A leader-follower single allocation hub location problem under fixed markups

Abstract

This study examines a scenario in which two competitors, called a leader and a follower, sequentially create their hub and spoke networks to maximize their profits. It is assumed that a non-hub node can be allocated to at most one hub. The pricing is regulated with a fixed markup. Demand is split according to the logit model, and customers patronize their choice of route by a price. Two variants of this Stackelberg competition are addressed: deterministic and robust. In both cases, it was shown how to present the problem as a bi-level mixed-integer non-linear program. When it comes to the deterministic variant, a mixed-integer linear reformulation of the follower's model is given. For the robust variant, it is shown how to reformulate the follower's program as a mixed-integer conic-quadratic one. The benefits of these reformulations are that they allow the usage of state-of-the-art solvers in finding feasible solutions. As a solution approach for the leader, an alternating heuristic is proposed. Computational experiments are conducted on the set of CAB instances and thoroughly discussed, providing some managerial insights.