A novel type I and II fuzzy approach for solving single allocation ordered median hub location problem

Hubs are facilities that can decrease the cost of many-to-many distribution systems by acting as an interconnector between the demand and supply nodes. This type of facility can reduce the number of direct links needed in a logistics network. Hub location problems (HLP) have been discussed by many authors for more than four decades, and different approaches have been developed for modeling and solving this problem. We propose a fuzzy type I and II programming approach for a new model presented in the literature, i.e., the single allocation ordered median problem. The level of flow among the nodes will be considered as a fuzzy parameter. In the fuzzy type I approach, a linear programming problem with fuzzy parameters is used, while for the fuzzy type II approach, the rules of interval arithmetic are developed to simplify the problem to the fuzzy type I case. Finally, we apply our method on Kalleh Dairy Co. data of transportation as a case study and compare crisp and fuzzy situations. We show that the results of the fuzzy approach could be 2% better than the crisp approach and also discuss the pros and cons of fuzzy type I and type II approaches.