×

Differential game analyses of logistics service supply chain coordination by cost sharing contract. (English) Zbl 1442.90022

Summary: Cooperation of all the members in a supply chain plays an important role in logistics service. The service integrator can encourage cooperation from service suppliers by sharing their cost during the service, which we assume can increase the sales by accumulating the reputation of the supply chain. A differential game model is established with the logistics service supply chain that consists of one service integrator and one supplier. And we derive the optimal solutions of the Nash equilibrium without cost sharing contract and the Stackelberg equilibrium with the integrator as the leader who partially shares the cost of the efforts of the supplier. The results make the benefits of the cost sharing contract in increasing the profits of both players as well as the whole supply chain explicit, which means that the cost sharing contract is an effective coordination mechanism in the long-term relationship of the members in a logistics service supply chain.

MSC:

90B06 Transportation, logistics and supply chain management
91A23 Differential games (aspects of game theory)
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Choy, K. L.; Li, C. L.; So, S. C. K.; Lau, H.; Kwok, S. K.; Leung, D. W. K., Managing uncertainty in logistics service supply chain, International Journal of Risk Assessment and Management, 7, 1, 19-25 (2007) · doi:10.1504/IJRAM.2007.011408
[2] Li, X. H.; Wang, Q. N., Coordination mechanisms of supply chain systems, European Journal of Operational Research, 179, 1, 1-16 (2007) · Zbl 1161.90309 · doi:10.1016/j.ejor.2006.06.023
[3] Cachon, G. P.; deKok, A. G.; Graves, S. C., Supply chain coordination with contracts, Supply Chain Management: Design, Coordination and Operation, 229-340 (2003), Amsterdam, The Netherlands: Elsevier, Amsterdam, The Netherlands · Zbl 1101.90311
[4] Pasternack, B. A., Optimal pricing and return policies for perishable commodities, Marketing Science, 27, 1, 166-176 (2008)
[5] Anupindi, R.; Bassok, Y., Centralization of stocks: retailers vs. manufacturer, Management Science, 45, 2, 178-191 (1999) · Zbl 1231.90007
[6] Chen, F.; Federgruen, A.; Zheng, Y.-S., Coordination mechanisms for a distribution system with one supplier and multiple retailers, Management Science, 47, 5, 693-708 (2001) · Zbl 1232.90109
[7] Dong, L.; Rudi, N., Supply Chain Interaction under Transshipments (2001), Washington University
[8] Lariviere, M. A.; Porteus, E. L., Selling to the newsvendor: an analysis of price-only contracts, Manufacturing and Service Operations Management, 3, 4, 293-305 (2001)
[9] Ni, D.; Li, K. W.; Tang, X., Social responsibility allocation in two-echelon supply chains: insights from wholesale price contracts, European Journal of Operational Research, 207, 3, 1269-1279 (2010) · Zbl 1206.91054 · doi:10.1016/j.ejor.2010.06.026
[10] Wang, X. H.; Wang, X. Y.; Su, Y. S., Wholesale-price contract of supply chain with information gathering, Applied Mathematical Modelling, 37, 6, 3848-3860 (2013) · Zbl 1270.91023
[11] Bassok, Y.; Anupindi, R., Analysis of contracts with total minimum commitment, IIE Transactions, 29, 5, 373-381 (1997)
[12] Tsay, A. A.; Lovejoy, W. S., Quantity flexibility contracts and supply chain performance, Manufacturing and Service Operations Management, 1, 2, 118-149 (1999)
[13] Plambeck, E. L.; Taylor, T. A., Sell the plant? The impact of contract manufacturing on innovation, capacity, and profitability, Management Science, 51, 1, 133-150 (2005) · doi:10.1287/mnsc.1040.0212
[14] Yazlali, Ö.; Erhun, F., Relating the multiple supply problem to quantity flexibility contracts, Operations Research Letters, 35, 6, 767-772 (2007) · Zbl 1180.90108 · doi:10.1016/j.orl.2007.01.002
[15] Lian, Z. T.; Deshmukh, A., Analysis of supply contracts with quantity flexibility, European Journal of Operational Research, 196, 2, 526-533 (2009) · Zbl 1163.90336 · doi:10.1016/j.ejor.2008.02.043
[16] Karakaya, S.; Bakal, I. S., Joint quantity flexibility for multiple products in a decentralized supply chain, Computers & Industrial Engineering, 64, 2, 696-707 (2013)
[17] Padmanabhan, V.; Png, I. P. L., Returns policies: make money by making good, Sloan Management Review, 65-72 (1995)
[18] Taylor, T., Channel coordination under price protection, midlife returns, and end-of-life returns in dynamic markets, Management Science, 47, 9, 1220-1234 (2001)
[19] Yao, Z.; Leung, S.; Lai, K. K., Analysis of the impact of price-sensitivity factors on the returns policy in coordinating supply chain, European Journal of Operational Research, 187, 1, 275-282 (2008) · Zbl 1149.90019 · doi:10.1016/j.ejor.2007.03.025
[20] Wang, Y. L.; Zipkin, P., Agents’ incentives under buy-back contracts in a two-stage supply chain, International Journal of Production Economics, 120, 2, 525-539 (2009) · doi:10.1016/j.ijpe.2009.04.008
[21] Hou, J.; Zeng, A. Z.; Zhao, L., Coordination with a backup supplier through buy-back contract under supply disruption, Transportation Research E: Logistics and Transportation Review, 46, 6, 881-895 (2010) · doi:10.1016/j.tre.2010.03.004
[22] Xiong, H. C.; Chen, B. T.; Xie, J. X., A composite contract based on buy back and quantity flexibility contracts, European Journal of Operational Research, 210, 3, 559-567 (2011) · Zbl 1213.90070 · doi:10.1016/j.ejor.2010.10.010
[23] Dana, J.; Spier, K. E., Revenue sharing and vertical control in the video rental industry, Journal of Industrial Economics, 49, 3, 223-245 (2001)
[24] Cachon, G. P.; Lariviere, M. A., Supply chain coordination with revenue-sharing contracts: strengths and limitations, Management Science, 51, 1, 30-44 (2005) · Zbl 1232.90173 · doi:10.1287/mnsc.1040.0215
[25] Yao, Z.; Leung, S. C. H.; Lai, K. K., Manufacturer’s revenue-sharing contract and retail competition, European Journal of Operational Research, 186, 2, 637-651 (2008) · Zbl 1138.91527 · doi:10.1016/j.ejor.2007.01.049
[26] Linh, C. T.; Hong, Y. S., Channel coordination through a revenue sharing contract in a two-period newsboy problem, European Journal of Operational Research, 198, 3, 822-829 (2009) · Zbl 1176.90172 · doi:10.1016/j.ejor.2008.10.019
[27] Pan, K.; Lai, K. K.; Leung, S. C. H.; Xiao, D., Revenue-sharing versus wholesale price mechanisms under different channel power structures, European Journal of Operational Research, 203, 2, 532-538 (2010) · Zbl 1177.91075 · doi:10.1016/j.ejor.2009.08.010
[28] Chen, J. M.; Cheng, H. L.; Chien, M. C., On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand, Applied Mathematical Modelling, 35, 10, 4886-4901 (2011) · Zbl 1228.90046 · doi:10.1016/j.apm.2011.03.042
[29] Omkar, D. P. D., Supply chain coordination using revenue-dependent revenue sharing contracts, Omega, 41, 4, 780-796 (2013)
[30] Kannan, G.; Maria, N. P., Reverse supply chain coordination by revenue sharing contract: a case for the personal computers industry, European Journal of Operational Research, 233, 2, 326-336 (2014) · Zbl 1305.90057
[31] Wu, D. J.; Kleindorfer, P. R., Competitive options, supply contracting, and electronic markets, Management Science, 51, 3, 452-468 (2005) · doi:10.1287/mnsc.1040.0341
[32] Wang, X.; Liu, L., Coordination in a retailer-led supply chain through option contract, International Journal of Production Economics, 110, 1-2, 115-127 (2007) · doi:10.1016/j.ijpe.2007.02.022
[33] Zhao, Y. X.; Wang, S. Y.; Cheng, T. C. E.; Yang, X. Q.; Huang, Z. M., Coordination of supply chains by option contracts: a cooperative game theory approach, European Journal of Operational Research, 207, 2, 668-675 (2010) · Zbl 1205.90061 · doi:10.1016/j.ejor.2010.05.017
[34] Liang, L.; Wang, X. H.; Gao, J. G., An option contract pricing model of relief material supply chain, Omega, 40, 5, 594-600 (2012) · doi:10.1016/j.omega.2011.11.004
[35] Zhao, Y. X.; Ma, L. J.; Xie, G.; Cheng, T. C. E., Coordination of supply chains with bidirectional option contracts, European Journal of Operational Research, 229, 2, 375-381 (2013) · Zbl 1317.90062
[36] Leng, M. M.; Parlar, M., Game-theoretic analyses of decentralized assembly supply chains: Non-cooperative equilibria vs. coordination with cost-sharing contracts, European Journal of Operational Research, 204, 1, 96-104 (2010) · Zbl 1178.90043 · doi:10.1016/j.ejor.2009.10.011
[37] Kunter, M., Coordination via cost and revenue sharing in manufacturer-retailer channels, European Journal of Operational Research, 216, 2, 477-486 (2012) · Zbl 1237.90125 · doi:10.1016/j.ejor.2011.07.001
[38] Tsao, Y. C.; Sheen, G. J., Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers and Operations Research, 39, 8, 1872-1878 (2012) · Zbl 1251.90041 · doi:10.1016/j.cor.2011.07.009
[39] Wei, Y. H.; Hu, Q. Y., Ordering, pricing and allocation in a service supply chain, International Journal of Production Economics, 144, 2, 590-598 (2013)
[40] Liu, W. H.; Xu, X. C.; Kouhpaenejad, A., Deterministic approach to the fairest revenue-sharing coefficient in logistics service supply chain under the stochastic demand condition, Computers & Industrial Engineering, 66, 1, 41-52 (2013)
[41] Cui, A. P.; Liu, W., Study on capability coordination in logistics service supply chain with options contract, Chinese Journal of Management Science, 17, 2, 59-65 (2009)
[42] Lu, Q. H., Coordinate with cost sharing strategy for service supply chain, Control and Decision, 26, 11, 1649-1653 (2011)
[43] Prasad, A.; Sethi, S. P., Competitive advertising under uncertainty: a stochastic differential game approach, Journal of Optimization Theory and Applications, 123, 1, 163-185 (2004) · Zbl 1114.90050 · doi:10.1023/B:JOTA.0000043996.62867.20
[44] Jørgensen, S.; Taboubi, S.; Zaccour, G., Retail promotions with negative brand image effects: is cooperation possible?, European Journal of Operational Research, 150, 2, 395-405 (2003) · Zbl 1137.90573 · doi:10.1016/S0377-2217(02)00641-0
[45] Navas, J.; Marín-Solano, J., Interactions between government and firms: a differential game approach, Annals of Operations Research, 158, 1, 47-61 (2008) · Zbl 1142.91021 · doi:10.1007/s10479-007-0248-3
[46] Jørgensen, S.; Taboubi, S.; Zaccour, G., Cooperative advertising in a marketing channel, Journal of Optimization Theory and Applications, 110, 1, 145-158 (2001) · Zbl 0980.91006 · doi:10.1023/A:1017547630113
[47] Fombrun, C. J.; Rindova, V., Who’s tops and who decides? The social construction of corporate reputations, Working Paper (1996), Stern School of Business, New York University
[48] Nha, N.; Gaston, L., Corporate image and corporate reputation in customers. Retention decisions in services, Journal of Retailing and Consumer Services, 8, 227-2361 (2001)
[49] Nerlove, M.; Arrow, K. J., Optimal advertising policy under dynamic conditions, Economica, 39, 129-142 (1962)
[50] Saxton, K., Where do reputations come from?, Corporate Reputation Review, 1, 4, 393-399 (1998)
[51] Nagler, M. G., An exploratory analysis of the determinants of cooperative advertising participation rates, Marketing Letters, 17, 2, 91-102 (2006) · doi:10.1007/s11002-006-4387-0
[52] Dockner, E.; Jorgensen, N.; Van, L., Differential Games in Economics and Management Science (2000), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 0996.91001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.