Fuzzy Programming Approach to Multi-Objective Capacitated Transportation Problem under 2-Vehicle

In this paper we represent a two-vehicle multi-objective cost varying transportation model to solve multi-objective capacitated transportation problem. In this multi-objective model the unit transportation cost varies due to capacity of vehicles as well as amount of transport quantities. The rim conditions of the multi-objective capacitated transportation problem redundance by the proper choice of vehicles. This converts to -vehicle multi-objective cost varying transportation model which is a Bi-level Mathematical programming model. To built this model, we propose an algorithm to determine unit transportation costs with initial allocation to the basic cells by North-West corner rule. Then determine unit transportation costs for non-basic cells. Then solve it by fuzzy programming technique. This methodology is illustrated through a numerical example with considering several type of membership functions.