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 only be numerically computed 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%.

A manufacturing facility consisting of two stations in tandem operates in a make-to-stock mode: After production, items are placed in a finished goods inventory that services an exogenous Poisson demand. Demand that cannot be met from inventory is backordered. Each station is modeled as a queue with controllable production rate and exponential service times. The problem is to control these rates to minimize inventory holding and backordering costs. Optimal controls are computed using dynamic programming and compared with the kanban, basestock and buffer control mechanisms that have been proposed for manufacturing facilities. Conditions are found under which certain simple controls are optimal using stochastic coupling arguments. Insights are gained into when to hold work-in-process and finished goods inventory, comparable to previous studies of production lines in make-to-order and unlimited demand environments.

Consider a two stage tandem queueing system, with dedicated machines in each stage. Additional reconfigurable resources can be assigned to one of these two stations without setup cost and time.In a clearing system (without external arrivals) both with and without machine failures, we show the existence of an optimal monotone policy. Moreover, when all of the machines are reliable, the switching curve defined by this policy has slope greater than or equal to -1. This continues to hold true when the holding cost rate is higher at the first stage and machine failures are considered.

This paper uses submodularity to obtain monotonicity results for a class of Markovian queueing network service rate control problems. Nonlinear costs of queueing and service are allowed. In contrast to Weber and Stidham [14], our monotonicity theorem considers arbitrary directions in the state space (not just control directions), arrival routing problems, and certain uncontrolled service rates. We also show that, without service costs, transitionmonotone controls can be described by simple control regions and switching functions. The theory is applied to queueing networks that arise in a manufacturing system that produces to a forecast of customer demand, and also to assembly and disassembly networks.

We study a manufacturing firm that builds a product to stock to meet a random demand. Production time is deterministic, so that if there is a backlog, customers are quoted a lead time that is proportional to the backlog. In order to represent the customers' response to waiting, we introduce a defection function-the fraction of customers who choose not to order as a function of the quoted lead time. Unlike models with backorder costs, the defection function is related to customer behavior. Using a continuous flow control model with linear holding cost and Markov modulated demand, we show that the optimal production policy has a hedging point form. The performance of the system under this policy is evaluated, allowing the optimal hedging point to be found.