects exert more efforts and are closer to the ash equlbrum under optmal competton than when n nventory or servce compettons. However, n many cases there are sgnfcant dfferences between supplers decsons and what s predcted by theory. We also evaluate nsghts to explan these devatons from the ash equlbrum and proft maxmzaton. We show that subjects loss averson can offer an explanaton for the optmal compettons, especally f the competng supplers have dentcal cost structures. Fndng that supplers do not make decsons that maxmze profts, and therefore do not behave ratonally from an economc standpont, has sgnfcant practcal mplcatons. We are specfcally nterested n the cases where supplers n an optmal competton do not act as theory promses, because the results have mportant mplcatons for how buyers should structure ther crtera for outsourcng among supplers n practce. In the remander of ths paper we frst brefly revew related lterature before descrbng the theoretcal development of our supply chan model and the ash equlbrum that predcts what the results of our experments should be. From that we draw our hypotheses, and then present our expermental desgn followed by our results. Fnally, a dscusson of those results leads to our conclusons. LITERATURE REVIEW
Whle not evaluated emprcally, others have modeled outsourcng problems through forms of servce-based competton n studes whch have consderable parallels to ours. Another paper that models outsourcng through effort-based competton s by Cachon and Zhang (2007). These authors model the competton between two dentcal make-to-order supplers who supply to a sngle buyer. The buyer allocates the demand to the supplers based on ther processng rates, and the authors show the mpact of dfferent allocaton schemes; n ther model, the buyer s objectve s to maxmze the servce level provded by the supplers. They show the form of a lnear allocaton functon that can produce the best results for the buyer. Glbert and Weng (1998) model a prncpal who allocates demand to two competng agents (servce facltes). The dentcal agents decde on the cost of ther servce rates to attract more demand shares. The prncpal ether allocates the demand to the agents from a sngle queue or from separate queues (equal expected watng tmes). They show the condtons whch one allocaton mght be superor to the other one. Ha et al. (2003) model two supplers who compete for supply to a customer wth determnstc demand. When the dentcal supplers compete based on delvery frequency, the authors (usng an EOQ model) show an allocaton scheme that mnmzes the customer s nventory cost. Jn and Ryan (2012) model two dentcal make-tostock supplers who compete based on both prce and servce level (fll rate) for demand shares of a sngle buyer. The buyer uses an allocaton functon n whch the allocated demand s proportonal to an exponental functon. Ths allocaton functon s characterzed by a parameter that shows the relatve mportance of prce versus servce level. The authors show the optmal value of ths parameter, whch mnmzes the buyer s cost. Ther model uses several of the same assumptons as we do for ours, albet for a dfferent applcaton than outsourcng. Benjaafar et al. (2007) compare two competton mechansms: suppler allocaton (SA) and suppler selecton (SS). In a suppler allocaton (SA) mechansm, each suppler receves a share of the buyer s demand whch ncreases wth the servce level that suppler provdes. In a suppler selecton (SS) mechansm, the buyer selects only one suppler to receve the entre demand. The probablty of a suppler beng selected ncreases by the servce level provded. They show SS can result n hgher servce levels. In addton to servce level, Benjaafar et al. (2007) ntroduced another competton parameter. The authors show a reformulaton of ther problem n whch they choose the demandndependent component of the servce cost (whch they name suppler s effort) as the competton parameter. They show that when the demand s allocated proportonal to a power functon of ths competton parameter, suppler servce level can be maxmzed. The authors acknowledge that the servce-based and effort-based compettons can lead to dfferent equlbrum servce levels. However, they do not actually compare the two types of compettons. In other works, Elah (2007) shows an optmal form of allocaton functon for a servce-based competton whch can result n maxmum feasble servce level for the buyer. A revew of servce-based outsourcng can be found n Zhou and Ren (2010). Elah (2013) models an outsourcng problem n whch make-to-stock supplers compete for the demand share of a sngle buyer. In that study the author consders compettons n whch supplers competton when the buyer s demand s allocated proportonal to a competton crteron (competton parameter). Elah focuses on the mpact of the dfferent competton crtera, and t s from ths work that we derve our model of supply chan outsourcng.
Our expermental results suggest a smlar behavor under servce and nventory competton. That s, when the supplers are heterogeneous, the sum of subjects decsons s hgher than what theory predcts. The lterature on expermental studes of rent seekng s not lmted to what s mentoned here. A comprehensve revew of ths lterature, however, s beyond the scope of ths paper. A more detaled revew of expermental studes on rent-seekng can be found n Houser and Stratmann (2012). There have been few studes to emprcally valdate these models. The only expermental paper n the supply chan lterature to evaluate smultaneous competton between decson makers that has smlarty to ours s by Chen et al. (2012). Ther study was of competton between retalers (buyers) for the lmted capacty of a common suppler (seller). It found that the subjects average order s much less than what ash equlbrum predcts, and they attrbute ths behavor to subjects bounded ratonalty (random errors). The Quantal Response Equlbrum s used to ncorporate random errors n subjects decsons. Smlarly to Chen et al., we model the smultaneous competton between decson makers and compare expermental results wth the ash equlbrum. We also explore reasons for these dfferences. However, our model consders the competton between supplers (sellers) for the lmted demand of a buyer. Moreover, our competton crtera s dfferent from those used by Chen et al., and we fnd addtonal nfluences that may account for the dfferences between theory and expermental results. THEORETICAL BACKGROUD In ths secton, we descrbe our supply chan model and present the theoretcal formulaton of the competton setup for our experments. We also show the ash equlbrum decsons for dfferent types of competton we consder n ths research. The supply chan setup n ths paper follows the setup presented n Elah (2013). The proofs of all the results of ths secton can also be found n ths reference. We consder the case of a sngle buyer who s outsourcng the producton of a product among potental supplers. Supplers manufacture ths product n a make-to-stock fashon accordng to a base-stock nventory polcy. Demand from the buyer s generated accordng to a Posson process wth rate λ, wth the fracton of demand allocated to suppler denoted by δ, where 0 < δ < 1 and =1. Accordngly, demand generated by the buyer arrves at each suppler wth a rate of δ λ. The varable δ can be vewed as the probablty that ongong demand s allocated to suppler ; n aggregate, ths translates to the market share awarded to the suppler. The supplers producton tmes are exponentally dstrbuted wth the rate µ, and n response to demand from the buyer, supplers adjust ther capacty (producton rate) to mantan a fxed target utlzaton ρ where ρ = δ λ / µ and 0 < ρ < 1 for suppler. Hence, for each suppler the producton system can be modeled as an M/M/1 queung system. The assumptons of Posson arrval and exponental processng tmes, n addton to beng plausble n many practcal cases, are common practce n ths feld snce they make the dervatons mathematcally tractable (see for nstance Glbert and Weng, 1998; Cachon and Zhang, 2007; Benjaafar et al. 2007). Fnshed goods at the supplers are managed accordng to a base-stock polcy wth base-stock level z (z >0) at suppler. Ths means that the arrval of demand at suppler always trggers a
replenshment order wth the suppler s producton system. Supplers ncur the nventory holdng cost. That s, each suppler ncurs a holdng cost h per unt of nventory per unt tme. Moreover, each suppler ncurs a producton cost c per unt produced, and a capacty cost k appled per unt of capacty (measured n terms of the assocated producton rate). The revenue for each suppler s based on the demand they are allocated and the prce of the product, p per unt, at whch the buyer procures t. We assume that ths prce s the same across all supplers. Ths can be the case when the buyer s powerful enough to set the prce, or when market mechansms set the prce (the case of a commodty product for nstance). Ths assumpton means the competton s based on crtera other than prce. When a suppler cannot fulfll the buyer s demand from on-hand nventory, we assume the buyer wll wat untl the suppler produces the backordered unts. We exclude the possblty of the buyer swtchng to another suppler. We also exclude the possblty of the buyer procurng the product from a suppler outsde of the pool of competng supplers, assumng that the product s not readly avalable n the market. The assumpton of backorderng the demand when t cannot be satsfed from on-hand nventory s consstent wth the assumptons n earler papers such as Cachon and Zhang (2007) and Benjaafar et al. (2007). etessne et al. (2006) also use ths assumpton n studyng the mpact of customers backorderng behavor on the performance of competng frms n a market. The assumpton of backorderng the unfulflled demand s partcularly essental n our competton model, snce swtchng to another suppler volates the demand allocaton rule, whch s (as we wll dscuss below) the bass of the competton. Backordered demand s costly for the buyer. It mght lead to delayed delvery or ncomplete orders shpped to the buyer s own customers. Backorders can also negatvely affect the buyer s producton system, whch are possbly accentuated f a just-n-tme system s used. Therefore, the buyer measures each suppler s servce level n terms of fll rate, s = Pr(I > 0). That s, the probablty that a unt demand allocated to a suppler s not backordered and can be fulflled mmedately from on-hand nventory (I s the nventory level at suppler ). Hence, the buyer s objectve s to maxmze the average servce level receved from supplers, q = δ 1 s =. (1) Maxmzng the average servce level s equvalent to mnmzng the probablty of backorders from the supplers, whch n turn means lower costs such as from mssng schedules for the buyer. The product beng outsourced s a commodty product; as such the buyer seeks to encourage supplers to provde the hghest level of servce. For ths, the buyer specfes a performance measure on whch demand wll be allocated to supplers. The buyer announces ths performance measure as the crtera for demand allocaton before the competton starts. The supplers then smultaneously commt to a level of the announced performance measure. As descrbed earler, we examne three dfferent types of performance measures, a servce competton for whch demand s allocated accordng to guaranteed fll rates, an nventory competton wth demand allocated accordng to guaranteed base-stock, and an optmal competton wth demand allocated usng a measure that combnes the measures for both servce and nventory compettons. We next offer the detals for each of these performance measures.
In a servce competton, each suppler s awarded a demand share proportonal to the fll rate S the suppler guarantees. The buyer uses a proportonal allocaton functon α ( s, s ) whch specfes the fracton of demand allocated to suppler based on the fll rate s and the fll rates s = ( s,..., s, s,..., s ) offered by suppler s compettors. Stated dfferently, 1 1 + 1 s S = ( s, s ) = s j= 1 j (2) δ α In an nventory competton, a suppler s demand share depends on the base-stock level the suppler wll assure the buyer. In ths type of competton, the buyer uses a proportonal I allocaton functon α ( z, z ) whch specfes the fracton of demand allocated to suppler based on that base-stock level z and the base-stock levels z = ( z1,..., z 1, z+ 1,..., z ) offered by suppler s compettors, whch means I z δ = α ( z, z ) =. (3) z For an optmal competton the buyer s demand s allocated accordng to a performance measure, ξ, that s a combnaton of fll rate and base-stock level: j= 1 1 h ρ ξ = z s λ( p c k / ρ ) 1 ρ j 1. (4) Therefore, the demand share allocated to suppler n an optmal competton wll be: O ξ α ( ξ, ξ ) =. (5) ξ Ths type of competton can nduce the maxmum feasble servce level for a buyer (supplers are bound to provde a postve servce level as a partcpaton condton under ths type of competton). The performance measure defned n (4) s more complcated and less ntutve than drect measures lke fll rate or base-stock level. It s, n fact, an abstract measure that can set the shape of the proft functon such that the competton equlbrum pont occurs when each suppler exerts the maxmum effort. In other words, ths performance measure can ntensfy the competton to ts maxmum level, where each suppler spends all ther revenue (and zeroes out proft) to provde the maxmum feasble level of ξ. ote that n the defnton of ths performance measure, z and s are nterdependent parameters (s = 1 - ρ z ). It s not very dffcult to show that ξ s an ncreasng functon of ether s or z. Therefore, when a suppler guarantees the maxmum feasble level of ξ, t means that t guarantees the maxmum feasble servce level for the buyer, as well. Elah (2013) shows a general form of the performance measure for optmal competton that has the ablty to nduce any predefned set of demand shares at the competton equlbrum. The specfc form shown n (4) nduces dentcal demand shares for all supplers (δ = 1/). Ths s an ntutve selecton when the supplers are dentcal. The buyer may also decde to allocate equal demand shares to heterogeneous supplers to mnmze the rsk of relyng on a specfc suppler The supplers proft functons for each the servce, nventory, and optmal compettons, respectvely are: j= 1 j
S ln(1 ) (, ) S s (, ) ( / ) ρ I I π s s = α s s λ p c k ρ h s, (6) π ( z, z ) = α ( ln ρ 1 ρ 1 O O λ( p c k / ρ ) (, ) (, ) ( / ) ( ) p c k π ξ ξ = α ξ ξ λ ρ ξ. (8) Ths formulaton of the problem assumes (a) the buyer can enforce the fll rates or base-stock levels chosen by the supplers, (b) supplers cost structures are common knowledge (a complete nformaton setup), and (c) supplers partcpate n the competton as long as they can earn a non-negatve expected proft. These three forms of competton have unque ash equlbrums. For the case of dentcal supplers, these equlbrum ponts can be found from: Servce Competton s * S 1 λ( p c k / ρ) 1 ρ h * (1 ss ) ln(1/ ρ) 1 ρ = 2 (9) Inventory Competton Optmal Competton z 1 λ( p c k / ρ) * I = 2 * zi + 1 ρ 1 h 1 ln 1 ρ ρ * 1 O (10) ξ = (11) Our hypotheses are based on the supply chan model and crtera on whch supplers compete as descrbed. HYPOTHESES Game theoretc models predct that ratonal player make decsons accordng to ash equlbrum. Our frst three man hypotheses are that subjects average decsons wll be equal to the correspondng ash equlbrum for the suppler cost structures (dentcal or non-dentcal) and types of competton that we are studyng. Each man hypothess relates to one of the cost structures and conssts of three sub-hypotheses related to one of the three types of compettons. Hypothess 1 states that supplers wth dentcal cost structures wll make decsons equal to the ash equlbrum and has three sub-hypotheses: Hypothess 1a: Supplers wth dentcal cost structures wll make decsons equal to the ash equlbrum when competng based on guaranteed servce levels (nventory fllrates). Hypothess 1b: Supplers wth dentcal cost structures wll make decsons equal to the ash equlbrum when competng based on guaranteed base stock nventory levels.
Hypothess 1c: Supplers wth dentcal cost structures wll make decsons equal to the ash equlbrum when competng based on the parameter desgned to optmze the supply chan n favor of the buyer. Hypothess 2 states that supplers wll make decsons equal to the ash equlbrum when they have heterogeneous cost structures wth one suppler havng a hgher producton cost, and t has three sub-hypotheses: Hypothess 2a: Supplers wth heterogeneous producton costs wll make decsons equal to the ash equlbrum when competng based on guaranteed servce levels (nventory fll-rates). Hypothess 2b: Supplers wth heterogeneous producton costs wll make decsons equal to the ash equlbrum when competng based on guaranteed base stock nventory levels. Hypothess 2c: Supplers wth heterogeneous producton costs wll make decsons equal to the ash equlbrum when competng based on the parameter desgned to optmze the supply chan n favor of the buyer. Hypothess 3 states that supplers wll make decsons equal to the ash equlbrum when they have heterogeneous cost structures wth one suppler havng hgher nventory holdng costs, and t has three sub-hypotheses: Hypothess 3a: Supplers wth heterogeneous nventory holdng costs wll make decsons equal to the ash equlbrum when competng based on guaranteed servce levels (nventory fll-rates). Hypothess 3b: Supplers wth heterogeneous nventory holdng costs wll make decsons equal to the ash equlbrum when competng based on guaranteed base stock nventory levels. Hypothess 3c: Supplers wth heterogeneous nventory holdng costs wll make decsons equal to the ash equlbrum when competng based on the parameter desgned to optmze the supply chan n favor of the buyer. EXPERIMETAL DESIG To test these hypotheses and nvestgate how decson makers wll perform under dfferent types of compettons and cost structures, we conducted a seres of experments usng nne dfferent treatments. These conssted of three treatments for each of the servce, nventory, and optmal compettons. For each type of competton, a sngle treatment was used for supplers wth dentcal cost structures, and two treatments were used for heterogeneous costs. The heterogenety n cost structure was mplemented as ether dfferent producton costs or dfferent nventory holdng costs. In all experments the buyer s demand was assumed to arrve at a rate of λ and the prce of the product, p, to be 100. The supplers ncurred a capacty cost of k = 5 per unt product per unt tme to adjust ther capacty and keep ther utlzaton at ρ = 0.93. When the supplers had dentcal cost structures, ther producton costs and nventory holdng costs were the same, wth c 1 = c 2 = 20 and h 1 = h 2 = 1, respectvely. For experments wth heterogeneous producton costs
the values c 1 = 20 and c 2 = were used for producton coasts. For heterogeneous nventory holdng costs, the values h 1 = 1 and h 2 = 2 were ncorporated. We delberately chose a relatvely large dfference between the producton costs and nventory holdng costs so that the extent of an mpact from heterogenety would be more clearly evdent. Subjects n our experments assumed the role of competng supplers wth the overall goal of maxmzng profts. Each experment conssted of 30 ndependent rounds n whch a decson needed to be made. In order to maxmze profts, the subjects needed to consder how the buyer wll allocate demand as well as possble decsons ther compettors mght make. Under all forms of competton the decsons subjects made were n the form of base-stock levels. It was mentoned earler that there s a one-to-one correspondence between dfferent performance measures. Therefore, when a subject selects a certan level of base-stock, the values of fll rate and optmal performance measure are also set. Subjects decsons were expressed n the form of base-stock levels n all forms of competton because t s the only measure that s drectly operatonal. For nstance, a suppler cannot drectly set a guaranteed fll rate n practce by choosng a base-stock level that assures the desred fll rate. The subjects for all of our experments were students at a large unversty located n the ortheast Unted States. The nstructors of selected courses allowed us to run the experments durng ther class tmes as a requred class actvty. To provde ncentve for students to focus on maxmzng profts durng the experment, we presented each experment as a contest through whch the students could fnd out how good they were at makng decsons under an uncertan compettve envronment. In addton, we offered cash przes ($40, $30, and $20) to the three students havng the hghest total profts after 30 rounds of decson-makng. We conducted the experments n a mx of graduate and undergraduate classes. Past expermental research n operatons management has found that decsons made by undergraduate and graduate students are not statstcally dfferent. See, for nstance, Katok and Wu (2009) and Elah (2013). Snce the calculaton of a suppler s proft could be complcated, the experment software provded an nteractve calculaton tool. Ths tool, whch was avalable throughout the experments, enabled subjects to enter a prospectve decson and see ther profts as a functon of the full range of decsons a compettor could make. The appendx shows the user-nterface ncludng the calculaton tool. A strct protocol was followed for conductng all experments. At the start of each experment sesson, subjects were asked to read a two-page handout descrbng the supply chan setup and the decson-makng process for the competton. The content of the handout and a short demonstraton of the experment software was presented orally next. Ths presentaton was followed by answerng any questons that subjects mght have. The next step n our protocol was to let subjects work wth the software and, n partcular, examne the calculaton tool. After subjects were famlar wth the software and had a sense of how ther decsons, n combnaton wth potental decsons by ther compettors, would affect ther profts, we had subjects compete n a 5-round practce sesson. Wth any remanng questons answered, we proceeded to start the actual competton. Durng the frst 10 rounds of competton, the subjects had 75 seconds to make a decson. Pre-testng showed that after 10 rounds subjects had grasped the competton and no longer needed as much tme. We therefore reduced the tme lmt to 45 seconds for each of the remanng rounds.
After all subjects had entered a decson or the tme lmt had expred, a round would end. The software then pared subjects as compettors randomly (any subject not makng a decson was not pared and assgned a proft of zero). Wth decsons and compettors assgned, the software calculated each subject s share of demand and proft, along wth ther compettor s share and proft. These results, alongsde the total proft the subject had accumulated, were dsplayed on the screen. At that pont, the next round of the competton was begun. See Appendx A for a sample screenshot of the user nterface durng a competton. Before the compettons started for experments nvolvng treatments wth heterogeneous supplers, the software randomly dvded subjects nto one of two sets. One set was assgned a hgher cost than the other for ether c or h, dependng on the partcular experment. We then apprsed all subjects of whch set they were assgned to and that those wth hgher costs could expect lower profts than ther compettors. Subjects were also made aware that, at the end of experments, we would normalze all subjects profts wth respect to ther costs; hence, everyone had a far chance of wnnng the prze money. RESULTS Tables 1 and 2 show the results of our experments as well as the correspondng theoretcal ash equlbrum for dentcal and heterogeneous supplers, respectvely. To analyze the results of our experments we use Wlcoxon rank sum test (Levne et al. 2011, pp. 447-451). The unt of our analyss s the average base-stock decson made by each subject, and the column of p- values n each table show where the dfferences between our results and the ash equlbrum are statstcally sgnfcant. As shown n Table 1, there are sgnfcant dfferences between supplers decsons and the ash equlbrum for all cases n whch supplers have dentcal cost structures. ote that we consder each of the subjects n our experments as a sngle sample, and that for our statstcal analyss we are usng the average of 30 decsons made by each subject, rather than the values of the ndvdual decsons made by each subject for each of 30 rounds. In other words, the analyss shown n Table 1 s based on data from decsons made by a total of 47 subjects over 30 rounds of decson-makng. Table 1: Subjects average decsons vs. ash equlbrum (Supplers wth dentcal costs) Base-stock Level Competton Type Sample Sze ash Equlbrum Expermental Results p-value (two tal) Servce 13 19 24 <0.01 Inventory 12 34 54 <0.01 Optmal 22 77 68 <0.01 Based on these results we reject Hypothess 1 and each of ts three sub-hypotheses, fndng that supplers wth dentcal cost structures wll make decsons sgnfcantly dfferent from the ash equlbrum for all three types of competton. Ths fndng does not always hold for competng supplers wth heterogeneous cost structures, and Table 2 dsplays the results wth a set of columns for each of the two supplers desgnated as Suppler 1 and Suppler 2. ote that Suppler 1 s the lower cost suppler and Suppler 2 the suppler wth hgher costs.
Table 2: Subjects average decsons vs. ash equlbrum (Supplers wth heterogeneous costs) Suppler 1 Base-Stock Level Suppler 2 Base-Stock Level Competton Type Sample Sze ash Expermental Results p-value (two taled) ash Expermental Results p-value (two taled) Heterogeneous Supplers wth dfferent producton costs (c 1 =20, c 2 =) Servce 18 19 19 >0.05 13 15 >0.05 Inventory 24 32 41 0.02 18 26 0.04 Optmal 28 77 51 <0.01 42 43 >0.05 Heterogeneous Supplers wth dfferent nventory holdng costs (h 1 =1, h 2 =2) Servce 17 19 21 >0.05 14 19 <0.01 Inventory 25 33 36 0.04 19 34 <0.01 Optmal 27 77 58 <0.01 44 51 0.01 Ths table shows results vary by the type of competton. In partcular, three of the four cases of servce competton shown no sgnfcant dfferences between supplers decsons and the ash equlbrum. Wth no sgnfcant dfferences for supplers wth heterogeneous producton costs, and for one of the two wth heterogeneous nventory holdng costs, we accept Hypotheses 2a and 3a. For nventory compettons there are sgnfcant dfferences between subjects decsons and the ash equlbrum for all cases. Ths s true whether a suppler has the hgher or the lower costs, and whether the dfference was n producton costs or nventory holdng costs. We therefore reject Hypotheses 2b and 3b and conclude the decsons do not match the ash equlbrum. For optmal compettons there are sgnfcant dfferences for cases n whch supplers have heterogeneous nventory holdng costs, but only one of the two cases, whch s for the more effcent low cost suppler. We therefore can reject Hypothess 3c. Although the results for the hgher-cost suppler dd dffer sgnfcantly from the ash equlbrum, we can also reject Hypothess 3b based on the results for the more effcent low-cost suppler. These are somewhat mxed results and a topcs explored n the dscusson secton. We see that the subjects average decsons are smaller than the correspondng ash equlbrum when the supplers have dentcal cost structures. We can observe the same behavor for the subjects who play the role of more effcent suppler (Suppler 1), when the supplers are not dentcal. The subjects who played the role of less effcent suppler (Suppler 2), however, do not follow ths pattern. Under the optmal competton, all the dfferences are sgnfcant except for the less effcent suppler when the producton costs are dfferent. Therefore, we can reject Hypotheses 3a and 3c. DISCUSSIO The results of our experments suggest that the assumpton of perfectly ratonal decsonmakers, an assumpton on whch the ash equlbrum s based, does not necessarly hold for the outsourcng compettons studed n ths research. Behavoral factors can nfluence decsonmakng and offer an explanaton of why subjects dd not reach the hghest level of potental profts. Whle other factors could also be n play, we examne how loss averson can be a behavoral nfluence and explanaton why competng supplers dd not maxmze profts as theory suggests.
Loss Averson Our results show that n compettons based on both servce and nventory crtera, subjects playng the role of supplers wth dentcal costs wll always reach stablty wth decsons sgnfcantly dfferent that the ash equlbrum ponts. However, when engaged n an optmal competton we do not see ths pattern. Subjects average decsons, under optmal competton, are smaller than the correspondng ash equlbrum, except for the less effcent suppler n the cases where the supplers have heterogeneous costs. To gan nsght nto ths behavor we frst look at a suppler s proft functon wth respect to the potental decsons that could made by compettors. Ths s because the share of demand allocated to a suppler depends on the decsons made by both the suppler and the suppler s compettors. More specfcally, we look at a suppler s proft when ther compettor chooses ether the ash equlbrum as ther decson as well as chooses the average decson observed n our experments. Fgures 1 to 3 show these proft functons. The curves n these fgures wth the sold lnes show a suppler s expected proft for dfferent decsons gven that the compettor s decson s at the ash equlbrum value. The curves wth a dashed lne represent the suppler s expected proft when a compettor s decson s the average of the decsons we observed n our experments. From these fgures t can be seen that the rate of change n a suppler s proft near ts maxmum pont s much steeper for a servce competton than ether for an nventory or optmal competton. In other words, any devaton from the optmal decson s more costly for supplers n a servce competton n any other type. Ths observaton mght explan the gap between subjects decsons and the correspondng ash equlbrum ponts n servce compettons and why t s (almost always) smaller than the dfference observed n ether nventory or optmal compettons. The fgures also show that n servce compettons wth heterogeneous supplers wth dfferent producton costs, subjects manage to (statstcally) capture the ash equlbrum. Ths s also the case for the more effcent suppler n servce compettons where supplers have dfferent nventory holdng costs. Ths can mean that, although an optmal competton can produce the best results for the buyer, t s dffcult for subjects to capture the best decsons n an optmal competton due to the relatvely flat proft functons around the decson whch maxmzes proft. The opposte s true for the servce competton, n whch the buyer receves a lower servce level because subjects are able to reach the pont where profts maxmzed. The fgures also show that f a suppler s compettor chooses the ash equlbrum as ther decson n an optmal competton (ndcated by z 2 = 77 n the rghtmost chart of Fgure 1), then any devaton the suppler makes other than matchng the compettor s decson wll produce a negatve proft. Ths means that subjects loss averson can play an mportant role when engaged n ths type of competton. When the supplers have dentcal costs n an optmal competton, the only way supplers can earn a postve proft s when both supplers decsons are lower than the ash equlbrum. Although ths s not an equlbrum condton, any movement away from t can result n a negatve proft, and ths s exactly subjects behavor n our experments. Instead of attemptng to make decsons that would yeld the maxmum profts, they appear to have made decsons that would avod recevng profts that were negatve.
Fgure 1: Proft functons for supplers wth dentcal cost structures Servce Competton Inventory Competton Optmal Competton 40 20 0-20 z 2=19 40 20 z 2=34 z 2=24 0 z 2=54 0 z 2=77-20 -20 0 20 40 80 100 0 20 40 80 100 0 20 40 80 100 z 1 z 1 z 1 ash Equlbrum (sold lnes) Expermental Results (dashed lnes) 40 20 z 2=68 Fgure 2: Proft functons for supplers wth heterogeneous costs dfferent capacty costs (c) 45 30 15 Servce Competton Proft 1 0 Proft 2 (ash & Exper.) -15 0 20 40 80 100 45 30 15 0-15 Inventory Competton Proft 1 Proft 2 0 20 40 80 100 45 30 15 0-15 Optmal Competton Proft 2 Proft 1 0 20 40 80 100 z 1 or z 2 ash Equlbrum (sold lnes) z 1 or z 2 z 1 or z 2 Expermental Results (dashed lnes) Fgure 3: Proft functons for supplers wth heterogeneous costs - dfferent holdng costs (h) 45 Servce Competton 45 Inventory Competton Proft 1 80 Optmal Competton 30 15 0-15 Proft 2 (ash & Exper.) 0 20 40 80 100 z 1 or z 2 Proft 1 30 15 0-15 0 20 40 80 100 ash Equlbrum (sold lnes) z 1 or z 2 Proft 2 40 20 0-20 Proft 2 0 20 40 80 100 z 1 or z 2 Proft 1 Expermental Results (dashed lnes)
COCLUSIOS Ths research contrbutes by examnng theoretcal results appled to a model of outsourcng derved from pror work, and evaluates the theores n an expermental study. For ths we conducted experments wth three types of competton between supplers: servce, nventory, and optmal. In each type of competton supplers would compete for a sngle buyer s demand allocated based on a measure of performance (competton crtera) defned and announced by the buyer pror to the start of compettons. Our expermental results show that the actual decsons competng supplers make do not always match the decsons predcted by the ash equlbrum. They show that the actual decsons are closest to the ash equlbrum value n servce compettons; n compettons based on the nventory and optmal crtera the dfferences are more pronounced. In most cases there are statstcally sgnfcant dfferences between the actual decsons and theoretcal predctons. The devaton of subjects decsons from the ash equlbrum ndcates that subjects do not always behave purely n a ratonal way as the ash equlbrum assumes. A ratonal decson maker always ams to fnd the decson that wll maxmze expected proft. When decsons devate from the ash equlbrum value there mght be behavoral nfluences that nduce decsons that do not maxmze proft. We therefore nvestgated reasons why subjects dd not, or could not, maxmze profts (.e. reach the ash equlbrum). In part, these devatons from theory can be accounted for by loss averson behavor. Our supply chan model has mportant smlartes to supply chans n the real world. Showng that the decsons that competng supplers make do not always maxmze profts, as theory predcts, s one mportant result from our study. Evaluatng a behavoral nfluence as a potental explanaton for ths behavor s another mportant contrbuton. The fndngs from our study can be useful for buyers to determne the best means by whch to award contracts, and for supplers who need to understand potental nfluences that can lead decsons away from maxmzng profts. Exstng theory as t relates to the supply chan model we study has not yet been valdated expermentally. Wthn the context of ths model we compare actual decsons wth theory by usng experments that nvolved dfferent forms of competton and varyng cost and ndustry structures. Further research could nvestgate addtonal scenaros and further generalze the fndngs from our study. In partcular, for ths study we could only conduct a lmted number of experments and therefore use a relatvely small set of parameters for supplers cost structures. We explored scenaros nvolvng only two supplers, and our model s based on specfc assumptons, such how demand s generated. Relaxng these assumptons, analyzng the senstvty of our results to the parameters we used, and expandng the range of scenaros could all be frutful topcs for further research. REFERECES Anderson, L., & Stafford, S. (2003). An expermental analyss of rent seekng under varyng compettve condtons, Publc Choce, 115(1 2), 199 216. Anderson, L., & Freeborn, B. (2010). Varyng the ntensty of competton n a multple prze rent seekng experment, Publc Choce, 143(1), 237 254.
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Zhou, Y., Ren, Z. J., (2010). Servce Outsourcng. In: Cochran et al. (Ed.), Wley Encyclopeda of Operatons Research and Management Scence, Wley. APPEDIX A Ths screen shot s from the software we developed for ths research and s of the screen subjects used whle experments were beng conducted. The results from each round are shown on the left of the screen as the competton progresses, and the calculaton tool used to analyze pro-forma profts based on potental decsons by a suppler and a compettor s dsplayed on the rght hand sde of the screen: