A linear fractional bilevel programming problem with multichoice parameters

Abstract

A bilevel programming problem (BLPP) is a hierarchical optimization problem where the constraint region of the upper level is implicitly determined by the lower level optimization problem. In this paper, a bilevel programming problem is considered in which the objective functions are linear fractional and the feasible region is a convex polyhedron. Linear fractional objectives in BLPP are useful in production planning, financial planning, corporate planning and so forth. Here, the cost coefficient of the objective functions are multi-choice parameters. The multi-choice parameters are replaced using interpolating polynomials. Then, fuzzy programming is used to find a compromise solution of the transformed BLPP. An algorithm is developed to find a compromise solution of BLPP. The method is illustrated with the help of an example.