A NEW FORMULATION AND RELAXATION OF THE SIMPLE PLANT LOCATION PROBLEM

In this paper a new formulation of the simple plant location problem (SPLP) is given that uses the style of Sharma and Sharma (European Journal of Operational Research, 122(3), 37–48). When the integer restrictions are relaxed, it results in a new relaxation of SPLP that is different from the already well known "strong" and "weak" relaxation of SPLP. It is shown that the bound given by the new relaxation is worse than the bound given by "strong relaxation" of SPLP. However, a numerical example illustrates that the bound given by the new relaxation can at times be better than the bound given by "weak relaxation" (already known) of SPLP. In this paper a new proof [which is different from the one given by Bilde and Krarup (Annals of Discrete Mathematics, 1, 79–97)] is given to establish relative strengths of various relaxations of SPLP.