A bi objective dynamic reliable hub location problem with congestion effects

In this paper, a new model of hub locating has been solved considering reliability and importance of flow congestion on hub nodes in a dynamic environment. Each of nodes considered as hubs and their communication paths with other non-hubs nodes have specific reliability. In order to reduce input flow to any hub and avoid creation unsuitable environmental and traffic conditions in that area, efficiency capacity is allocated to each hub, which is subject to a penalty in case of exceeding this amount. Another capability of this model is the ability of deciding whether hubs are active or inactive in each period, so hub facilities can be established or closed due to different conditions (such as changes in demand, legislative, etc.). The model is non-linear and bi-objective that the first goal is reducing transportation costs, hub rental fees and extra flow congestion penalties on hub nodes and the second goal is to increase the minimum designed network reliability. After linearization of the model, using ε-constraint method, optimal boundary is obtained. Also, to demonstrate the performance of the model, we use IAD dataset for solving problem. To evaluate the model, sensitivity analysis is presented for some of important parameters of the model.