Scheduling a make-to-stock queue: Index policies and hedging points

A single machine produces several different classes of items in a make-to-stock mode. We consider the problem of scheduling the machine to regulate finished goods inventory, minimizing holding and backorder, or holding and lost sales costs. Demands are Poisson, service times are exponentially distributed, and there are no delays or costs associated with switching products. A scheduling policy dictates whether the machine is idle or busy and specifies the job class to serve in the latter case. Since the optimal solution can be numerically computed only for problems with several products, our goal is to develop effective policies that are computationally tractable for a large number of products. We develop index policies to decide which class to produce, including Whittle's ''restless bandit'' index, which possesses a certain asymptotic optimality. Several idleness policies are derived, and the best policy is obtained from a heavy traffic diffusion approximation. Nine sample problems are considered in a numerical study, and the average suboptimality of the best policy is less than 3%.