Revised July 2008 To appear in International Journal of Production Economics

Transcription

1 Multperod effects of corporate socal responsblty on supply chan networks, transacton costs, emssons, and rsk Jose M. Cruz* and Tna Wakolbnger Department of Operatons and Informaton Management School of Busness, Unversty of Connectcut, Storrs, CT Department of Marketng and Supply Chan Management Fogelman College of Busness and Economcs, Unversty of Memphs Memphs, TN Revsed July 2008 To appear n Internatonal Journal of Producton Economcs Abstract Ths paper develops a framework for the analyss of the optmal levels of corporate socal responsblty actvtes n a multperod supply chan network consstng of manufacturers, retalers, and consumers. Manufacturers and retalers determne ther producton quanttes, transacton quanttes, and the amount of socal responsblty actvtes they want to pursue that maxmze net return, mnmze emsson, and mnmze rsk over the plannng horzon. We nvestgate the nterplay of the heterogeneous decson-makers and compute the equlbrum pattern of product outputs, transactons, prces, and levels of socal responsblty actvtes. The paper provdes nsghts concernng the optmal allocaton of resources to CSR actvtes when consderng a mult-perod tme frame. Keywords: Supply chans; Envronment; Corporate socal responsblty; Rsk management; Network equlbrum; Prcng, Varatonal Inequaltes, Multcrtera decson-makng; *Correspondng author: Tel.: ; fax: E-mal address: jcruz@busness.uconn.edu (J. Cruz). 1

2 1 Introducton Corporate socal responsblty encompasses the economc, legal, ethcal, and phlanthropc expectatons placed on organzatons by socety at a gven pont n tme (Carroll and Buchholtz, 2002). Today, corporate socal responsblty s not only a promnent research theme but t can also be found n corporate mssons and value statements (Svendsen et al., 2001). Companes ncreasngly realze that ther actons n purchasng and supply chan management strongly affect ther reputaton and long-term success (Castka and Balzarova, 2008 and references theren). Corporatons are held accountable for promotng and protectng the envronmental, health, and safety regulatons of workers that make ther products, regardless f they are drect employees or work for ther supplers. For example, corporatons lke Nke, Lz Claborne, Dsney, and Wal-Mart have faced damagng meda reports, external pressure from actvsts, and nternal pressure from nvestors demandng that companes acknowledge responsblty for labor rghts abuses n factores that make ther products (Arraga, 2008). McDonalds, Mtsubsh, Monsanto, Nestle, Nke, Shell, and Texaco have suffered damage to ther reputatons and sales as a result of publc awareness campagns by advocacy groups about ther CSR practces (Svendsen et al. 2001). As a consequence, companes start expandng ther responsblty for ther products beyond ther sales and delvery locatons (Bloemhof-Ruwaard et al., 1995) and they start managng the CSR of ther partners wthn the supply chan (Kolk and Tudder, 2002; Emmelhanz and Adams, 1999). Many researchers have tred to understand busness motvaton to adopt CSR programs (Delmas and Terlaak, 2001; Marcus et al., 2002), legal and nsttutonal factors shapng CSR, the effects of atttudes of managers and consumers towards CSR (Wllams and Agulera, 2008), the effects of the dssemnaton of ndustry standards such as ISO (Castka and Balzarova, 2008) and the relatonshp between the three concepts, CSR, rsk, and proft (Dowlng, 2001; Fombrun, 2001; Clarkson, 1991; Kotter and Heskett, 1992; Collns and Porras, 1995; Waddock and Graves, 1997; Berman et al., 1999; Roman et al., 1999). Indeed, frms engage n CSR actvtes as a way to enhance ther reputaton (Fombrun, 2005), preempt legal sancton (Parker, 2002), respond to NGO acton (Spar and La Mure, 2003), manage ther rsk (Fombrun et al., 2000; Husted, 2005), and to generate customer loyalty (Bhattacharya and Sen, 2001, 2004). CSR can potentally decrease producton neffcences, reduce cost and rsk and at the same tme allow companes to ncrease sales, ncrease access to captal, new markets, and brand recognton. Whle many companes see CSR as a means for damage control or PR, companes ncreasngly realze that CSR actvtes offer opportuntes to create value (Porter and Kramer, 2006). The practce of CSR s an nvestment n the company s future; as such, t must be planned specfcally, supervsed carefully, and evaluated regularly (Falck and Heblch, 2007, 1 p.248). It s very mportant that organzatons take the long-term benefts of CSR nto 2

3 consderaton when determnng ther optmal nvestment n CSR actvtes. Merck & Co. Inc. s an example of a company that beneftted from reputatonal captal created by CSR actvtes n the past (Fombrun, 1996). In 1995, Merck & Co. Inc. s Flnt Rver plant n Albany, New York, leaked phosphorous trchlorde. As a result of the leak, forty-fve people were taken to hosptal and 400 workers were evacuated (Svendsen et al. 2001). However, the communty response ranged from ndfference to laudatory support of Merck. Merck was gven the beneft of the doubt because t had been a good CSR ctzen (Svendsen et al. 2001). Whle Merck & Co. Inc. beneftted from ts reputatonal captal, BP suffered negatve fnancal and reputatonal consequences due to nsuffcent attenton to CSR actvtes n the past. In 2004, BP was fned a record $1.42 mllon for health and safety offenses n Alaska even as the chef executve of BP, was establshng hmself as a leadng advocate for CSR (Doane, 2005). In realty, determnng the deal level of CSR actvtes (McWllams and Segel, 2001) s dffcult. Even more dffcult, s t to set the rght ncentve structures nto place to ensure that ths level s reached snce pressures for short-term performance are often very strong (Falck and Heblch, 2007). However, to plan and communcate the value of CSR actvtes, ts long-term effects need to be better understood (Porter and Kramer, 2006). To contrbute to ths understandng, we buld a mult-tered multperod supply chan model where decson-makers can not only decde about the product flows that they want to transact wth each other but where they can also strategcally allocate resources to CSR actvtes. The analyss of the model allows for nsghts on how CSR actvtes mpact companes performance n the long run and how deal levels of CSR actvtes are nfluenced by factors wthn as well as outsde the frm. Several of the assumptons n the model are smlar to the assumptons of the conceptual model by McWllams and Segel (2001). As n McWllams and Segel (2001) we assume that frms try to maxmze profts and that CSR can be vewed as an nvestment. However, we do not model CSR as a dfferentaton strategy but consder ts effect on transacton costs, emssons and rsk. As n McWllams and Segel (2001), we assume that frms must devote resources for CSR actvtes. We, hence, consder the tradeoff between the costs to generate CSR attrbutes and the benefts, whch nclude lower rsk, lower emssons and lower costs n the long run. We explctly nclude the behavor of decson-makers wthn the supply chan as well as the supply chan structure whle we mplctly nclude nsttutonal factors n the cost and rsk functons. The model s flexble enough to analyze how dfferent objectves of frms (McWllams and Segel, 2001), legal and nsttutonal factors (Wllams and Agulera, 2008), and country dfferences (Matten and Moon, 2008) mpact optmal CSR levels. Cruz (2008) consdered corporate socal responsblty actvtes and rsk management 3

4 n a sngle perod settng n addton to the concept of envronmental decson-makng. In ths paper, however, we turn to the crtcal ssue of socal responsblty actvtes and rsk management n a multperod supply chan network framework. As the prevous secton hghlghted, CSR actvtes lead to many long-term effects that are essental n the costbeneft analyss of CSR actvtes. These long-term effects were not consdered n Cruz (2008). The multperod framework allows us to explctly capture these long-term effects and, hence, provdes a valuable extenson of prevous research. Furthermore, t allows us to see how changes n the plannng framework mpact the decson-makng, the resultng payoffs and costs. Ths paper s organzed as follows. In Secton 2, we develop the multtered, multperod supply chan network model. We descrbe decson-makers optmzng behavor and establsh the governng equlbrum condtons along wth the correspondng varatonal nequalty formulaton. In Secton 3, we propose an algorthm and present computatonal studes. In Secton 4, we dscuss the results. We conclude the paper wth Secton 5 n whch we summarze our results and suggest drectons for future research. 2 The Multperod Supply Chan Network Model In ths secton, we develop the multperod supply chan network model wth rsk management. We assume that all decson-makers consder a fxed plannng horzon whch s dscretzed nto perods: 1,..., t,..., T. The model conssts of I manufacturers, J retalers, and K demand markets as depcted n Fgure 1. We denote a typcal manufacturer by, a typcal retaler by j, and a typcal demand market by k. The lnks between the ters represent transacton lnks. The varables for ths model are gven n Table 1. The equlbrum soluton s denoted by *. All vectors are assumed to be column vectors, except where noted. The top-tered nodes n Fgure 1 represent the I manufacturers n the T tme perods wth node (, t) denotng manufacturer n tme perod t. The manufacturers are the decsonmakers who produce a homogeneous product and sell t to the retalers n the second ter of nodes n the supply chan network n Fgure 1. A node (j, t) corresponds to retaler j n tme perod t, where j = 1,..., J and t = 1,..., T. The consumers at the demand markets are represented by the nodes n the bottom ter of the supply chan network. They acqure the product from the retalers. Demand market k at tme perod t s denoted by node (k, t) wth k = 1,..., K and t = 1,..., T. The model developed n ths secton s based on the assumpton that manufacturers and retalers can perfectly predct the benefts of CSR actvtes durng ther plannng horzon T. All prces and costs are expressed n terms of ther value n perod 1. We now turn to the descrpton of the functons. We frst dscuss the producton cost, 4

5 transacton cost, handlng, and unt transacton cost functons gven n Table 2. At each tme perod t, each manufacturer s faced wth a certan producton cost functon that depends on hs producton output and the levels of socal responsblty actvtes of current and prevous tme perods. Furthermore, each manufacturer and each retaler are faced wth transacton costs. The transacton costs are affected by the amount of the product transacted and the levels of socal responsblty actvtes of current and prevous tme perods. Each retaler s also faced wth what we term a handlng/converson cost (cf. Table 2, Nagurney and Dong, 2002), whch may nclude, for example, the cost of handlng the product. The handlng cost of a retaler s a functon of how much he has obtaned of the product from the varous manufacturers n tme perod t. The consumers at each demand market are faced wth a unt transacton cost. As n the case of the manufacturers and the retalers, hgher levels of socal responsblty actvtes may potentally reduce transacton costs, whch means that they can lead to quantfable cost reductons over the plannng horzon. The unt transacton costs depend on the amounts of the product that the retalers transact wth the demand markets as well as on retalers socal responsblty actvtes of current and prevous perods. We assume that the producton cost, the transacton cost, and the handlng cost functons are convex and contnuously dfferentable and that the unt transacton cost functons are contnuous. We now turn to the descrpton of cost functons for socal responsblty actvtes, the emsson functons, the rsk functons and the demand functons. We assume that the cost functons for socal responsblty actvtes, the emsson functons, and the rsk functons are convex and contnuously dfferentable. The demand functons are assumed to be contnuous. We start by descrbng the cost functons for socal responsblty actvtes that are gven n Table 3. We assume that at each tme perod each manufacturer and each retaler may spend money, for example, n the form of tme/servce, nvestment n new technology, tranng employees, and nformaton sharng to promote socal responsblty actvtes. Here, socal responsblty actvtes are actvtes that promote qualty assurance, envronmental preservaton, and complance. The costs for socal responsblty actvtes at tme t depend on levels of socal responsblty actvtes of current and past perods. These cost functons for socal responsblty actvtes may be dstnct for each manufacturer, each retaler, and each tme perod. We assume that these levels of socal responsblty actvtes (cf. Table 1) take on a value that les n the range [0, 1. No socal responsblty actvty s ndcated by a level of zero and the strongest possble level of socal responsblty actvty s ndcated by a level of one. Ths s consstent wth the Corporate Responsblty (CR) Report from Busness n Communty where busnesses are graded on a scale of 0 to 100% for ther CSR performance. The levels of socal responsblty actvtes, along wth the product flows, are endogenously determned n the model. 5

6 We now descrbe the emsson functons as presented n Table 4. Envronmental ssues surroundng supply chans have only recently come to the fore, notably, n the context of conceptual and survey studes (Hll, 1997 and the references theren) as well as appled studes (Htchens et al., 2000). In response to growng envronmental concerns, researchers have begun to deal wth envronmental rsks (Qo et al., 2001). More sgnfcantly, the ncreased focus on the envronment s sgnfcantly nfluencng supply chans. Legal requrements and changng consumer preferences ncreasngly make supplers, manufacturers, and dstrbutors responsble for ther products beyond ther sales and delvery locatons (Bloemhof-Ruwaard et al., 1995). Nevertheless, n the supply chan context, models that explctly nclude mnmzaton of emssons as an mportant goal are clearly needed. We assume that the amount of emssons generated depends on the amount of product produced and transacted as well as on decson-makers levels of socal responsblty actvtes n current and prevous perods (see, e.g., Lammng and Hampson, 1996; Florda, 1996; Clft and Wrght, 2000; Geffen and Rothenberg, 2000; Hall, 2000). We assume that each manufacturer and each retaler seek to mnmze the total emsson generated n the producton process as well as n the process of product delvery to the next ter of decson-makers. Hence, we truly capture the envronmental decson makng n the supply chan framework. In terms of rsk management, most of the research has focused on the study of the relatonshp between corporate socal responsblty (CSR) and fnancal performance (Graves and Waddock, 1994; Grffn and Mahon, 1997; McGure et al., 1988; McWllams and Segel, 2000; Preston and OBannon, 1997; Roman et al., 1999; Waddock and Graves, 1997). A subset of these studes began to look at the relatonshp between CSR and rsk. Spcer (1978) looked drectly at the CSR-rsk relatonshp and found evdence for a negatve correlaton between the two: as CSR ncreased, rsk decreased. Orltsky and Benjamn (2001) also found support for negatve relatonshp between CSR and rsk. Bowman (1980) asserts that frms wth proactve CSR that engage n manageral practces lke envronmental assessment and stakeholder management (Wood, 1991) tend to antcpate and reduce potental sources of busness rsk, such as potental governmental regulaton, labor unrest, or envronmental damage (Orltzky and Benjamn, 2001). Feldman et al. (1996) suggest that adoptng a more envronmentally proactve posture has, n addton to any drect envronmental and cost reducton benefts, a sgnfcant and favorable mpact on the frm s perceved rskness to nvestors and, accordngly, ts cost of equty captal and value n the market place. Table 5 descrbes the rsk functons. Most research on CSR and rsk relatonshp has been emprcal or conceptual research and dd not focus on rsk management as a functon of CSR actvtes on supply chan. Rsk functons n our model are functons of both the product transactons and the levels of socal responsblty actvtes n current and prevous perods. Jüttner et al. (2003) suggest that supply chan-relevant rsk sources fall nto three categores: envronmental rsk sources (e.g., fre, socal-poltcal actons, or acts of God), organzatonal rsk sources (e.g., producton uncertantes), and network-related rsk sources. 6

7 Johnson (2001) and Norrman and Jansson (2004) argue that network-related rsk arses from the nteracton between organzatons wthn the supply chan, e.g., due to nsuffcent nteracton and cooperaton. We use levels of socal responsblty actvtes as a way of possbly reducng rsks. The demand functons as gven n Table 6 are assocated wth the bottom-tered nodes of the supply chan network. The demand of consumers for the product at a demand market at tme t depends, n general, not only on the prce of the product at that demand market but also on the prces of the product at the other demand markets. Consequently, consumers at a demand market, n a sense, also compete wth consumers at other demand markets. We now turn to descrbng the behavor of the varous economc decson-makers. The model s presented, for ease of exposton, for the case of a sngle homogeneous product. It can also handle multple products through a replcaton of the lnks and added notaton. We frst focus on the manufacturers. We then turn to the retalers, and, subsequently, to the consumers at the demand markets. 2.1 Multcrtera Decson-Makng Behavor of the Manufacturers and Ther Optmalty Condtons Let ρ 1jt denote the prce charged for the product by manufacturer n transactng wth retaler j n perod t. The prce ρ 1jt s an endogenous varable and wll be determned once the entre multperod supply chan network equlbrum model s solved. The quantty of the product produced by manufacturer n tme perod t must satsfy the followng conservaton of flow equaton: J qt = qjt, (1) whch states that the quantty of the product produced by manufacturer n tme perod t s equal to the sum of the quanttes transacted between the manufacturer and all retalers. The frst objectve of the manufacturers s to maxmze the total proft over the plannng horzon T. The decson varables for manufacturer are the dstrbuton quanttes n each perod, q jt; j = 1,..., J; t = 1,..., T, and the levels of socal responsblty actvtes at each perod, η t. Thus, manufacturer s faced wth an optmzaton problem whch can be expressed as follows: Maxmze [ T J J ρ 1jtqjt ft (qt, ηt) 1 c jt(qjt, ηt) 1 b t(ηt) 1 (2) subject to the non-negatvty constrants: q jt 0, and 0 η t 1,, j, t. 7

8 The frst term n (2) represents the revenue and the subsequent three terms the producton costs, the transacton costs, and the costs for socal responsblty actvtes for manufacturer. Note that we allow the specfcatons of all the cost functons to be tme-dependent. In addton to the crteron of proft maxmzaton, we assume that each manufacturer also seeks to mnmze the total emssons (waste) generated n the producton of the product as well as ts delvery to the next ter of decson-makers, the retalers, over the plannng horzon T. Hence, the second crteron of each manufacturer can be expressed mathematcally as: Mnmze T e t(q 1 t, ηt) 1 (3) subject to the non-negatvty constrants: q jt 0, and 0 η t 1,, j, t. The thrd crteron faced by manufacturer, thus, corresponds to rsk (cf. Table 5) mnmzaton and can be expressed mathematcally as: Mnmze T rt(q 1 t, ηt) 1 (4) subject to the non-negatvty constrants: q jt 0, and 0 η t 1,, j, t. We can now construct the multcrtera decson-makng problem facng a manufacturer whch allows hm to weght the crtera of proft maxmzaton (cf. (2)), total emsson mnmzaton (cf. (3)), and total rsk mnmzaton (see (4)) n an ndvdual manner. Assume that manufacturer assgns a nonnegatve weght ω2 to total emsson generated by producton and transacton processes. Furthermore, assume that he assgns the nonnegatve weght ω3 to rsk. The weght assocated wth proft maxmzaton serves as the numerare and s set equal to 1. The nonnegatve weghts measure the mportance of emsson and rsk, and, n addton, transform these values nto monetary unts. We can now construct a value functon for each manufacturer (cf. Keeney and Raffa, 1993) usng a constant addtve weght value functon. Therefore, the multcrtera decson-makng problem of manufacturer can be expressed as: [ T J J Maxmze ρ 1jtqjt ft (qt, ηt) 1 c jt(qjt, ηt) 1 b t(ηt) 1 ω 2e t(q 1 t, η 1 t) ω 3r t(q 1 t, η 1 t) (5) subject to the non-negatvty constrants: q jt 0, and 0 η t 1,, j, t. 8

9 The frst four terms n (5) represent the proft whch s to be maxmzed, the next term represents the weghted total emsson, whch s to be mnmzed, and the last term represents the weghted total rsk, whch s to be mnmzed. We assume that manufacturers compete n a noncooperatve manner n the sense of Nash (1950, 1951). The optmalty condtons for all manufacturers ; = 1,..., I, smultaneously, can then be expressed as the followng varatonal nequalty (cf. Cruz, 2008; Bazaraa et al., 1993; Gabay and Mouln, 1980): determne (Q 1, η 1 ) K 1 satsfyng: T I =1 + J T [ f t (q t, η 1 t ) q jt I =1 + c jt(qjt, ηt 1 ) + ω 2 J [ T f t (qt, η 1 η t +ω2 T e t(q 1 t, ηt 1 ) + ω T ηt 3 [ qjt qjt t ) r t(q 1 ηt e t(q 1 t, ηt 1 ) + ω 3 + T c jt(qjt, ηt 1 ) + T ηt t, η 1 where K 1 [ (Q 1, η 1 ) q jt 0, 0 η t 1,, j, t. t ) rt(q 1 t, ηt 1 ) ρ 1jt b jt(ηt 1 ) ηt [ η t ηt 0, (Q 1, η 1 ) K 1, (6) 2.2 Multcrtera Decson-Makng Behavor of the Retalers and Ther Optmalty Condtons The retalers, n turn, are nvolved n transactons both wth the manufacturers snce they wsh to obtan the product for ther retal outlets, as well as wth the consumers, who are the ultmate purchasers of the product. Thus, as depcted n Fgure 1, a retaler conducts transactons both wth the manufacturers and wth the consumers. The retalers are also assumed to be multcrtera decson-makers who seek to maxmze profts, to mnmze ther ndvdual rsk assocated wth ther transactons and to mnmze the emssons generated by ther transactons. Let ρ j 2kt denote the prce charged by retaler j for the product at tme perod t. Ths prce wll be determned endogenously after the complete model s solved. We assume that the objectve of a retaler s to maxmze hs total proft over the plannng horzon T. The decson varables of retaler j nclude the transacton amounts n each perod, qjt; = 1,..., I; t = 1,..., T wth total procurement q j t = I =1 q jt, the sales made wth the demand markets at each perod, q j kt ; k = 1,..., K; t = 1,..., T, and the levels of socal responsblty actvtes at each perod, η j t ; t = 1,..., T. Hence, the proft maxmzaton problem faced by retaler j s 9

10 gven by: Maxmze subject to: [ T K ρ j 2kt qj kt cj t(q j t ) k=1 I c j t (q jt, ηjt) 2 =1 K q j kt k=1 K c j kt (qj kt, η2 jt) b j t(ηjt) 2 k=1 I =1 ρ 1jtq jt (7) I qjt t, (8) and the non-negatvty constrants: q jt 0, q j kt 0, 0 ηj t 1,, k, t. =1 The frst term n the objectve functon (7) represents the revenue of retaler j, whereas the next four terms represent varous costs (see Table 2), and the last term represents the payout to the manufacturers. Constrants (8) state that the amount of product avalable for dstrbuton to the demand markets n a tme perod t s less or equal to the amount obtaned n that perod from the manufacturers. In addton, we assume that each retaler seeks to mnmze the emssons and waste assocated wth hs transactons wth manufacturers and demand markets over the entre plannng horzon (cf. Cruz, 2008). Hence, the second crteron of each retaler can be expressed mathematcally as: T Mnmze e j t(q 2 jt, ηjt). 2 (9) Furthermore, we assume that each retaler s also concerned wth rsk mnmzaton. For the sake of generalty, we assume, as gven, a rsk functon r j t (Table 5), for retaler j n tme perod t. The rsk functons are assumed to be contnuous and convex and a functon of both the product transactons and the levels of socal responsblty actvtes n current and prevous perods. The thrd crteron of each retaler can be expressed mathematcally as: T Mnmze r j t (Q 2 jt, ηjt). 2 (10) Retaler j assgns the nonnegatve weght ω j 2 to total emssons generated, and the nonnegatve weght ω j 3 to total rsk. The weght assocated wth proft maxmzaton s set equal to 1 and serves as the numerare (as n the case of the manufacturers). We are now ready to construct the multcrtera decson-makng problem faced by a retaler, whch combnes wth approprate ndvdual weghts the crtera of proft maxmzaton gven by (7), emsson mnmzaton gven by (9), and rsk mnmzaton gven by (10). Let ntermedary j s multcrtera decson-makng problem be expressed as: [ T K I K Maxmze ρ j 2kt qj kt cj t(q j t ) c j t (q jt, ηjt) 2 c j kt (qj kt, η2 jt) b j t(ηjt) 2 k=1 =1 10 k=1

11 subject to: I ρ 1jtqjt ω2e j j t(q 2 jt, ηjt) 2 ω3r j j t (Q 2 jt, ηjt) 2, (11) =1 K q j kt k=1 I qjt t, (12) and the non-negatvty constrants: q jt 0, q j kt 0, 0 ηj t 1,, k, t. =1 We assume that the retalers also compete n a noncooperatve manner. The optmalty condtons for all retalers smultaneously can be expressed as the varatonal nequalty: determne (Q 1, Q 2, η 2, λ ) K 2 satsfyng: T + J K k=1 T I =1 + + [ c j kt (qj kt, η2 jt ) q j + ω j e j t(q 2 2 kt q j kt J T J [ c j t (q jt, ηjt 2 ) I =1 J [ T jt ) jt, η 2 + cjt(q j t ) + ω j e j t(q 2 2 cj t (q jt, ηjt 2 ) η j t +ω j T ej t(q 2 jt, ηjt 2 ) 2 η j t [ T I qjt =1 K k=1 q j kt [ q jt q jt + ω j r j t (Q 2 jt, ηjt 2 ) 3 q j + λ jt ρ j 2kt kt jt ) jt, η 2 + T cj kt (qj kt, η2 jt ) η j t + ω j T rj t (Q 2 jt, η 2 3 η j t [ q j kt qj kt + ω j r j t (Q 2 jt, ηjt 2 ) 3 + ρ 1jt λ jt jt ) + T bj t(η 2 jt ) η j t [ η j t η j t [ λ jt λ jt 0, ((Q 1, Q 2, η 2, λ) K 2, (13) where K 2 [ (Q 1, Q 2, η 2, λ) q jt 0, q j kt 0, 0 ηj t 1, λ jt 0,, j, k, t. Here λ jt denotes the Lagrange multpler assocated wth constrant (12) and λ s the column vector of all the retalers Lagrange multplers. These Lagrange multplers can also be nterpreted as shadow prces. Indeed, accordng to the ffth term n (13), λ jt serves as the prce to clear the market at retaler j at tme t. 2.3 Equlbrum Condtons for the Demand Markets We now descrbe the behavor of the consumers located at the demand markets. The consumers take nto account n makng ther consumpton decsons not only the prces charged for the product by the retalers, ρ j 2kt ; j = 1,..., J; t = 1,..., T, but also the unt transacton costs to obtan the product. The equlbrum condtons for consumers at demand market 11

12 k, (cf. Samuelson, 1952) take the form: for all retalers j; j = 1,..., J and tme perods t; t = 1,..., T : { ρ j 2kt + ck jt(q j = ρ kt, k η2 3t, f q j kt jt ) > 0 ρ k 3t, f q j kt = 0, (14) and d k t (ρ 3t) = J J q j kt, f ρk 3t > 0 q j kt, f ρk 3t = 0. Condtons (14) state that, n equlbrum, at each tme perod, f the consumers at demand market k purchase the product from retaler j, then the prce charged by the retaler for the product at that tme perod plus the unt transacton cost s equal to the prce that the consumers are wllng to pay for the product at that tme perod. If the prce plus the unt transacton cost s hgher than the prce the consumers are wllng to pay at the demand market then there wll be no transacton between the retaler and demand market par at that tme perod. Condtons (15) state, n turn, that f the equlbrum prce the consumers are wllng to pay for the product at the demand market at the tme perod s postve, then the quanttes purchased of the product from the retalers at that tme perod wll be precsely equal to the demand for that product at the demand market at that tme perod. In equlbrum, condtons (14), and (15) wll have to hold for all demand markets and these can be expressed as an nequalty analogous to those n (6) and (13) and gven by: determne (Q 2, ρ 3) K 3, such that J K T k=1 [ ρ j 2kt + ck jt(q j kt, [ η2 jt ) ρ k 3t q j kt K qj kt + k=1 [ (Q 2, ρ 3 ) K 3, where K 3 [ T J q j kt dk t (ρ 3t) (Q 2, ρ 3 ) (Q 2, ρ 3 ) R (1+J)KT + (15) [ ρ k 3t ρ k 3t 0,. (16) 2.4 The Equlbrum Condtons of the Multperod Supply Chan Network In equlbrum, the optmalty condtons for all manufacturers, the optmalty condtons for all retalers, and the equlbrum condtons for all demand markets must hold smultaneously so that no decson-maker can be better off by alterng hs decsons. Also, the shpments that the manufacturers shp to the retalers must be equal to the shpments that the retalers accept from the manufacturers. Smlarly, the quanttes of the product obtaned by the consumers at the demand markets must concde wth the amounts sold by the retalers. 12

13 Defnton 1: Multperod Supply Chan Network Equlbrum The equlbrum state of the multperod supply chan network s one where the sum of (6), (13), and (16) s satsfed, so that no decson-maker has any ncentve to alter hs decsons. Theorem 1: Varatonal Inequalty Formulaton The equlbrum condtons governng the multperod supply chan network model are equvalent to the soluton of the varatonal nequalty problem gven by: determne (Q 1, Q 2, η 1, η 2, λ, ρ 3) K T T I =1 J + cj t (q jt, ηjt 2 ) J J q jt K k=1 + + [ f t (q t, η 1 t ) q jt + c jt(qjt, ηt 1 ) + ω 2 + cj t(q j t ) + ω j e j t(q 2 2 [ c j kt (qj kt, η2 jt ) q j + ω j e j t(q 2 2 kt q j kt T I =1 J [ T f t (qt, η 1 η t jt ) jt, η 2 jt ) jt, η 2 [ q j kt qj kt t ) +ω2 T e t(q 1 t, ηt 1 ) + ω T ηt 3 T I J [ T =1 [ T I qjt =1 cj t (q jt, ηjt 2 ) η j t +ω j T ej t(q 2 jt, ηjt 2 ) 2 K k=1 q j kt η j t e t(q 1 t, ηt 1 ) + ω 3 + ω j r j t (Q 2 jt, ηjt 2 ) 3 λ jt + ω j r j t (Q 2 jt, ηjt 2 ) 3 q j kt + T c jt(qjt, ηt 1 ) + T ηt r t(q 1 ηt t, η 1 t ) + T cj kt (qj kt, η2 jt ) η j t + ω j T rj t (Q 2 jt, η 2 3 [ K λ jt λ jt + k=1 η j t jt ) r t(q 1 t, η 1 t ) q jt [ qjt qjt + c k jt(q j kt, η2 jt ) + λ jt ρ k 3t b jt(ηt 1 ) ηt [ η t ηt + T bj t(η 2 jt ) η j t [ η j t η j t [ T J q j kt dk t (ρ 3t) [ ρ k 3t ρ k 3t 0, (Q 1, Q 2, η 1, η 2, λ, ρ 3 ) (17) where K 4 [ (Q 1, Q 2, η 1, η 2, λ, ρ 3 ) q jt 0, q j kt 0, 0 η t 1, 0 η j t 1, λ jt 0, ρ k 3t 0,, j, k, t. Proof: Summaton of nequaltes (6), (13), and (16), yelds, after algebrac smplfcaton, the varatonal nequalty (17). We now establsh the converse, that s, that a soluton to varatonal nequalty (17) satsfes the sum of condtons (6), (13), and (16) and s, hence, 13

14 an equlbrum accordng to Defnton 1. To nequalty (17) add the term +ρ 1jt - ρ 1jt to the ffth set of brackets precedng the multplcaton sgn. Smlarly, add the term +ρ j 2kt ρj 2kt to the term precedng the sxth multplcaton sgn n (17). The addton of such terms does not alter (17) snce the value of these terms s zero. The resultng nequalty can be rewrtten to become equvalent to the prce and materal flow pattern satsfyng the sum of the condtons (6), (13), and (16). The proof s complete. We now put varatonal nequalty (17) nto standard form whch wll be utlzed n the subsequent sectons. For addtonal background on varatonal nequaltes and ther applcatons, see the book by Nagurney (1999). In partcular, we have that varatonal nequalty (17) can be expressed as: F (X ), X X 0, X K 4, (18) where X (Q 1, Q 2, η 1, η 2, λ, ρ 3 ) and F (X) (F jt, F jkt, F t, F jt, ˆF jt, F kt ) wth ndces: = 1,..., I; j = 1,..., J; k = 1,..., K; t = 1,..., T, and the specfc components of F gven by the functonal terms precedng the multplcaton sgns n (17), respectvely. The term, denotes the nner product n N-dmensonal Eucldean space. We now descrbe how to recover the prces assocated wth the frst two ters of nodes n the supply chan network. Clearly, the components of the vector ρ 3 are obtaned drectly from the soluton of varatonal nequalty (17). To recover the second ter prces assocated wth the retalers one can (after solvng varatonal nequalty (17) for the partcular numercal problem) ether (cf. (16)) set ρ j 2kt = [ ρ k 3t c k jt(q j kt, η2 jt ), for any j, k, t such that q j kt > 0, or [ (cf. (13)) for any q j kt > 0, set ρj 2kt = c j kt (qj kt,η2 jt ) + ω j e j t (Q2 jt,η2 jt ) q j 2 + ω j r j t (Q2 jt,η2 jt ) kt q j 3 + λ kt q j jt. kt Smlarly, from (6) we can nfer that the top ter prces comprsng the vector ρ 1 can be recovered (once the varatonal nequalty [ (17) s solved wth partcular data) thus: for any, j, t, such that qjt > 0, set ρ f t (qt 1jt=,η1 t ) + c jt (q jt,η1 t ) + ω e t (Q1 t,η1 t ) 2 + ω r t (Q1 t,η1 t ) 3, or, equvalently [ to λ jt cj t (q jt,η2 q jt jt ) cj t (qj t ) ω j 2 e j t (Q2 jt,η2 jt ) ω j 3 r j t (Q2 jt,η2 jt ) (cf. (13)). Under the above prcng mechansm, the optmalty condtons (6) and (13) as well as the equlbrum condtons (16) also hold separately (as well as for each ndvdual decson-maker at any tme perod). 3 Computatonal Procedure and Studes In ths secton, we consder an algorthm for the computaton of solutons to varatonal nequalty (17). The algorthm that s proposed s the Euler-type method, whch s nduced 14

15 by the general teratve scheme of Dupus and Nagurney (1993). 3.1 The Dscrete-Tme Algorthm The Euler Method Step 0: Intalzaton Set X 0 = (Q 10, Q 20, η 10, η 20, λ 0, ρ 0 3) K 4. Let T denote an teraton counter and set T = 1. Set the sequence {a T } so that T =1 a T =, a T > 0, a T 0, as T (such a sequence s requred for convergence of the algorthm). Step 1: Computaton = (Q 1T, Q 2T, η 1T, η 2T, λ T, ρ T 3 ) K 4 by solvng the varatonal nequalty sub- Compute X T problem: X T + a T F (X T 1 ) X T 1, X X T 0, X K 4. (19) Step 2: Convergence Verfcaton If X T X T 1 ɛ, wth ɛ > 0, a pre-specfed tolerance, then stop; otherwse, set T := T +1, and go to Step 1. Note that ths algorthm has been appled to-date to solve a plethora of network models (see, e.g., Cruz, 2008; Nagurney et al., 2005; Nagurney and Dong, 2002). 3.2 Computatonal Studes In ths computatonal study, we analyze the mpact of changes n parameters n the multperod supply chan network model on equlbrum product flows, prces, and CSR levels. The supply chan model s represented n Fgure 2. It conssts of 2 manufacturers, = 1, 2; 2 retalers j, j = 1, 2; 2 demand markets k, k = 1, 2; and 2 tme perods t, t = 1, 2. CSR levels create the lnks between the frst and the second tme perod. The functons used n the numercal analyss are shown n Table 7. Manufacturers ncur transacton costs and rsk for ther transactons wth retalers. Retalers ncur transacton costs and rsk for ther transactons wth demand markets. Demand markets face unt transacton costs when transactng wth retalers. Transactons between manufacturers and retalers and between retalers and demand markets cause emssons. We assume that all the prces and costs at the second perod are measured n terms of ther dollar value at the frst perod. 15

16 We assume that producton costs, transacton costs, and emssons are lnear ncreasng n the amount of products produced/transacted. Fxed costs are assumed sunk costs and are not consdered. Demand at each demand market s lnear decreasng wth the prce at ths demand market. Rsk s a quadratc functon of product transacted. In the feld of fnance, the measurement of rsk has ncluded the use of varance-covarance matrces, yeldng quadratc expressons for rsk (see also, e.g., Nagurney and Sokos, 1997). In addton, n fnance, the bcrteron optmzaton problem of net revenue maxmzaton and rsk mnmzaton s farly standard (see also, e.g., Dong and Nagurney, 2001). We use quadratc rsk functons n a supply chan context n ths senstvty analyss as t has been suggested n, for example, Nagurney et al. (2005). Emssons, transacton costs, and rsk n the frst perod are a functon of CSR levels n the frst perod. Emssons, transacton costs, and rsk n the second perod are a functon of CSR levels n the frst and second perod. These assumptons are consstent wth many emprcal studes. The emprcal work of Dyer and Chu (2003) ndcate that, as the levels of socal responsblty actvtes ncrease the overall cost would decrease. Furthermore, as we menton n the ntroducton, Spcer (1978) and Orltsky and Benjamn (2001) looked drectly at the CSR-rsk relatonshp and found evdence for a negatve correlaton between the two: as CSR ncreased, rsk decreased. Ths s because frms wth proactve CSR that engage n manageral practces lke envronmental assessment and stakeholder management (Wood, 1991; Bowman, 1980) tend to antcpate and reduce potental sources of busness rsk, such as potental governmental regulaton, labor unrest, or envronmental damage (Orltzky and Benjamn, 2001). Moreover, n addton to any drect envronmental and cost reducton benefts, CRS actvtes has a sgnfcant and favorable mpact on the frm s perceved rskness to nvestors and, accordngly, ts cost of equty captal and value n the market place (Feldman et al., 1996). The costs for CSR actvtes are quadratc. Ths ndcates that t gets more expensve to ncrease CSR levels, the hgher they already are. F 1t and A 1jt represent parameters =1,2,,2, and,2. At the begnnng of the study we set A 1jt = 0.2, j, and t, and F 1t = 1, t. Our parameter settngs reflect that producton costs are typcally larger than the transacton costs. All the weghts are set equal to 1. The Euler method was mplemented n Matlab to solve these numercal examples. Alpha s set to 1/(2+0.4t). The parameter for convergence s set to Dscusson of Results The ntal settngs lead to the followng equlbrum product flows, prces, and CSR levels: The product transacton amounts qjt = qjkt = for =1,2,,2, n the frst tme perod. 16

17 qjt = qjkt = for =1,2,,2 n the second tme perod. The CSR levels are at ther upper lmt of 1 for all tme perods. The prces at the manufacturers ρ 1jt = for =1,2,,2 at the frst tme perod and ρ 1jt=40.20 for =1,2,,2 at the second tme perod. The prces that retalers charge ρ j 2kt = for j = 1, 2, k = 1, 2 at the frst tme perod and = for j = 1, 2, k = 1, 2 at the second tme perod. ρ j 2kt Transacton costs, emssons, and rsk n the frst perod are a functon of CSR levels n the frst perod. Transacton costs, emssons, and rsk n the second perod are a functon of CSR levels n the frst and second perod. In equlbrum, all decson-makers establsh CSR levels of 1 n both perods. Hence, decson-makers face a stronger reducton n transacton costs, emssons, and rsk n the second perod than n the frst perod. Ths leads to hgher product flows and lower prces n the second perod. Ths hghlghts that to understand the development of product flows and prces, t s of utmost mportance to consder CSR levels and ther mpact n all tme perods. There are a lot of debates concernng the measurement of the costs for CSR actvtes as well as the measurement of ther mpact. Hence, n ths analyss we want to show how changes n these parameters mpact equlbrum results n the supply chan network. Due to strong uncertanty n the measurement, we consder a wde range of values. In the frst two numercal examples we look at the mpact of an ncrease n costs for CSR actvtes on CSR levels, product flows, and prces. In the thrd numercal example, we look at the effect of a change n the mpact that CSR levels have on transacton costs on CSR levels, product flows, and prces. In all the examples we use the followng abbrevatons: M1: manufacturer 1, M2: manufacturer 2, R1: retaler 1, R2: retaler 2, DM: demand market, T1: tme perod 1 and T2: tme perod 2. Example 1 In Example 1 we vary the parameter n the cost functon for CSR actvtes, F 1t, for both manufacturers n the range 1 to 25. The effects of these changes on CSR levels are shown n Fgure 3(a). An ncrease n the parameters n manufacturers cost functons for CSR actvtes leads to decreasng manufacturers CSR levels. CSR levels n the second perod react to smaller changes n the parameters than CSR levels n the frst perod. The reason s that transacton costs, emssons, and rsk n the frst perod are nfluenced by CSR levels n the frst perod; however, transacton costs, emssons, and rsk n the second perod are nfluenced by CSR levels n the frst and second perod. Hence, CSR levels n the frst perod have a stronger total postve mpact than CSR levels n the second perod. Ths hghlghts that the equlbrum CSR levels wll be strongly nfluenced by the plannng horzons of dfferent companes. Fgure 3(b) shows the mpact of these changes on product flows. 17

18 We can see from Fgure 3(b) that n the orgnal scenaro product flows n perod 2 are hgher than product flows n perod 1. The reason s that CSR levels n the frst and second perod postvely mpact emssons, rsk and costs n the second perod. However, we see that product flows n the second perod are the frst to declne snce they are mpacted by CSR levels n the second perod whch declne earler. Example 2 In Example 2, we analyze the effects of changes n parameters n manufacturer 1 s cost functons for CSR actvtes. Fgure 4 shows the effects of changes n F 11t n the range 1 to 25. Increasng cost parameters lead to decreasng CSR levels for manufacturer 1. Frst CSR levels n the second perod decrease and then the CSR levels n the frst perod decrease. The CSR levels for manufacturer 2 do not change. Fgure 4(b) hghlghts the mpact of these changes on product flows. When manufacturer 1 s CSR levels decrease, product flows orgnatng from manufacturer 1 decrease and product flows orgnatng from manufacturer 2 ncrease. Product flows reachng demand markets decrease n both tme perods. Snce overall product flows decrease, prces at demand markets ncrease. Hence, we can see that manufacturer 2 benefts from ths change n the cost structure of manufacturer 1. Example 3 In Example 3 we want to hghlght the effects of an ncrease of the mpact of CSR levels on transacton costs. Specfcally, we want to hghlght how the equlbrum soluton changes f the transacton costs of manufacturer 2 respond stronger to changes n CSR levels. We chose the mpact of CSR levels on transacton costs due to the hgh and rsng mportance of transacton costs. Results from ths secton can also be used to understand the effects of changes of the mpact of CSR levels on emssons and rsk. We keep all the parameters as n the base case, except for the parameter for the cost for CSR actvtes whch we set to 6. We vary manufacturer 1 s parameter that measures the mpact of CSR actvtes on transacton costs (A 11jt ) between 0 and 0.9. Table 8 ndcates how these changes mpact CSR levels. We see that when A 11jt = 0 CSR levels for manufacturer 1 for perod 2 are below 1. Manufacturer 1 s CSR levels ncrease as the mpact of CSR levels on transacton costs ncreases untl they reach ther upper lmt of 1. Startng from A 11jt = 0.3, CSR levels for manufacturer 2 for perod 2 start decreasng. The reason for ths change can be found n Fgure 5. We can see that wth an ncrease n A 11jt, product flows for manufacturer 1 ncrease and product flows for manufacturer 2 18

19 decrease. Ths s true for both tme perods. Snce the beneft of CSR levels depends on the product flows, reduced product flows lead to reduced CSR levels n the second perod. These changes do not mpact CSR levels at perod 1 whch stay at ther upper lmt. Total product flows ncrease and prces at demand markets decrease. These examples, although stylzed, have been presented to show both the model and the computatonal procedure. Obvously, dfferent nput data and dmensons of the problems solved wll affect the equlbrum product transacton, levels of socal responsblty actvtes, and prce patterns. They hghlght that changes n benefts or costs assocated wth CSR levels do not only mpact the optmal CSR levels and product flows of the company that faces these changes. These changes also have the potental to mpact optmal CSR levels, product flows and prces of other companes n the supply chan. Furthermore, these changes can potentally mpact compettors performance. The numercal examples hghlght that the best outcome for the supply chan as a whole mght not always be acheved f each member n the supply chan determnes the optmal levels of CSR based only on hs/her own costs and benefts. Hence, the optmal nvestment n CSR levels n a supply chan consttutes a socal dlemma as descrbed n McCarter and Northcraft (2007) where decson-makers must choose between dong what s n ther own best nterest or the overall supply chan best nterest. We llustrate that f supply chan decson-makers choose to do what s n ther own best nterest, ths wll lead to an outcome that does not provde benefts for the supply chan (Dawes, 1980; McCarter and Northcraft, 2007). In realty, we can see that many companes deal wth ths dlemma by expandng ther responsblty for ther products beyond ther sales and delvery locatons (Bloemhof-Ruwaard et al., 1995) and by managng the CSR of ther partners wthn the supply chan (Kolk and Tudder, 2002; Emmelhanz and Adams, 1999). The model developed n ths paper allows managers to see how changes n supply chan partners CSR actvtes affect ther own operatons. The model, hence, provdes managers wth nsghts concernng potental ncreases n supply chan performance that mght be acheved f CSR actvtes are coordnated among supply chan companes or centrally managed. The framework developed n ths paper represents a powerful decson-makng tool wth whch the potental stake holders, such as manufacturers, dstrbutors, and/or retalers, wll be able to model a current market stuaton and explore the effects of varous perturbatons to the data, dfferent envronmental strateges as well as the effects of changes n the number of manufacturers, retalers, and demand markets. Moreover, each decson-maker can also use ths framework to determne what should be the optmal level of nvestment n CSR that mnmzes potental rsk and envronmental mpact. In addton, our framework s not only useful for these stake holders, but also for the polcy makers. It wll allow the polcy makers to model the market and explore the potental benefts of dfferent polces related 19

20 to emsson/waste regulatons. The proposed computatonal procedure allows for massve parallelzaton whch, n turn, makes the computaton of large models quck and effcent. 5 Conclusons CSR can potentally decrease producton neffcences, reduce cost and rsk and at the same tme allow companes to ncrease sales. As a result of lower costs, lower rsk and ncrease n sales, companes become more proftable. However, we expect that as the nvestment n CSR actvtes ncreases, the return on nvestment s decreasng. Therefore, t s very mportant for managers to fnd the optmal level of nvestment n CSR actvtes so that he\she can allocate the approprate amount of resources to these actvtes over tme. The optmal levels of CSR actvtes are mpacted by factors wthn the frm as well as ts busness envronment. In ths paper, we develop a framework for the analyss of the optmal levels of corporate socal responsblty actvtes n a multperod supply chan network consstng of manufacturers, retalers, and consumers. The framework explctly ncludes the behavor of decsonmakers wthn the supply chan as well as the supply chan structure whle t mplctly ncludes nsttutonal factors n the cost and rsk functons. Manufacturers and retalers are multcrtera decson-makers who decde about ther producton and transacton quanttes as well as the amount of socal responsblty actvtes they want to pursue to maxmze net return, mnmze emssons, and mnmze rsk over the multperod plannng horzon. We construct the fnte-dmensonal varatonal nequalty governng the equlbrum of the multperod compettve supply chan network. The model allows us to nvestgate the nterplay of the heterogeneous decson-makers n the supply chan network and to compute the resultant equlbrum pattern of product outputs, transactons, product prces, and levels of socal responsblty actvtes. A computatonal procedure that explots the network structure of the problem s proposed and then appled to several numercal examples. We analyze the mpact of the cost of CSR on the nvestment level n CSR actvtes. We found that as the cost of CSR actvtes ncreases the frm wll have less ncentve to nvest n them. Here, as n McWllams and Segel (2001), the deal level of CSR should be determned by a long term cost beneft analyss. In the short run, the cost of CSR may seem hgh, however, ths cost would be less n the long run compared to the cost of lablty for polluton, complance wth regulaton, dangerous operatons, use of hazardous raw materals, producton of hazardous waste, and for health and safety ssues. Moreover, these labltes may cost companes ther reputaton (Dowlng, 2001; Frombrun, 2001), brand mage, sales, access to markets and fnancal nvestments (Feldman et al., 1997). In concluson, managers should treat ther decson regardng CSR as they treat all ther long term nvestment decsons. 20

21 The numercal examples hghlght that the best outcome for the supply chan as a whole mght not always be acheved f each member n the supply chan determnes the optmal levels of CSR only based on hs/her own costs and benefts. It s mportant that CSR actvtes are coordnated among dfferent frms n the supply chan. Increased coordnaton among frms n the supply chan leads to a multtude of addtonal postve effects. It has the potental to reduce network related rsk (Johnson, 2001; Norrman and Jansson, 2004). Furthermore, Smpson and Power (2005) ndcate that strong relatonshps n the network are capable of leadng to programs of collaboratve waste reducton, envronmental nnovaton at the nterface, cost-effectve envronmental solutons, the rapd development and uptake of nnovaton n envronmental technologes, and allows frms to better understand the envronmental mpact of ther supply chans. The model s flexble enough to analyze how dfferent objectves of frms (McWllams and Segel, 2001), legal and nsttutonal factors (Wllams and Agulera, 2008), and country dfferences (Matten and Moon, 2008) mpact optmal CSR levels. The model developed n ths paper provdes a foundaton for future studes that attempt to test assumptons n the conceptual lterature. As a frst step t s necessary to emprcally valdate the followng relatonshps: 1) the relatonshp between levels of socal responsblty actvtes and transacton costs; 2) the relatonshp between levels of socal responsblty actvtes and total emsson (waste) generated; and 3) the CSR\Rsk\Proft relatonshps. Second, as operatons of the frms become more globalzed t s mportant to analyze how the concept of CSR s appled n dfferent countres wth dfferent culture, as well as rules and regulaton. Future research wll also nclude the extenson of ths framework to the nternatonal arena. Fnally, we shall develop a dynamc model that takes nto consderaton the rate of change n prce, cost, rsk and proft as the nvestment n CSR ncreases or decreases over tme. Acknowledgements The authors gratefully acknowledge the constructve and helpful comments of two anonymous referees on the earler verson of the manuscrpt. References Arraga, A., Busness and human rghts. Amnesty Internatonal USA. Avalable from < Bazaraa, M. S., Sheral, H. D., Shetty, C. M, Nonlnear programmng: Theory and algorthms. John Wley & Sons, New York. Berman, S. L., Wcks, A. C., Kotha, S., Jones, T. M, Does stakeholder orentaton 21