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1、298Vol.29, No.820098Systems Engineering Theory &PracticeAug., 2009:1000-6788(200908-0028-08(, 510632Stackelberg Stackelberg Nash,. :, . ,. , . , .; ;F224.32AClosed-loop supply chain game models with product remanufacturingYI Yu-yin(Schoolof Management, Jinan University, Guangzhou 510632, ChinaAb
2、stract The closed-loop supply chain game models with product remanufacturing are studied under three market structures, Manufacturer-Stackelberg market, Retailer-Stackelberg market, and Manufacturer and Retailer-Nash market. The optimal product return rates, wholesale price, retail prices, manufactu
3、rer and retailersprotsand total channel protsare analyzed under the three market power structures. The results show that the return rate is highest when there is no market leadership, lowest when Retailer is leader. The wholesale price is highest when Manufacturer is leader, lowest when Retailer is
4、leader. The retail price is highest when Retailer is leader, lowest when there is no market leadership. The industry as a whole as well as consumer benetfrom lower prices and larger protswhen there is no market leadership. However, an individual member has an incentive to play the leadersrole.Keywor
5、ds remanufacturing; closed-loop supply chain; game1, ,:, , . , . , , , , . , WTO8:2930298:31(6C (b A (A , p N =(4C (b A (A +2Ccm6C (b A (A 1, , 1 ; 2; 3 (. pN b>0, wN 12 . 1, . , w N , p N N (2(1, N M =4C 2(cm 2(6C (A (b A 2N T =C (8C (b A 2(cm 2(4C (A b 2 , M =(b A (w2(b (b A (cm (4C (A (b A , M
6、 =(b A (cm 3229b<0, M b>0(b >5+3A2(4C (b A (A , M R =C (4C (b A 2(cm 24(4C (b A (A 25, b =.M M, b , . , b =.5:,. , , .5-Stackelberg, , :1 p 2 w, ,.(5,w R =p+cm (b (8C (A 2 , R =(A (c m (8C (A 27, , 1 ; 2; 3 .pR b=0, wR (8C (A 2 2, R R =C (cm 2à × ¨ , , , , ° éè
7、 à ó ¨ í ì ê éè y ò × á ਠut ¨ . 9. 9 10 9 8 , : . M N R M = . . , wR < wN < wM . , . , , , 1 ± °¨ ¨§¤ u ¨ ¨ s T R ¨ E ¨Dz s I H w ¨ E ¨D '%eG á d & l
8、 "F o i k ¨ E t C B I ¨D TS ggggS A b b ± ¨ A g S I a $ é S h! m i%$6 c ¨ 4 t 97 8 ¨ e ü h k t iy 7 % $ 6 g ec gfXuh l , , 7 . b A, , R R R T = M + R = × : e 8 6 xw y z s x w v u t r q p o n l mmmmk j ihgfe d y u x w v u t s aWWaaWfWecaWXWWRRSRQRP r
9、q p i o n h g d b q Y V U T b = , 1. -Stackelberg , , C(12C ( A2 ( cm 2 (8C ( A2 2 . 8 b A, . . , b = . . . . , -Stackelberg xw | p M w , (4C ( A2 + 2Ccm (6C ( A2 ( A( cm 6C ( A2 2C + (4C ( A2 cm (6C ( A2 4C 2 ( cm 2 (6C ( A2 2 C(4C ( A2 ( cm 2 (6C ( A2 2 C(8C ( A2 ( cm 2 (6C ( A2 2 , R < M <
10、N . ( A3 ( cm <0 2(8C (A 2 (4C (A 2 (2C ( A2 ( cm ( A = <0 2(4C (A 2 (6C (A 2 5 (3C ( A2 + Ccm (4C ( A2 ( A( cm 8C 2( A2 + cm 2 C( cm 2 2(4C ( A2 C( cm 2 4(4C ( A2 3C( cm 2 4(4C ( A2 . , : , . (6C ( A2 + 2Ccm (8C ( A2 ( A( w 8C ( A2 2C + (6C ( A2 cm (8C ( A2 4C 2 ( cm 2 (8C ( A2 2 C( cm 2 (8C
11、( A2 C(12C ( A2 ( cm 2 (8C ( A2 2 . 1 33 h & F g c 8 d f& dc (' B E D ê I W # " ê Q ó X 8 ¨ Y DVUT C B E B , R M N T < T < T . ê e ¨ Q ' P ¨ F s a F Q P G R F 7 ' I H . , , . 12 , : ° &ê ¨ 0 (' é è &qu
12、ot; # ! 11. 11 12 , : . , pN p M = pM pR ° 8 , q . R 7 ' ¨ 6 5 4 ( 3 2 1 ° % $ ¤ t . . , , , ± ° ° ¨ § ¨ § ¨ ¤ t éè ¤ ± 34 . 10. 10 11 . : , wN wM wR wN = pN < pM < pR . , 4C 2 ( cm <0 (8C (A 2 (6C (A 2
13、 (2C (A 2 ( cm <0 = 2(6C (A 2 , , . , q R < q M < q N . , . ü ú ù ÷ WWWWaWWW qN . R M N T < T < T . M N R R < R < R . R N M M < M < M . ± 12 N R R R M N R R = : Hbs ! S A¨ 9 . , , R M T T M N T T = . , N M M M R N M M = , C(28C 2 20C(A 2 + 3 2
14、 (A 4 ( cm 2 <0 4(6C (A 2 2 (4C (A 2 4C 3 ( cm 2 = <0 (8C (A 2 (6C (A 2 2 C(20C 2 12C(A 2 + 2 (A 4 ( cm 2 <0 4(6C (A 2 2 (4C (A 2 C(16C (A 2 (A 2 ( cm 2 = <0 4(4C (A 2 (8C (A 2 2 16C 3 (7C (A 2 ( cm 2 <0 (8C (A 2 2 (6C (A 2 2 C(2C (A 2 2 ( cm 2 = <0 2(6C (A 2 2 (4C (A 2 . C(2C (A 2
15、 ( cm (6C (A 2 (4C (A 2 C(A 2 ( cm = (4C (A 2 (8C (A 2 : R N M M < M < M , , M N R R < R < R . < qM < 29 , 1 Spengler T, Pue chert H, Penkuhn T, et al. Environmental integrated production and recycling managementJ. European Journal Operation Research, 1997, 97: 308326. 2 Jayaraman
16、V, Guide Jr V D R, Srivastava R. A closed-loop logistics model for remanufacturingJ. Journal of the Operational Research Society, 1999, 50: 497508. 3 Jayaraman V, Patterson R A, Rolland E. The design of reverse distribution networks: Models and solution procedures J. European Journal of Operational
17、Research, 2003, 150(2: 128149. 4 , , . J. , 2005, 23(1: 7478. Ma Z J, Dei Y, Liu F. Robust optimal design of remanufacturing logistics networksJ. Systems Engineering, 2005, 23(1: 7478. 5 , , . J. , 2006, 17(8: 809813. Dai Y, Ma Z J, Liu F. Optimization model for closed-loop logistics network design
18、in a remanufacturing environmentJ. Chinese Mechanical Engineering, 2006, 17(8: 809813. , , . J. , 2007, 18(4: 442445. 6 Yue H, Zhong X Y, Ye H Z. Stochastic optimal design of remanufacturing reverse logistics networkJ. Chinese Mechanical Engineering, 2007, 18(4: 442445. 7 Savaskan R, Bhattacharya C
19、S, Van Wassenhove L. Closed-loop supply chain models with product remanufacturingJ. Management Science, 2004, 50: 239253. 8 Savaskan R C, Van Wassenhove L. Reverse channel design: The case of competing retailersJ. Management Science, 2006, 52: 114 9 Chan C S. Price competition in a channel structure with a common retailerJ. Marketing Science, 1991, 10(4: 271296. 10 Chan C S. Price competition in a duopoly common retailer channelJ. Journal of Retailer, 1996, 72(2: 117134. 11 Park
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