# American Institute of Mathematical Sciences

April  2017, 13(2): 573-586. doi: 10.3934/jimo.2016032

## A parametric simplex algorithm for biobjective piecewise linear programming problems

 1 Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, China 2 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

1 Corresponding author

Received  October 2014 Revised  November 2015 Published  May 2016

Fund Project: This work was partially supported by the National Science Foundation of China (11471230 and 11201042), the Scientific Research of the Education Department of Sichuan Province(16ZA0213), and the Scientific Research Foundation of CUIT (J201216).

In this paper we attempt to develop a parametric simplex algorithm for solving biobjective convex separable piecewise linear programming problems. The algorithm presented in this paper can be regarded as an extension of the parametric simplex algorithm for solving biobjective linear programming problems to the piecewise linear case. Analogous to the linear case, this parametric simplex algorithm provides a decomposition of parametric space. A numerical example is presented to illustrate the implementation of the algorithm.

Citation: Rong Hu, Ya-Ping Fang. A parametric simplex algorithm for biobjective piecewise linear programming problems. Journal of Industrial & Management Optimization, 2017, 13 (2) : 573-586. doi: 10.3934/jimo.2016032
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##### References:
Feasible set X and efficient solutions obtained by Algorithm in decision space
F(X) and efficient frontier in objective space
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