An optimal production and shutdown strategy when a supplier offers an incentive program

Motivated by the incentive programs that have been offered by energy companies under tight market conditions in the past few years, we consider a production control problem in which time alternates randomly between peak and nonpeak periods. During peak periods, the energy supplier offers the manufacturing firm – the energy user – an incentive program to reduce its energy usage by shutting down its production facility. Participation in the incentive program, however, is totally voluntary, and the user firm is rewarded for each unit of time that it participates in the program. We consider two problems that face the manufacturing firm. The first is whether it is worth shutting down production to participate in the incentive program when it is offered, and in which part (portion) of the peak period the firm should participate. The second problem is how the firm should decide on its production policy in both the peak and nonpeak periods in the presence of such an incentive program. In this paper, we provide simple models to give insight into the nature of these problems. Two cases are studied. In the first case, the peak duration is assumed to be exponentially distributed, and in the second, its length becomes known at the beginning of a peak period. In both cases, the occurrence times of the peak periods are uncertain. We characterize the optimal production and shutdown policy for both the peak and nonpeak periods. We also study the effect of seasonality on the optimal control policies.