Pricing decisions of a two-echelon supply chain in fuzzy environment. (English) Zbl 1264.90009

Summary: Pricing decisions of a two-echelon supply chain with one manufacturer and duopolistic retailers in fuzzy environment are considered in this paper. The manufacturer produces a product and sells it to the two retailers, who in turn retail it to end customers. The fuzziness is associated with the customers’ demand and the manufacturing cost. The purpose of this paper is to analyze the effect of two retailers’ different pricing strategies on the optimal pricing decisions of the manufacturer and the two retailers themselves in MS Game scenario. As a reference model, the centralized decision scenario is also considered. The closed-form optimal pricing decisions of the manufacturer and the two retailers are derived in the above decision scenarios. Some insights into how pricing decisions vary with decision scenarios and the two retailers’ pricing strategies in fuzzy environment are also investigated, which can serve as the basis for empirical study in the future.


90B05 Inventory, storage, reservoirs
90B90 Case-oriented studies in operations research
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI


[1] A. H. L. Lau and H. S. Lau, “Effects of a demand-curve’s shape on the optimal solutions of a multi-echelon inventory/pricing model,” European Journal of Operational Research, vol. 147, no. 3, pp. 530-548, 2003. · Zbl 1026.90002 · doi:10.1016/S0377-2217(02)00291-6
[2] A. H. L. Lau, H. S. Lau, and Y. W. Zhou, “A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain,” European Journal of Operational Research, vol. 176, no. 1, pp. 295-316, 2007. · Zbl 1137.90351 · doi:10.1016/j.ejor.2005.06.054
[3] J. Zhao, W. Tang, R. Zhao, and J. Wei, “Pricing decisions for substitutable products with a common retailer in fuzzy environments,” European Journal of Operational Research, vol. 216, no. 2, pp. 409-419, 2012. · Zbl 1237.91104 · doi:10.1016/j.ejor.2011.07.026
[4] H. J. Zimmermann, “Application-oriented view of modeling uncertainty,” European Journal of Operational Research, vol. 122, no. 2, pp. 190-198, 2000. · Zbl 0955.91029 · doi:10.1016/S0377-2217(99)00228-3
[5] L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338-353, 1965. · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[6] S. Nahmias, “Fuzzy variables,” Fuzzy Sets and Systems, vol. 1, no. 2, pp. 97-110, 1978. · Zbl 0383.03038 · doi:10.1016/0165-0114(78)90011-8
[7] A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, D. Van Nostrand Reinhold Company, New York, NY, USA, 1985. · Zbl 0644.03021 · doi:10.1305/ndjfl/1093870925
[8] B. Liu, “A survey of credibility theory,” Fuzzy Optimization and Decision Making, vol. 5, no. 4, pp. 387-408, 2006. · Zbl 1133.90426 · doi:10.1007/s10700-006-0016-x
[9] B. Liu and Y. K. Liu, “Expected value of fuzzy variable and fuzzy expected value models,” IEEE Transactions on Fuzzy Systems, vol. 10, no. 4, pp. 445-450, 2002. · doi:10.1109/TFUZZ.2002.800692
[10] Y. Xie, D. Petrovic, and K. Burnham, “A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand,” International Journal of Production Economics, vol. 102, no. 1, pp. 37-50, 2006. · doi:10.1016/j.ijpe.2005.01.016
[11] B. Liu, Uncertainty Theory: An Introduction to its Axiomatic Foundations, Springer, Berlin, Germany, 2004. · Zbl 1247.62311
[12] B. Liu, Theory and Practice of Uncertain Programming, Physica, Heidelberg, Germany, 2002. · Zbl 1029.90084
[13] L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3-28, 1978. · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
[14] C. Wang, W. Tang, and R. Zhao, “On the continuity and convexity analysis of the expected value function of a fuzzy mapping,” Journal of Uncertain Systems, vol. 1, no. 2, pp. 148-160, 2007.
[15] Y. K. Liu and B. Liu, “Expected value operator of random fuzzy variable and random fuzzy expected value models,” International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, vol. 11, no. 2, pp. 195-215, 2003. · Zbl 1074.90056 · doi:10.1142/S0218488503002016
[16] T. W. McGuire and R. Staelin, “An industry equilibrium analyses of down stream vertical integration,” Marketing Science, vol. 2, no. 2, pp. 161-191, 1983.
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