Mathematical Modeling of a Hierarchical Hub Routing Problem and Using the Benders Decomposition and Artificial Bee Colony Algorithms to Solve it

The hierarchical hub routing network consists of 3 levels (customer, the non-central and
The hierarchical hub routing network consists of 3 levels (customer, the non-central and
central hubs), which aims to find the optimum location of the central and non-central hubs, allocation of customers to established hubs to find the optimal path between customers and non-central hubs. Among the functions of this model are for post, banks, and sending and receiving services. In this study, a MIP mathematical model is proposed. The hierarchical hub routing is based on the traveling salesman problem. So it is an NP-hard problem too, and to solve this model in the medium and large sizes, Benders’ decomposition and artificial bee colony algorithms are proposed respectively. The proposed artificial bee colony algorithms has some changes while it has been developed for continuous type problems. Results showed good performance of Benders decomposition and artificial bee colony in order to solve the model in medium and large sizes. Also the numerical examples and sensitivity analysis confirms validity of the proposed mathematical model.