Pricing decisions of complementary products in a two-level fuzzy supply chain

Pricing decisions of two complementary products in a two-level fuzzy supply chain with two manufacturers and one common retailer are studied in this paper. By considering the two manufacturers and one common retailer’s leader–follower relationship, the two manufacturers’ pricing strategy and the fuzzy uncertainties associated with the manufacturing costs and customer demands of the complementary products, seven pricing games are considered. The corresponding closed-form optimal pricing decisions are obtained in the seven pricing games. Through using numerical studies and sensitivity analysis of parameters’ fuzzy degree, we compare the analytical results of different games and investigate the firms’ optimal decisions facing changing pricing environments. At last, we analyse the effect of the fuzzy degree of key parameters on optimal prices, maximal expected demands and maximal expected profits of different games. Some interesting and valuable managerial insights are established.

[1]  Samar K. Mukhopadhyay,et al.  A Bertrand model of pricing of complementary goods under information asymmetry , 2006 .

[2]  Sean X. Zhou,et al.  Exclusive Channels and Revenue Sharing in a Complementary Goods Market , 2011, Mark. Sci..

[3]  Hans-Jürgen Zimmermann,et al.  An application-oriented view of modeling uncertainty , 2000, Eur. J. Oper. Res..

[4]  Jean Jaskold Gabszewicz,et al.  On price competition with complementary goods , 2001 .

[5]  Tsan-Ming Choi,et al.  Price Wall or War: The Pricing Strategies for Retailers , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[6]  Chi-Bin Cheng,et al.  Group opinion aggregationbased on a grading process: A method for constructing triangular fuzzy numbers , 2004 .

[7]  Stephen M. Gilbert,et al.  Selling and Leasing Strategies for Durable Goods with Complementary Products , 2005, Manag. Sci..

[8]  Keith J. Burnham,et al.  A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand , 2006 .

[9]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[10]  M. Amparo Vila,et al.  A fuzziness measure for fuzzy numbers: Applications , 1998, Fuzzy Sets Syst..

[11]  D. Simchi-Levi,et al.  Coordination of Pricing and Inventory Decisions: A Survey and Classification , 2004 .

[12]  Juzhi Zhang,et al.  Supply chain pricing decisions with price reduction during the selling season , 2014 .

[13]  Yeu-Shiang Huang,et al.  Dynamic pricing for fashion goods with partial backlogging , 2014 .

[14]  Ruiliang Yan,et al.  The profit benefits of bundle pricing of complementary products , 2011 .

[15]  Bo Li,et al.  Dual-channel supply chain pricing decisions with a risk-averse retailer , 2014 .

[16]  Christopher S. Tang,et al.  Joint Ordering and Pricing Strategies for Managing Substitutable Products , 2007 .

[17]  Wansheng Tang,et al.  Two-echelon supply chain games in a fuzzy environment , 2008, Comput. Ind. Eng..

[18]  Jiang Zhang,et al.  Pricing and two-tier advertising with one manufacturer and one retailer , 2009, Eur. J. Oper. Res..

[19]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[20]  Oded Koenigsberg,et al.  Complementary Goods: Creating, Capturing, and Competing for Value , 2013, Mark. Sci..

[21]  Srinivasan Raghunathan,et al.  Retailer- vs. Vendor-Managed Inventory and Brand Competition , 2004, Manag. Sci..

[22]  W. Kamakura,et al.  Optimal Bundling and Pricing Under a Monopoly: Contrasting Complements and Substitutes from Independently Valued Products , 2003 .

[23]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  Wansheng Tang,et al.  Pricing decisions for substitutable products with a common retailer in fuzzy environments , 2012, Eur. J. Oper. Res..

[25]  Wansheng Tang,et al.  On the Continuity and Convexity Analysis of the Expected Value Function of a Fuzzy Mapping , 2007 .

[26]  Robert Handfield,et al.  Production, Manufacturing and Logistics Ðq ; Rþ Inventory Policies in a Fuzzy Uncertain Supply Chain Environment , 2022 .

[27]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[28]  Samar K. Mukhopadhyay,et al.  A Stackelberg model of pricing of complementary goods under information asymmetry , 2011 .

[29]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[30]  Kumar Rajaram,et al.  Joint pricing and inventory control with a Markovian demand model , 2007, Eur. J. Oper. Res..

[31]  Yongjian Li,et al.  Pricing decisions for complementary products with firms' different market powers , 2013, Eur. J. Oper. Res..

[32]  Jing Zhao,et al.  Reverse channel decisions for a fuzzy closed-loop supply chain , 2013 .