An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems

Abstract

This paper considers a class of bilevel linear programming problems in which the coefficients of both objective functions are fuzzy random variables. The main idea of this paper is to introduce the Pareto optimal solution in a multi-objective bilevel programming problem as a solution for a fuzzy random bilevel programming problem. To this end, a stochastic interval bilevel linear programming problem is first introduced in terms of α-cuts of fuzzy random variables. On the basis of an order relation of interval numbers and the expectation optimization model, the stochastic interval bilevel linear programming problem can be transformed into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In order to compare different optimal solutions depending on different cuts, two criterions are given to provide the preferable optimal solutions for the upper and lower level decision makers respectively. Finally, a production planning problem is given to demonstrate the feasibility of the proposed approach.

Keywords:

• bilevel linear programming
• fuzzy random variables
• interval number programming
• Pareto optimal solution
• expectation optimization

Acknowledgements

The work was supported by National Natural Science Foundation of China (No. 61272119). The authors would like to thank the anonymous referees for their valuable comments.