Optimal control of a make-to-stock system with adjustable service rate

We consider a multiclass make-to-stock system served by a single server with adjustable capacity (service rate). At any point in time, the decision-maker must determine the capacity level, make a production decision (i.e., whether to produce an item to stock or to satisfy a backorder), and make a rationing decision (i.e., whether to satisfy a new order from stock or place it on backorder). In this article we characterize the structure of optimal capacity adjustment, production, and stock rationing policy for both finite- and infinite-horizon problems. We show that an optimal policy is monotone in current inventory and backorder levels, and we characterize its properties. In a numerical study we compare the optimal policy with heuristic policies and show that the savings from using an optimal policy can be significant.