A fuzzy approach to the multiobjective transportation problem

The aim of this paper is to present a fuzzy compromise programming approach to multiobjective transportation problems. A characteristic feature of the approach proposed is that various objectives are synthetically considered with the marginal evaluation for individual objectives and the global evaluation for all objectives. The decision-maker’s preference is taken into account by his/her assigning the weights of objectives. With the global evaluation for all objectives, a compromise programming model is formulated. This model covers a wide spectrum of methods with Zimmermann’s fuzzy programming approach essentially equivalent to one of its special cases. Using ordinary optimization technique, we solve the fuzzy compromise programming model to obtain a non-dominated compromise solution at which the synthetic membership degree of the global evaluation for all objectives is maximum. A numerical example is given to demonstrate the efficiency of the proposed fuzzy compromise programming approach. Scope and purpose In many real-world situations for transportation problems, decisions are often made in the presence of multiple, conflicting, incommensurate objectives. Intensive investigations on multiobjective linear transportation problem have been made. Among them Zimmermann’s fuzzy programming appears to be an ideal approach for obtaining the optimal compromise solution to a multiobjective transportation problem. However, due to the ease of computation, the aggregate operator used in Zimmermann’s fuzzy programming is the “min” operator, which does not guarantee a non-dominated solution. In this paper, we propose a new fuzzy compromise programming approach to multiobjective transportation problems. It is shown that the approach proposed can give a compromise solution that is not only non-dominated but also optimal in a certain sense. The proposed approach is robust enough to cover a wide spectrum of methods. Zimmermann’s fuzzy programming approach is essentially equivalent to one of the proposed method’s special cases.