Forecast horizons and dynamic facility location planning

We consider a dynamic facility location model in which the objective is to find a planning horizon, x*, and a first period decision, XI*, such that XI* is a first period decision for at least one optimal policy for all problems with planning horizons equal to or longer than x*. In other words, we seek a planning horizon, "r*, such that conditions after x* do not influence the choice of the optimal initial decision, XI*. We call x* a forecast horizon and X~ an optimal initial decision. For the dynamic uncapacitated fixed charge location problem, we show that simple conditions exist such that the initial decision depends on the length of the planning horizon. Thus, a strictly optimal forecast horizon and initial policy may not exist. We therefore introduce the concepts of e-optimal forecast horizons and e-optimal initial solutions. Our computational experience inicates that such solutions can be found for practical problems. Although computing e-optimal forecast horizons and initial decisions can be cumbersome, this approach offers the potential for making significantly better decisions than those generated by other approaches. To illustrate this, we show that the use of the scenario planning approach can lead to the adoption of the worst possible initial decision under conditions of future uncertainty. On the basis of our results, it appears that the forecast horizon approach offers an attractive tool for making dynamic location decisions.