The competitive hub location under the price war

Abstract

Two transportation companies want to enter the market and they are aware of each other. The objective for the both of competitors is to maximize their respective profits by finding the best hub and spoke networks and price structures. One company wants to establish r hubs and the other wants to establish p hubs. It is assumed that the customers choose the route by price and the logistic regression based model is used to estimate how the demand is shared. After setting their networks, the competing companies engage in the price war. We propose a new model for finding a Stackelberg strategy that includes a price game, as bi-level nonlinear mixed-integer program, called the (r|p) hub-centroid problem under the price war. It is shown that there is a unique finite Bertrand-Nash price equilibrium. On the basis of this result, we show the solution existence, propose a new equations for the best response pricing, and address the computational complexity of the problem. Finally, we discuss some possible future research directions that concern the solution approach and some other competitive scenarios that involve pricing.