Computation of a multi-objective fuzzy stochastic transportation problem

Abstract

This paper is concerned with the solution methodology of a multi-objective transportation problem where fuzziness and randomness occur under one roof. In the present transportation problem, supplies and demands are considered as fuzzy random variable. In the first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain multi-objective stochastic transportation problem. By using the chance constrained technique, the multi-objective stochastic transportation problem is transformed to equivalent crisp multi-objective transportation problem. Then, introducing the concept of membership function, multi-objective deterministic transportation problem is converted into single objective mathematical programming problem. Finally, it is solved with the help of existing technique. A numerical example and a case study are provided in order to illustrate the methodology.