Genetic Algorithm-Based Fuzzy Programming Method for Multi-objective Stochastic Transportation Problem Involving Three-Parameter Weibull Distribution

In real-life situations, it is difficult to handle multi-objective stochastic transportation problems. It can’t be solved directly using traditional mathematical programming approaches. In this paper, we proposed a solution procedure to handle the above problem. The proposed solution procedure is a hybridization of the evolutionary algorithm called a genetic algorithm and a classical mathematical programming technique called fuzzy programming method. This hybrid approach is called a genetic algorithm-based fuzzy programming method. The supply and demand parameters of the constraints follow a three-parameter Weibull distribution. To complete the proposed problem a total of three steps are required. Initially, the probabilistic constraints are handled using stochastic simulation. Then, we checked the feasibility of probability constraints by the stochastic programming with the genetic algorithm without deriving the deterministic equivalents. Then, the genetic algorithm-based fuzzy programming method is considered to generate non-dominated solutions for the given problem. Finally, a numerical case study is presented to illustrate the methodology.