Location strategy for a firm under competitive delivered prices

This paper addresses the location problem for an entering firm that will play a Bertrand game with other pre-existing firms in order to maximize its profit. Demand for a homogeneous product is price-sensitive and firms use delivered pricing. Under some specific conditions, it is shown that the aggregate profit of the pre-existing facilities increases as the number of facilities of the entrant increases. The problem is analyzed for a network and for a discrete location space, showing that in both cases it can be solved by a Mixed Integer Linear Programming (MILP) formulation. This formulation is used to solve an illustrative example in a variety of scenarios, where profits for both the entering firm and its competitors are analyzed. In some scenarios is seen that the aggregate profit of the pre-existing facilities increases in the number of facilities of the entrant. It is also shown that locations are stabler with respect to changes in number of new facilities than with respect to changes in demand function.