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Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

Author

Listed:
  • Min Jiang
  • Zhiqing Meng
  • Xinsheng Xu
  • Rui Shen
  • Gengui Zhou

Abstract

This paper extends an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents). First, we define an s -optimal joint solution with weight vector to multi-objective interaction programming problem with interaction constraint for two players and get some properties of it. It is proved that the s -optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Then, we define another s -optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties. It is proved that the s -optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain. Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.

Suggested Citation

  • Min Jiang & Zhiqing Meng & Xinsheng Xu & Rui Shen & Gengui Zhou, 2012. "Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-14, August.
    • Handle: RePEc:hin:jnlmpe:618928
    DOI: 10.1155/2012/618928
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