Developing Hub Location Problem Based on Economy Flows by Using Capacity of Vehicle and Limitation of Entrance Flow to Hub

Hubs are special facilities acting as mediating stations in distribution systems to organize flow transmission between origins and destinations through the best possible paths. Penalty parameters such as χ and δ can seriously affect hubs number and location in a network، however in most of the existing hub location models، these parameters are set as greater than one coefficient in the objective function with no consideration for the amount of exchanged flow between hubs and spokes. Also in classic models of hub location problem، unlimited entrance flows to a hub is assumed. Since this assumption may lead to a structure in which one hub is forced to handle a large percent of flow distribution، in cases like bad weather conditions، heavy traffics or terrorist attacks، the hub become unavailable. To address the above issues، in this study، instead of penalty parameters between hubs and spokes، capacitated transportation vehicles are implemented. Hub entrance flow is also considered limited. To do so، transportation costs from hubs (spokes) to spokes (hubs) are calculated according to the number of vehicles. Due to the complexity of the proposed model، a hybrid metaheuristic approach based on genetic algorithm and variable neighborhood search descent algorithm is developed. Results show higher performance of the proposed hybrid metaheuristic.