An Analysis of Network Location Problems with Distance Constraints

This paper concerns a class of network location problems with minimum or maximum separation requirements between (uncapacitated) facilities or between demand points and the facilities, or both. Its purpose is three-fold. First, it is to recognize distance constraints as increasing real life restrictions through various motivating illustrations. Using a new classification scheme, the paper introduces a variety of distance-constrained problems defined in a unified manner. These include a number of new problems. Second, it is to survey existing solution techniques, available only for a few of such constrained problems. Finally, it is to shed some light on yet unstudied problems by exploring possible extensions of some of the known solution techniques or discussing varying degrees of difficulties involved. In particular, the paper presents integer programming formulations of several new problems along with the results of applying linear programming relaxation methods. Although the computational experience is somewhat disappointing for some of these problems, the results provide greater insight into the problems. With the stated purpose, it is hoped that this paper will stimulate future research in this important problem area.