Decision and forecast horizons for one-dimensional optimal control problems: Existence results and applications

This paper obtains decision and forecast horizons for undiscounted, continuous-time one-dimensional control systems. Some general conditions for the existence of horizons arising from the constraints imposed on the system are derived by using the optimality principle. These conditions are applicable to a variety of problems, including those of production planning, machine maintenance and cash management. Also derived are existence results that depend on the interplay between various costs involved in the context of a generalized production-inventory model. Horizons are obtained explicitly in some cases. The model includes as special cases a version of the wheat-trading problem and some other inventory problems that have appeared in the literature. The paper concludes with an application of the model to a continuous-time concave production-planning problem not yet treated in the horizon context.