Competitive multiple allocation hub location problem considering primary and backup routes

The hub location problem (HLP) has a pivotal role in designing many-to-many transportation networks with increasing applications in logistics, postal services, passenger air transportation, etc. While developing their hub networks, firms need to take account of their competitors’ network structure to determine the optimal location of their hubs, so that the highest market share is captured. However, due to potential natural or man-made disruptions on the located hubs, decision-makers need to consider backup paths for routing the origin–destination (OD) flows. This paper introduces the competitive multiple allocation hub location problem considering primary and backup routes in a duopoly market consisting of a leader–follower pair of firms that locate their hubs sequentially in the spirit of Stackelberg competition. The firms also try to hedge the risk of inadequate customer service by considering backup routes for the OD flows. The backup routes differ from the primary ones based on one of the two strategies called the partial and complete backup strategies. The problem is modeled as a bilevel MILP formulation, and an enumeration algorithm, as well as a simulated annealing heuristic, are proposed for solving instances from two well-known existing data sets. A large set of computational experiments is performed to test the efficiency of two solution algorithms and analyze the impact of various input parameters on the optimal solutions. The results indicate the necessity of paying a special attention to the possibility of disruptions, particularly for the leader firm.