Proceedings of the 2nd International Conference On Systems Engineering and Modeling (ICSEM-13)

Transcription

1 Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) Research on the Proft Dstrbuton of Logstcs Company Strategc Allance Based on Shapley Value Huang Youfang 1, a, Ye Welong 1,b and Zhou Fefe 1,c 1 Shangha Martme Unversty, Chna a yhuang@shmtu.edu.cn, b sqhuang@163.com, c aprlzet@126.com Key Words: Shapley value; Strategc allance; Logstc company; Internatonalzaton Abstract. Strategc allance s an mportant busness mode for Chnese logstcs companes nternatonalzaton, and the proft dstrbuton among companes s the key ssue mantanng the allance s stablty. Ths artcle tres to solve the proft dstrbuton ssues n the nternatonal strategc allance based on Shapley value, meanwhle, ponts out the problems stll reman n the orgnal model, establshes a new model by revsng Shapley value method based on consderng elements ncludng rsks, nvestments, extra contrbuton and company capablty. The new model has been tested and verfed, and can ensure more reasonable proft dstrbuton among allance members, and can beneft the persstency of the allance. Introducton The total value of logstcs n Chnese socety reached the number of trllon Yuan n 2010, ncreased by 15%. The coeffcent of logstcs demand s 1:3.13, whch means every GDP output needs 3.13 unts of support from logstcs. Meanwhle, the foregn drect nvestment of Chna has ncreased 1.2 tmes snce 5 years ago. Wth the development of both the logstcs ndustry and the foregn trade, logstcs servce must support the growth wth lower cost and hgher effcency, local companes gong global s more than necessary. However, t s hard for a sngle company to realze the nternatonalzaton due to the complcated operatons and lmted resources. Companes can unte the enterprses that have advantages n dfferent parts of the nternatonal supply chan through strategc allance. The fnal purpose of a strategc allance s to optmze each members own benefts. The method of proft dstrbuton affects the stablty and the profts of the allance drectly. Thus, there are numbers of researches on the methods of dstrbutng proft. Durng 1950s, Nash and Shapley researched on the problem usng game theory. The method of Shapley value was put forward by Shapley L.S., and s a mathematc way amng to solve the dstrbuton problems among multple members. Chen Zh and Duan Gujun(2005) revsed Shapley model by ntroducng a comprehensve factor G; Zhang Yawen(2009) revsed Shapley model by takng nto account the possble relatonshp wthn the allance; L Ouyang(2011) establshed a horzontal proft dstrbuton model for strategc allance for 3rd-party logstcs companes. Ths paper focuses on the research and presentaton of Shapley Value method, and revses the model by combnng the facts of Chnese logstcs companes nternatonalzaton. Shapley Value Method[1] When there are multple companes n pursut of profts whle ther actvtes are not aganst each other, the ncrease of cooperaton among members won t decrease benefts. The cooperaton among the total N enterprses wll brng the maxmum beneft V(N). Assume a set N = { 1,2...n}, f any subset S( S N ) corresponds to an egenfuncton V(S), there nto Eq. 1. V ( ) = 0, V( S1 S2) V( S1) + V( S2), S1 S2 =,( S1 N, S2 N). (1) V(S) practcally means the proft created by strategc allance S, and s the maxmum total revenue among the members of S. [N,V] s called the cooperatve game among n people. X means Publshed by Atlants Press, Pars, France. 0205

2 Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) company s maxmum gross ncome n the cooperaton whch reaches the maxmum beneft V(N). In the cooperaton N the cooperatve game dstrbuton strategy can be shown as x = ( x1, x2... xn ). The allance can only be successful wth the condtons that n x = V N) = 1 (,and x V ( ), = 1,2... n. The beneft got by each member under strategc allance N s called Shapley Value, based on Shapley method, wrtten as ( V ),( = 1,2,... n), the soluton s Eq. 2 and Eq. 3. s stands for the numbers of elements n the subset S; n stands for the numbers of elements n set N. V( s the benefts under the combnaton of subset S; w ( s ) s a weghted term; v ( s \ ) stands for the benefts of S after removng the beneft of company. ( V) = w( [ v( s\ )], = 1, 2,..., n. (2) S S ( n s )!( s 1)! w( s ) =. (3) n! Shapley Value s a weghted average n consder of the contrbutons gven by the members n the strategc allance. The model takes nto account the contrbutons of each member to the total outcome of the strategc allance, and reflects the mportance of each member to the allance s benefts. The Revsed Shapley Value Method[2,3] Shapley value method assumes that each member faces the exactly same nfluental factors, whch s mpossble n practce. The nfluental factors nclude the rsks each member faces, the captal nvested n the allance, the extra contrbuton made to the allance durng cooperaton and the comprehensve strength dfferences of each member respectvely. These factors should be consdered n the Shapley model to better reflect the real stuaton, thus a more reasonable proft dstrbuton wll be made. The Rsk Revson Factor. Frst of all, dfferent companes favor dfferent rsks, even n cooperaton each member s confronted wth rsks of dfferent knds. The nternatonal logstcs allance should embody the prncple of sharng both the benefts and rsks. The company whch undertakes bgger rsks should get more benefts. However n Shapley model, t assumes each member faces rsks of 1/n, whch means an average level. Now a rsk revson factor Δ r = r -1/n s ntroduced to the model. r stands for the rsks faced by company, and could be calculated by usng comprehensve fuzzy evaluaton. The value dfference Δ r s the revson to dfferent rsks faced. When r 0, t means company confronts a hgher rsk level than average, whch means t should get more proft as Δr ϕ(v) ; When r 0, t means that the company s wth lower rsk, and ts beneft should be reduced by Δr ϕ(v). Thus, by ntroducng a rsk factor nto the model, company should get beneft as Eq. 4. ϕ (v) = ϕ(v) + Δr ϕ(v). (4) The Investment Proporton. Regardless of a companys scale or compettveness, the captal nvested n the allance by each member should be taken nto consderaton. Certan weght should be attached to show the nflow captal, equpment, staff, brand value and the market value nvested by each company. The nvestment vector can be wrtten as I = {I1,I2,..In}; the proft dstrbuton after revson s Eq. 5. n ϕ (v) = I/( I) (N), = (1,2,..,n). (5) = 1 The Compensaton for Extra Contrbuton. The coeffcent of compensaton for extra contrbuton s θ [0,1]. In the practcal operaton of logstcs, emergences lke transportaton delay and cost ncrease n stock control due to terrble weather, transportaton equpment damage, exchange rate fluctuaton n nternatonal trades constantly brng extra fees to allance members. Publshed by Atlants Press, Pars, France. 0206

3 Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) Consderatons should be gven to t durng proft dstrbuton. The value of the coeffcent can be determned by negotaton among allance members accordng to the stuaton. After θ s determned, the real revson amount of extra contrbuton can be wrtten as Δ e = θ -1/ n. So the actual dstrbuted proft should be Eq. 6. ϕ (v) = ϕ(v) + Δe (N). (6) The Revson Consderng the Comprehensve Strength. In Shapley method t s assumed that the members n the strategc allance have more or less the same strength. However, there are plenty of typcal allances consst of both strong and weak members. The comprehensve strength of a logstcs company can nclude the scale of the company, the core compettveness, brand, strategc management ablty and so on. If a member has a strong comprehensve ablty, certan addtonal proft should be dstrbuted to t to mantan the stablty of the allance. AHP (Analytc Herarchy Proces method could be used to decde the weght of the comprehensve ablty. The weght vector can be expressed as w = {w1, w 2,..,w n}. Use the weghted vector to revse the factor as Δ w = w -1/ n. Thus, the revsed dstrbuton amount s Eq. 7. ϕ (v) = ϕ (v) + Δw (N). (7) Algorthm Assume a strategc allance conssts of 3 companes, A, B and C. If the 3 companes run separately, company A can realze a proft of 100 thousand, B can get 300 thousand whle C get 150 thousand. If A and B cooperate as an allance, the beneft wll be 600 thousand; f A and C cooperate, the proft s 400 thousand, f B and C, the beneft wll be 750 thousand. If A, B and C found a strategc allance, they would realze a 1500-thousand proft. If the 3 companes share the proft, each wll get 500 thousand. Although ths ncome s hgher than what they can get f they run the busness separately, the companes are not nterested n t. The Applcaton of Shapley Value Method. The strategc allance of the 3 companes s N={1,2,3}; ther respectve benefts are v(1)=100, v(2)=300, v(3)=150. The beneft earned by company A and B s v(1 2) =600, A and C s v(1 3) =400, B and C s v() =750, the 3 together s v(1 ) =1500. The proft of company A n dfferent allances s shown n Table 1. Add the fgures n the last row of the dagram and we can get the Shapley Value of company A s 375 thousand. In the same way, we can get company B and company C s proft dstrbuton. As shown n Table 2 and Table 3. Company B can get a proft of 650 thousand whle company C gets 475 thousand. The Shapley value method dstrbuton shows how mportant each member s to the whole strategc allance. In the dstrbuton, v (1 ) = 1500, meanwhle, the beneft summaton of every 2 companes n the 3-company allance s hgher than 2-company allance, thus ths s the most stable allance. The prncple of dstrbutng accordng to contrbuton n Shapley value gets rd of the dsadvantages of dvdng the proft equally, thus to nterest members and brng stablty to the allance. Table 1 the Proft Dstrbuton to Company A S v(s) v (s \1) v( s \1) s \1)] 100/ /6 250 Table 2 the Proft Dstrbuton to Company B S v(s) Publshed by Atlants Press, Pars, France. 0207

4 Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) v (s \ 2) v( s \ 2) s \ 2)] / /3 Table 3 the Proft Dstrbuton to Company C S v(s) v (s \ 3) v( s \ 3) s \ 3)] / /3 The Applcaton of Revsed Shapley Value Model. Frstly, ntroduce n the rsk factor. Assume by usng a comprehensve fuzzy evaluaton method we get the coeffcents of the rsks the 3 companes n cooperaton face, whch are r 1 =0.3, r 2 =0.3, r 3 =0.4; accordng to Δ r = r -1/n, the rsk revsed factor can be calculated as Δ r 1 = -1/ 30, Δ r 2 = -1/ 30, Δ r 3 = 1/15. Thus after ntroducng the rsk factors nto the model, each company s benefts dstrbuted are φ (v) 1 =362.5, φ (v) 2 =628.33, φ (v) 3 = Secondly, ntroduce n the nvestment weght. Assume that the 3 companes nvested 300, 450 and 350 thousand Yuan respectvely on jonng the allance (ncludng ntangble value), the revsed Shapley value can be calculated as φ (v) 1 =409.09, φ (v) 2 =613.64, φ (v) 3 = Thrdly, ntroduce n the compensaton for extra contrbuton. Assume that the coeffcents of each company for extra contrbuton are θ 1 =0.3, θ 2 =0.4, θ 3 =0.3 accordng to the negotaton, G3=0.3, thus the revsed values consderng extra contrbuton are Δe 1-1/30, Δ e2 =1/15, Δ e3 =-1/30. The revsed Shapley values are φ (v) 1 =325, φ (v) 2 =750, φ (v) 3 =425 respectvely. Fourthly, revse accordng to the comprehensve strength. Assume that the weghts of comprehensve strength of the 3 companes are w 1 =0.2, w 2 =0.5, w 3 =0.3 usng AHP method, the revsed value dfferences are Δ w1 =-2/15, Δ w 2 =1/6, Δ w 3 =-1/30. Thus the proft dstrbuton taken comprehensve ablty of each company nto consderaton should be φ (v) 1 =175, φ (v) 2 =900, φ (v) 3 =425. The Comparson of Methods Assume that the weght of each revsed factor usng AHP method s 0.4, 0.3, 0.2 and 0.1 respectvely, the fnal proft dstrbuton method usng the revsed Shapley value model s shown n Table 4. The fnal proft dstrbuton method consderng all the factors s that company A gets thousand Yuan, company B gets thousand Yuan and company C gets thousand Yuan. The revsed Shapley model gets rd of the dsadvantages of average dstrbuton, and exceeds Shapley model tself n better reflectng the real condtons. Usng ths dstrbuton method, each member n the strategc allance obtans more ncome than by runnng solely or n 2-member allance, whch contrbutes to the stablty of the allance. Table 4 the Dfferent Dstrbuton Methods Comparson Dstrbuted Proft A B C Weght Runnng Separately Dstrbute Averagely Shapley Value Method Wth Rsk Factor Wth Investment Factor Extra Contrbuton Strength Factor Fnal Dstrbuton Publshed by Atlants Press, Pars, France. 0208

5 Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) Concluson In order to solve the proft dstrbuton problem n strategc allances, Shapley model consders how much each member contrbutes to the total ncome of the allance; provdes a better dstrbuton method than the average one. However, the condtons assumed n Shapley model that each member company confronts the same envronment s nflexble n real condtons. The revsed Shapley value ntroduces factors such as rsk, nvestment, extra contrbuton and companes comprehensve strength nto the model, whch makes Shapley model more flexble and more realstc. Through the examples, a comparatvely reasonable dstrbuton method can be obtaned. References [1] Chen Zh, Duan Gujun. Research on the Proft Dstrbuton of Lner Shppng Allance Based on Shapley Value [J]. Journal of Transportaton Engneerng and Informaton, 2005, No.4 Vol.3:55-64 [2] L Ouyang. Research on the Interests Dstrbuton of the Thrd-party Logstcs Enterprses Strategc Allance [D]. Central South Unversty,2011 [3] Ju Xaotao, Xu Q. Rsk-consdered Shapley Proft Dstrbuton Model of Apparel Supply Chan[J].Logstcs Technology, 2009,No.12 Vol.28: [4] M. Frsk, M. Göthe-Lundgren, K. Jörnsten, M. Rönnqvst. Cost allocaton n collaboratve forest transportaton[j]. European Journal of Operatonal Research, 2010, 205(2): [5] Tan X, Le TT. Applcaton of the Shapley value on transmsson cost allocaton n the compettve power market envronment[j]. IEE Proceedngs Generaton, Transmsson and Dstrbuton, 2002, 149(1):15-20 Publshed by Atlants Press, Pars, France. 0209