A Semi-Lagrangian Relaxation Heuristic Algorithm for the Simple Plant Location Problem with Order

The Simple Plant Location Problem with Order (SPLPO) is a variant of the Simple Plant Location Problem (SPLP) where the customers have preferences over the facilities that will serve them. In particular, customers define their preferences by ranking each of the potential facilities from the most preferred to the least preferred. Even though the SPLP has been widely studied in the literature, the SPLPO, which is a harder model to deal with, has been studied much less and the size of the instances that can be solved is very limited. In this paper, we study a Lagrangian relaxation of the SPLPO model and we show that some properties previously studied and exploited to develop efficient SPLP solution procedures can be extended for their use in solving the SPLPO. We propose a heuristic method that takes a Lagrangian relaxation solution as the starting point of a semi Lagrangian relaxation algorithm. Finally, we include some computational studies to illustrate the good performance of this method, which quite often ends with the optimal solution.