A fuzzy bi‐criteria transportation problem

In this paper, a fuzzy bi‐criteria transportation problem is studied. Here, the model concentrates on two criteria: total delivery time and total profit of transportation. The delivery times on links are fuzzy intervals with increasing linear membership functions, whereas the total delivery time on the network is a fuzzy interval with a decreasing linear membership function. On the other hand, the transporting profits on links are fuzzy intervals with decreasing linear membership functions and the total profit of transportation is a fuzzy number with an increasing linear membership function. Supplies and demands are deterministic numbers. A nonlinear programming model considers the problem using the max–min criterion suggested by Bellman and Zadeh. We show that the problem can be simplified into two bi‐level programming problems, which are solved very conveniently. A proposed efficient algorithm based on parametric linear programming solves the bi‐level problems. To explain the algorithm two illustrative examples are provided, systematically.