Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 204263, 13 pages
Research Article

Some Properties of Multiple Parameters Linear Programming

1Department of Mathematics, Taizhou University, Taizhou, Zhejiang 317000, China
2Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Received 20 August 2009; Revised 9 March 2010; Accepted 12 May 2010

Academic Editor: Kok Lay Teo

Copyright © 2010 Maoqin Li 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.


We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function f can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of f at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.