Detection of minimal forecast horizons in dynamic programs with multiple indicators of the future

Many sequential planning problems can be represented as a shortest path problem in an acyclic network. This includes all deterministic dynamic programs as well as certain stochastic sequential decision problems. In this article, the authors identify a large class of shortest path problems for which a general efficient algorithm for the simultaneous solution and detection of minimal forecast horizons is developed. Detection of such minimal forecast horizons is essential when accurate information regarding various relevant parameters is obtained progressively, i.e., when the initial information is restricted to a limited horizon of ‘future’ stages only. The authors describe five classes of planning problems which can be efficiently addressed by the general algorithm. These classes deal with multi-item joint replenishment systems, combined inventory and routing problems, machine scheduling issues, single item stochastic inventory settings and routing problems in the plane and in space.