The grey linear programming approach and its application to multi-objective multi-stage solid transportation problem

The multi-objective solid transportation problem (MOSTP) constitutes one of the foremost areas of application for linear programming problem. The aim of this problem is to obtain the optimum distribution of goods from different sources to different destinations with different mode of conveyances which minimizes the total transportation cost and time. But it may contain one or more stage to transport the commodities with different mode of transport. In this paper, two new multi-objective multi-stage solid transportation problems (MOMSSTP) are investigated under grey uncertainty. Since using interval grey number theory we can absorb stochastic and interval uncertainty at a time, for this reason we developed two multi-stage STP under interval grey environment. The goal programming approach and fuzzy goal programming approach are used to reduce the multi-objective programming problem into a single-objective programming problem. Finally, the equivalent crisp models are solved using generalized reduced gradient technique (LINGO. 13.0 optimization software) and the nature of the results is discussed.