Annals of Operations Research

, Volume 242, Issue 2, pp 505–528 | Cite as

Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments

  • Jie Wei
  • Jing Zhao


This paper considers the pricing decisions of substitutable products which are produced by duopolistic manufacturers respectively and then sold by one common retailer to the consumers. Both the manufacturing cost and the customer demand for each product are characterized as fuzzy variables. Six expected value models are developed to explore the effects of the duopolistic manufacturers’ three pricing strategies (i.e. Bertrand competition, Stackelberg competition, cooperation) and vertical competition between the manufacturers and the retailer on the optimal pricing decisions and channel profit-split of a two echelon supply chain, and the corresponding analytical solutions are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed models, and to gain additional managerial insights.


Price decisions Substitutable products Fuzzy variable Game theory 



The authors wish to express their sincerest thanks to the editors and anonymous referees for their constructive comments and suggestions on the paper. We gratefully acknowledge the support of (i) National Natural Science Foundation of China, Nos. 71371186, and 71001106 for J. Wei; (ii) National Natural Science Foundation of China, Nos. 71301116, 71372100, and 71002106 for J. Zhao.


  1. Almehdawe, E., & Mantin, B. (2010). Vendor managed inventory with acapacitated manufacturer and multiple retailers: Retailer versus manufacturer leadership. International Journal of Production Economics, 128(1), 292–302.CrossRefGoogle Scholar
  2. Amid, A., Ghodsypour, S., & O’Brien, C. (2006). Fuzzy multiobjective linear model for supplier selection in a supply chain. International Journal of Production Economics, 104(2), 394–407.CrossRefGoogle Scholar
  3. Chen, J., & Bell, P. (2013). The impact of customer returns on supply chain decisions under various channel interactions. Annals of Operations Research, 206(1), 59–74.Google Scholar
  4. Choi, S. (1991). Price competition in a channel structure with a common retailer. Marketing Science, 10, 27l–296.CrossRefGoogle Scholar
  5. Ertek, G., & Griffin, P. (2002). Supplier- and buyer-driven channels in a two-stage supply chain. IIE Transactions, 34(8), 691–700.Google Scholar
  6. Giannaoccaro, I., Pontrandolfo, P., & Scozzi, B. (2003). A fuzzy echelon approach for inventory management. European Journal of Operational Research, 149, 185–196.CrossRefGoogle Scholar
  7. Handfield, R., Warsing, D., & Wu, X. (2009). (q, r) inventory policies in a fuzzy uncertain supply chain environment. European Journal of Operational Research, 197(2), 609–619.CrossRefGoogle Scholar
  8. Hu, W., & Li, Y. (2012). Retail service for mixed retail and e-tail channels. Annals of Operations Research, 192, 151–171.CrossRefGoogle Scholar
  9. Ingene, C., & Parry, M. (1995). Channel coordination when retailers compete. Marketing Science, 14(4), 360–377.CrossRefGoogle Scholar
  10. Ingene, C., & Parry, M. (2000). Is channel coordination all it is cracked up to be? Journal of Retailing, 76, 511–547.CrossRefGoogle Scholar
  11. Lau, H., & Lau, A. (2003). Effects of a demand-curves shape on the optimal solutions of a multi-echelon inventory/pricing model. European Journal of Operational Research, 147, 530–548.CrossRefGoogle Scholar
  12. Lee, E., & Staelin, R. (1997). Vertical strategic interaction: Implications for channel pricing strategy. Marketing Science, 16(3), 185–207.CrossRefGoogle Scholar
  13. Liang, T. (2006). Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 157, 1303–1316.CrossRefGoogle Scholar
  14. Liu, B. (2002). Theory and practice of uncertain programming. Heidelberg: Physica-Verlag.CrossRefGoogle Scholar
  15. Liu, S., & Kao, C. (2004). Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research, 153, 661–674.CrossRefGoogle Scholar
  16. McGuire, T., & Staelin, R. (1983). An industry equilibrium analyses of down stream vertical integration. Marketing Science, 2, 161–191.CrossRefGoogle Scholar
  17. Mehrbod, M., Tu, N., Miao, L., & Dai, W. (2012). Interactive fuzzy goal programming for a multi-objective closed-loop logistics network. Annals of Operations Research, 201, 367–381.CrossRefGoogle Scholar
  18. Petrovic, D., Roy, R., & Petrovic, R. (1998). Modelling and simulation of a supply chain in an uncertain environment. European Journal of Operational Research, 109(2), 299–309.CrossRefGoogle Scholar
  19. Petrovic, D., Xie, Y., Burnham, K., & Petrovic, R. (2008). Coordinated control of distribution supply chains in the presence of fuzzy customer demand. European Journal of Operational Research, 185(1), 146–158.CrossRefGoogle Scholar
  20. Ryu, K., & Ycesan, E. (2010). A fuzzy newsvendor approach to supply chain coordination. European Journal of Operational Research, 200(2), 421–438.CrossRefGoogle Scholar
  21. Sethi, S., Yan, H., & Zhang, H. (2005). Analysis of a duopoly supply chain and its application in electricity spot markets. Annals of Operations Research, 135(1), 239–259.CrossRefGoogle Scholar
  22. Sinha, S., & Sarmah, S. (2010). Coordination and price competition in a duopoly common retailer supply chain. Computers & Industrial Engineering, 59(2), 280–295.CrossRefGoogle Scholar
  23. Trivedi, M. (1998). Distribution channels: An extension of exclusive retailership. Management Science, 44, 896–909.CrossRefGoogle Scholar
  24. Wei, J., & Zhao, J. (2011). Pricing decisions with retail competition in a fuzzy closed-loop supply chainexpert systems with applications. Expert Systems with Applications, 38(9), 11209–11216.CrossRefGoogle Scholar
  25. Wu, C., Chen, C., & Hsieh, C. (2011). Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition. International Journal of Production Economics, 135(1), 265–274.CrossRefGoogle Scholar
  26. Xiao, T., & Qi, X. (2008). Price competition, cost and demand disruptions and coordination of a supply chain with one manufacturer and two competing retailers. Omega, 36, 741–753.CrossRefGoogle Scholar
  27. Xiao, T., Yu, G., Sheng, Z., & Xia, Y. (2005). Coordination of a supply chain with one-manufacturer and two-retailers under demand promotion and disruption management decisions. Annals of Operations Research, 135(1), 87–109.CrossRefGoogle Scholar
  28. Xie, Y., Petrovic, D., & Burnham, K. (2006). A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand. International Journal Production Economics, 102, 37–50.CrossRefGoogle Scholar
  29. Yang, S., & Zhou, Y. (2006). Two-echelon supply chain models: considering duopolistic retailers different competitive behaviors. International Journal of Production Economics, 103(1), 104–116.CrossRefGoogle Scholar
  30. Ycel, A., & Gneri, A. (2011). A weighted additive fuzzy programming approach for multicriteria supplier selection. Expert Systems with Applications, 38(5), 6281–6286.CrossRefGoogle Scholar
  31. Zadeh, L. (1965). Fuzzy sets. Information and Control, 8, 338–353.CrossRefGoogle Scholar
  32. Zhang, D., Zhang, J., Lai, K., & Lu, Y. (2009). An novel approach to supplier selection based on vague sets group decision. Expert Systems with Applications, 36(5), 9557–9563.CrossRefGoogle Scholar
  33. Zhao, J., Tang, W., Zhao, R., & Wei, J. (2012). Pricing decisions for substitutable products with a common retailer in fuzzy environments. European Journal of Operational Research, 216(2), 409–419.CrossRefGoogle Scholar
  34. Zhou C., Zhao R., & Tang W. (2008). Two-echlon supply chain games in a fuzzy environment. Computers & Industrial Engineering, 55, 390–405.CrossRefGoogle Scholar
  35. Zimmermann, H. (2000). An application-oriented view of modelling uncertainty. European Journal of Operational Research, 122, 190–198.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.General Courses DepartmentMilitary Transportation UniversityTianjinPeople’s Republic of China
  2. 2.School of ScienceTianjin Polytechnic UniversityTianjinPeople’s Republic of China

Personalised recommendations