A NOTE ON A PERFECT FORWARD PROCEDURE FOR A SINGLE FACILITY DYNAMIC LOCATION RELOCATION PROBLEM

In a recent paper, M. Bastian and M. Volkmer (Oper. Res. Lett. 12, 11–16) [1] proposed a perfect forward algorithm for the solution of a single facility dynamic location/relocation problem. Here, we first provide a numerical example to demonstrate that this problem does not always have a finite forecast horizon. Secondly, we restate the original problem in terms of a shortest path problem in an acyclic network and give an obvious condition (which is both necessary and sufficient) for the existence of a finite forecast horizon for obtaining an optimal initial decision. Then a simple perfect forward algorithm for obtaining an optimal initial decision (when a finite forecast horizon exists) is presented. This algorithm can be considered as a version of Dijkstra's algorithm. It is our opinion that the formulation proposed here is substantially simpler than the one presented in [1] and helps a bit more to understand the real nature of the problem.