A Best Path Problem: Fuzzy Decision-Making Methodology

In most of the real-life applications we deal with the problem of transporting some special commodities, as banana, mango and date, which have particular production and distribution processes. In fact, these fruits are picked unripe and continuation of the ripening process is done until reaching consumers, so in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objective. In this paper, a bi-objective best path problem is formulated and solved, which the first objective tries to minimize the total traversing cost and the second one maximizes the quality of delivered commodities, as much as possible. Dependence of the quality and transit time of fruits is defined as a fuzzy trapezoidal number, and traversing costs are assumed as crisp numbers. In order to solve the presented problem, at first, we fuzzify the objective functions and then use the Bellman- Zadeh‘s max-min criterion, to reformulate the problem as a crisp single-objective linear programming problem, which is easily solvable. An illustrative example is solved, to explain the presented details.

Keywords:

Best path problem , Fuzzy number , Bi-objective problem , Fuzzy decision-making , Bellman-Zadeh‘s criterion