Mohammad Rahimian - Department of Mathematics, Islamic Azad University, Masjed-Soleiman Branch, Masjed-Soleiman, Iran
Esmaiel Keshavarz - Department of Mathematics, Islamic Azad University, Sirjan Branch, Sirjan, Iran;
Hamid Hassasi - Faculty of Management Sciences, Islamic Azad University, Central Tehran Branch, Tehran, Iran

In most of the real-life applications we deal with the problem of transporting some special fruits, as banana, which has particular production and distribution processes. In this paper we restrict our attention to formulating and solving a new bi-criterion problem on a network in which in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objective. However, the fruits are possibly stored at some intermediate node for practical purposes. We call the new model the best shipping pattern problem with intermediate storage. Here, it is assumed that both arc costs and times are crisp numbers. The main contribution of this model is an actual interpretation of the given fuzzy trapezoidal number, as the quality of delivered commodities. Since the presented problem has a fuzzy structure, the Bellman and Zadeh's max-min criterion can be used to treat it as a crisp single-objective problem, which is easily solvable. An illustrative example is solved, to explain the presented details.

multiple criterion optimization, best shipping pattern, fuzzy number, Bellman-Zadeh's principle