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.