Competitive network restructuring with spatially loyal customers. A bilevel facility delocation problem

In this paper we address the problem faced by a company that needs to decide the number and location of facilities to close in order to reduce the size of their retail distribution network, whilst minimising the market share that is lost to their competitor, who is also engaged in a network reduction process. The problem is modelled as a bilevel competitive delocation model and is formulated as a variant of the well-known (r|p)-centroid problem. The formulation takes into account the existence of a certain level of customer loyalty, which implies that customers may decide to visit a more distant facility of their regular provider rather than rely on a closer competitor's facility. A depth-first search implicit enumeration algorithm is proposed for solving a diverse set of instances of the problem. The analysis of an instance based on a real-life setting, and intensive numerical experimentation, provide evidence of the effectiveness of the algorithm for the solution of real-size problems, and confirm the practical validity of our modelling approach. Our results also highlight the importance of considering spatial loyalty in network restructuring scenarios.