A discrete competitive facility location model with variable attractiveness

We consider the discrete version of the competitive facility location problem in which new facilities have to be located by a new market entrant to compete against already existing ones that may belong to one or more competitors. The objective of the firm is to determine the locations of the new facilities and their attractiveness levels to maximize the profit. We formulate a mixed-integer nonlinear programming model for this problem and propose three methods for its solution: a Lagrangean heuristic, two branch-and-bound methods using Lagrangean and nonlinear programming relaxations.