On "A fuzzy bi-criteria transportation problem": A revised algorithm

Keshavarz and Khorram formulated a fuzzy bi-criteria transportation problem with fuzzy delivery time and fuzzy profit of transportation, as two conflicting objectives (Keshavarz & Khorram, 2011). They used the max-min criterion of Bellman and Zadeh to reformulate the presented fuzzy bi-criteria transportation problem as a single objective non-linear programming problem, then showed that the optimal solution of this non-linear programming can be found by solving a bi-level programming problem. Finally, they proposed an algorithm based on the parametric linear programming for solving this bi-level problem. In this paper, a shortcoming of Keshavarz and Khorram's algorithm is pointed out and a revised algorithm is proposed to solve the problem. In order to illustrate the performance of this algorithm, Keshavarz and Khorram's example is used and its optimal solution is improved. (C) 2016 Elsevier Ltd. All rights reserved.