An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality

In this paper, a multi-objective, solid transportation problem (STP) with imprecise unit costs and route-wise travel-times (general fuzzy numbers) is considered. The sources’ availabilities, destinations’ demands and capacities of conveyances are also represented by different types of fuzzy numbers like general, trapezoidal and triangular numbers. The transportation problem (T. P.) has been formulated with and without entropy function defined by Shannon’s measure of entropy. Multi-objective problems are formed with different criteria and reduced to single objective optimization problems using Zimmermann’s approach and possibility measure of the fuzzy equality. For the entropy based model, the multi-objective problem is converted to a single objective problem using weighted average of the objectives. Generalized Reduced Gradient (GRG) method is used to find the optimal solutions for a set of given numerical data. The models under two types of formulation are numerically solved and compared. The results of the models with and without entropy are also obtained and compared.