A fuzzy bi-criteria transportation problem

Authors:
Esmaile Keshavarz;Esmaile Khorram
Affiliations:
Islamic Azad University, Sirjan Branch, Department of Mathematics, Sirjan, Iran;Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, 424, Hafez Ave., 15914 Tehran, Iran
Venue:
Computers and Industrial Engineering
Year:
2011

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Abstract

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.