Solving Fuzzy Bi-Criteria Fixed Charge Transportation Problem Using a New Fuzzy Algorithm

The bi-criteria fixed charge transportation problem is an extension of the classical transportation problem. The bi-criteria fixed charge transportation problem in a crisp environment is, often, not effective in dealing with imprecision or vagueness in the values of the problem parameters. To deal with such situations, it has been proposed that the parameters should be represented as fuzzy numbers. Hence, bi-criteria fixed charge transportation problem in fuzzy environment is considered here. In existing approaches, the programming problems in fuzzy environment are solved by converting them into crisp environment by choosing appropriate membershipfunctions and thus, the solutions are also crisp numbers. However, in this paper, a new algorithm is proposed to solve the above said problem using a linear ranking function, without converting it into crisp environment and the solutions derived are fuzzy numbers. The algorithm is suitably illustrated with a numerical example. Numerical results are compared for both fuzzy and crisp versions of the problem.