Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 618928, 14 pages
http://dx.doi.org/10.1155/2012/618928
Research Article

Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

Min Jiang,1 Zhiqing Meng,1 Xinsheng Xu,1,2 Rui Shen,1 and Gengui Zhou1

1College of Business and Administration, Zhejiang University of Technology, Hangzhou 310023, China
2Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, China

Received 19 March 2012; Accepted 25 May 2012

Academic Editor: Yuping Wang

Copyright © 2012 Min Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.