Hybrid Fuzzy Capacitated Hub Center Allocation Problem with Both Qualitative and Quantitative Variables

Hubs are facilities which are used to switch and transfer commodities between terminals (supplies and demands) in many-to-many distribution systems. The p-hub center allocation problem is concerned with allocating demand and supply nodes to hubs in order to route the traffic between origindestination pairs in minimum time. The capacities of the hubs are given. Most of the researches have discussed this subject considering the quantitative parameters such as cost, capacity and time, in this paper we aim to consider qualitative aspects besides quantitative variables like service agility, zone traffic, capability for development in future and other aspects which DMs are interested in. Two models are presented, in first model we want to locate hub facilities based on qualitative variables. We had to decide in a fuzzy environment according to the linguistic terms about the future market demands, zone traffic and the other criteria. We will use fuzzy TOPSIS in order to find the location of p hubs then use an IP formulation to allocate terminal nodes to hubs. In second model a hybrid formulation performs both location and allocation phases with qualitative and quantitative criteria simultaneously. A numerical example is presented to illustrate the application of the proposed models and a comparison is described.