Stochastic Horizons for the Aggregate Planning Problem

This paper develops a methodology for showing how forecast horizons for stochastic planning problems relate to the planning procedures and the information system within the organization. To illustrate the approach we have chosen a relatively straightforward production problem where the firm can meet a fluctuating demand pattern through a combination of overtime and inventory-related options. We show that the optimal production plan is monotonically non-decreasing in the demand sequence so that bounds can be placed on the optimal first period production plan for an N-period problem. These bounds together with information and computationally-related costs are used in specifying a methodology for determining forecast horizons. An illustrative example suggests that such horizons are likely to be small in many realistic cases. The concluding section indicates how this methodology can be utilized for specifying stochastic horizons for more general aggregate planning decisions in organizations.