Linearization approach to multi objective set covering problem with imprecise nonlinear fractional objectives

Abstract

The Set Covering Problem is one of most important NP-complete 0–1 integer programming problems as it serves as a model for many real world problems, like crew scheduling problems, facility location problems, vehicle routing etc. This paper develops an enumerative technique for solving the multiobjective set covering problem with fuzzy nonlinear fractional objectives, under certain convexity conditions. To mirror real life situations in the covering problem we have taken the objective functions in a nonlinear fractional form. In addition to that, the coefficients of the objective functions are of a fuzzy nature, as in most cases the decision maker is unable to provide information of a precise nature. The algorithm provided in this paper aims to not only solve this covering problem to obtain a set of efficient cover solutions, but also to provide the decision maker with a fuzzy solution for the same. It is based on a linearization technique with the subsequent application of the cutting plane approach, but it employs a more generalized and much deeper form of the Dantzig cut. An example to illustrate the technique is presented, and a few applications of this problem are also described.