A Model for the Design of Hub-and-Spoke Logistics Networks with Multiple Lines under Investment Restrictions

In this paper we study a logistics hub location problem in which the network could not be formed as a full interconnected hub-level network because of the investment restrictions. Nevertheless, the hubs to be located must form a set of interconnecting lines. Logistics hubs can be connected with highly efficient pathways, enabling economies of scale to be achieved on the transportation cost (or transport time) between hubs. The objective is to minimize the total weighted transport time between all pairs of nodes while considering the logistics operation time taken on each key connected component of the network. Besides, a budget constraint on the total set-up cost of the hub network is also taken into account. A mathematical model is presented to solve the hub line location problem (HLLP) through pure integer nonlinear programming (PINLP). Numerical results on a test case confirms the validity of the proposed PINLP model and indicates the impact of the budget constraint on the topology of the network.