Network equilibrium of production, transportation and pricing for multi-product multi-market

Jiuping Xu (), Guomin Fang () and Zezhong Wu
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Jiuping Xu: Sichuan University
Guomin Fang: Sichuan University
Zezhong Wu: Chengdu University of Information Technology

Mathematical Methods of Operations Research, 2016, vol. 84, issue 3, No 6, 567-595

Abstract: Abstract In this paper, we consider a production, transportation and pricing problem for multi-product multi-market (PTPMM) as a system, and develop a PTPMM network equilibrium model. After allocating each product’s production cost and revenue to each path, we establish a profit network graph. An equilibrium PTPMM matrix and a $$\lambda $$ λ -combination equilibrium are proposed based on a generalization of the well-known Wardrop’s equilibrium principle. The necessary and sufficient conditions for the $$\lambda $$ λ -combination equilibrium are proposed using a linear scalarized profit function. We prove that solving the PTPMM network equilibrium problem can be reduced to the solving of the weak vector variational inequality problem, which proposes an algorithm for the PTPMM problem. Finally, an illustrative example is given to demonstrate an application of these theoretical results.

Keywords: Production; Transportation; Pricing; Network equilibrium; Vector variational inequality; $$\lambda $$ λ -Combination equilibrium; Multi-product; Multi-market (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00186-016-0557-x

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