A GOAL PROGRAMMING APPROACH TO MULTI-CHOICE MULTI OBJECTIVE STOCHASTIC TRANSPORTATION PROBLEMS WITH LOGISTIC DISTRIBUTION

Abstract

This thesis presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multichoice coefficient and multiple aspiration levels to achieve, and the parameters of supply and demand are random variables that are not predetermined. The random variables are assumed to follow logistic distribution, and the demand and supply constraints are converted from a probabilistic case to a deterministic one using a logistic distribution. A transformation method using binary variables is used to reduce the MCMOTP into a multiobjective transportation problem (MOTP) and selecting one aspiration level for each objective from multiple levels. To find the compromise optimal solution for all objectives simultaneously, we apply goal programming approach. The main focus of the proposed approach is to minimize the all objectives simultaneously and to obtain the solution nearly close to the aspiration level of objective. The reduced problem is solved with goal programming. Finally, a mathematical model has been formulated by utilizing LINGO 19 software, and the optimal solution of the proposed model is obtained. Finally, a numerical example is presented to demonstrate the effectiveness and usefulness of the specified proposed mathematical programming model indetail