Solving multiobjective fuzzy transportation problem with extension principle

Nowadays, transportation models which have deterministic parameters with supply and demand constraints are replaced with the models which have fuzzy parameters with three or more constraints. In this study, a multiobjective transportation problem where the objective coefficients and constraint parameters are fuzzy numbers is discussed. Objectives are minimizing the total transportation cost and total transportation time. Constraints are, production capacities of factories, demand quantities of warehouses, budgets of warehouses and carrying capacities of conveyances. Solution procedure contains two steps which are solving objectives separately with extension principle and using fuzzy programming for the compromise solution. With solving objectives by extension principle, approximated membership functions of objective values were found, fuzzy objective values were derived. In order to find the compromise solution of objectives, first all of the parameters and objective values were defuzzified with the centroid method, then fuzzy programming approach was used. A case study was done in veterinary medicine producing firms Topkim and Biyoteknik to illustrate the proposed solution procedure. The problem is transportation of these firms? common product to fifteen warehouses in Turkey by two vehicles which have different capacities. After applying the procedure it was seen that total transportation cost occured at approximately 11880 New Kurus, total transportation time occured at approximately 248 hour. The advantage of extension principle is that decision maker can see the interval values at different possibility levels and the values most likely to occur for every objective. However when there isn?t any fuzzy coefficient in the objective function, the model can not be solved with this method. Besides, in the conditions where there are so many constraints, setting up the model takes long time. In addition to this, it can be said that solving multiobjective problems with fuzzy programming is simple. Keywords: Multiobjective fuzzy transportation problem, fuzzy logic, extension principle, fuzzy programming.