Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs

Abstract

Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization technique is used to obtain an optimal solution to this parametric problem. This optimal solution will also be the fuzzy optimal solution for the original problem. An example is also provided to illustrate the algorithm.

Solving fuzzy linear fractional set covering problem by a goal programming based solution approach

“…The performance of the proposed approach is evaluated by some numerical examples taken from the literature or generated randomly. The obtained results show the superiority of the proposed approach over those of the literature such as the method of Gupta and Saxena [14]. Remainder of the paper is organized by five sections.…”

“…This problem has been solved in the literature very rarely. The only study of literature on this problem has been done by Gupta and Saxena [14]. Their method has some disadvantages such as 1) an initial feasible solution must be generated and the method starts with this solution by applying the gradient of the objective function, 2) the method is highly depended on the generated initial feasible solution, 3) for the case of problem instances with high number of variables, the method becomes inefficient.…”

“…Linear set covering problems. As mentioned by Gupta and Saxena [14], the set covering problem is one of the most applicable problems to the real world situations. It can be applied to the popular real world problems such as facility location problem, airlines scheduling problem, etc.…”

“…As a solution approach, Gupta and Saxena [14] proposed a method to solve the FLFSCP. Their method has some disadvantages that are summarized by below points,…”

“…The fractional objective functions of the models (11)- (14) are linearized using the method introduced by Charnes and Cooper [6]. To show this linearization procedure, as an example model (11) is linearized here.…”