Heuristic algorithms for delivered price spatially competitive network facility location problems

The authors review previous formulations of models for locating a firm’s production facilities while simultaneously determining production levels at those facilities so as to maximize the firm’s profit. They enhance these formulations by adding explicit variables to represent the firm’s shipping activities and discuss the implications of this revised approach. In these formulations, existing firms, as well as new entrants, are assumed to act in accordance with an appropriate model of spatial equilibrium. The firm locating new production facilities is assumed to be a large manufacturer entering an industry composed of a large number of small firms. The previously reported proof of existence of a solution to the combined location-equilibrium problem is briefly reviewed. A heuristic algorithm based on sensitivity analysis methods which presume the existence of a solution and which locally approximate price changes as linear functions of production pertrubations resulting from newly established facilities is presented. The authors provide several numerical tests to illustrate the contrasting locational solutions which this paper’s revised delivered price formulation generates relative to those of previous formulations. An exact, although computationally burdensome, method is also presented and employed to check the reliability of the heuristic algorithm.