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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
Article

Abstract

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.

Keywords

Price decisions Substitutable products Fuzzy variable Game theory 

Notes

Acknowledgments

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.

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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

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