On “A fuzzy bi-criteria transportation problem”: A revised algorithm

• A fuzzy bi-criteria transportation problem is addressed.
• An existing solving method is discussed.
• A shortcoming of existing algorithm is pointed out.
• A revised algorithm is designed.
• A numerical example is used to illustrate the effectiveness of presented 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.