Hub Location-Routing Network Design under Incomplete Hub Links and Direct Shipment

In a hub location problem network, the flow originated from an origin and shipped to a destination via some selected intermediate nodes called hub nodes since using discount factor of hubs. The hub nodes are fully interconnected in traditional hub location problem. In any origin-destination path there exists at least one hub element. Rather than directly connecting any pair of locations, all the paths are handled by the hub node. In this paper, a general configuration of hub location problems is considered. The model is presented for hub location-routing problem which any network topology can be structured. This model application is in the public transportation, telecommunication systems and financial networks. Incomplete hub network is designed in the model. Furthermore, location and routing decisions are considered simultaneously in the model besides multiple allocation strategy. Moreover, non-hub nodes can be connected directly. Objective function of this model is minimized Trans shipment cost of flows and cost of constructing the network. Family of valid inequalities and some pre-processing are proposed to strengthening the model linear relaxation lower bound and improving solution time. Computational results over test problems driven from the literature show that using all valid inequalities and pre-processing perform better than using each of them separately and solve the model in a reasonable solution time