Simulation approach to solve fuzzy fixed charge multi-item solid transportation problems under budget constraint

Abstract

In this paper, we have developed a dominate-based genetic algorithm to solve fuzzy fixed charge multi-item solid transportation problems (FFCMISTPs) under budget constraint in fuzzy environment, in which sources, demands, capacities of conveyances, unit selling prices, unit purchasing costs, fixed charges, unit transportation costs and transportation times are fuzzy in nature. Here, transportation problems are formulated in the form of profit maximisation problems and solved. For maximisation, a dominate-based genetic algorithm (DBGA) with varying population size, cyclic crossover, two-point mutation is developed which can deal with single-objective transportation problems. The developed algorithm is tested against some test functions and its efficiency is established in terms of iteration numbers for single objective. The fuzzy objective function and constraints are reduced to corresponding deterministic ones using graded mean integrating value, possibility/necessity measures and chance constrained programming method. The reduced crisp problems are solved using developed genetic algorithm. The models are illustrated with numerical examples. The real life practical implication of the model is also presented.