An interval number programming approach for bilevel linear programming problem

Abstract

In this paper, we propose a mathematical formulation of bilevel linear programming problem to deal with an interval number programming approach. Bilevel linear programming problem is usually viewed as a problem with two decision makers at two different hierarchical levels. The upper-level decision maker, the leader, selects his or her decision vector first and the lower decision maker, the follower, selects his or her afterward based on the decisions of the upper level. In mathematical programming problem, the coefficients in the objective function and the constraint functions are always determined as crisp values. In practice, however, there are many decision situations where the objective functions and/or the constraints are uncertain to some degree. Over the last two decades, interval programming based on the interval analysis has been developed as a useful and simple method to deal with this type of uncertainty. The interval numbers will be in both of the objective function and the constraints. An Illustrative numerical example is provided to clarify the proposed approach.