A Study of the Optimal Switching Point in a Limited-cycle Problem with Multiple Periods(Theory and Methodology)

Abstract

In a social system or production line, the restrictions of the cost and the due-time exist in each period (or process). Generally, whether this restriction is satisfied is not only dependent on the risks of this period, but also the risks generated beforehand. We consider controlling the production process by switching to a faster processing rate at a given point (period). This paper considers the optimal switching period to minimize the total expected cost of the production process. In this paper, first, the optimal switching problem is systematically classified and the corresponding model is presented. Next, the mathematic formulation of the total expectation for the above case is proposed. Finally, the policy of an optimal switching period is investigated in detail through numerical experiments.