Using a fuzzy approach for a new bi-objective model for a multi-modal tree p-hub median location problem

Abstract

One main group of transportation networks is a hub location problem that deals with finding the location of hub nodes and allocation of non-hub nodes to located hubs. This paper presents a capacitated multi-modal p -hub median location problem with a single assignment, in which different transportation modes can be established between hub nodes. This problem makes a decision on how the hub networks with different possible transportation modes should be designed. Moreover, high setup costs for links lead to use incomplete hub network; so we allow the connected hubs by means of a tree and consider a fixed cost for establishing hub links. The objectives of this model are to minimise the total cost and minimise the total transportation time (including the transportation time between nodes and the operation time at hub nodes). As the real values of parameters are not precisely known in advance, a fuzzy approach is proposed to cope with the uncertain parameters. The multi-objective model is also converted into a single objective one by the TH method. Furthermore, some numerical examples are provided to illustrate the correctness of the proposed model. Finally, the conclusion is provided.