A new modelling for p-hub median problem by considering flow-dependent costs

The p-hub median problem is to determine a number of p hubs and allocate the remaining non-hub nodes to them such that total cost of the network is minimized. Normally, this cost is considered as a linear function of distance between nodes. However, such assumption results in a naive modeling of the hub networks of the real world. For example, cost of establishing a hub can be different across nodes. Moreover, this cost can also be affected by the flow that is routed via each hub node. To cover this gap, in this paper we developed a new modeling considering flow-dependent costs. The combined cost considered here includes fixed costs, Health, Safety and Environment costs (H.S.E), energy costs and personnel costs. Such way of seeing costs, to the best knowledge of authors, is new to the existing literature.