A theory of rolling horizon decision making

In this paper, the authors develop a theoretical framework for the common business practice of rolling horizon decision making. The main idea of the present approach is that the usefulness of rolling horizon methods is, to a great extent, implied by the fact that the forecasting the future is a costly activity. The authors therefore, consider a general, discrete-time, stochastic dynamic optimization problem in which the decision maker has the possibility to obtain information on the uncertain future at given-cost. For this non-standard optimization problem with optimal stopping decisions, they develop a dynamic programming formulation. The authors treat both finite and infinite horizon cases. They also provide a careful interpretation of the dynamic programming equations and illustrate the present results by a simple numerical example. Various generalizations are shown to be captured by straightforward modifications of our model.