Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables

Abstract

This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.