Competitive facility location model with concave demand

We consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other, as well as with some pre-existing facilities to capture the market expansion and the market cannibalization effects. Customer demand is assumed to be a concave non-decreasing function of the total utility derived by each customer from the service offered by the facilities. The problem is formulated as a non-linear Knapsack problem, for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function. This allows us to develop exact and alpha-optimal solution approaches capable of dealing with relatively large-scale instances of the model. We also develop a fast Heuristic Algorithm for which a tight worst-case error bound is established. (c) 2006 Elsevier B.V. All rights reserved.