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- Michael H. Veatch, Lawrence M. Wein
- Operations Research
- 1996

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… (More)

- Michael H. Veatch, Lawrence M. Wein
- Operations Research
- 1994

A manufacturing facility consisting of two stations in tandem operates in a maketo-stock mode: after production, items are placed in a finished goods inventory that services an exogenous demand. Demand that cannot be met from inventory is backordered. Each station is modelled as a queue with controllable production rate, and the problem is to control these… (More)

- Michael H. Veatch, Lawrence M. Wein
- Queueing Syst.
- 1992

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,… (More)

This paper demonstrates the feasibility of using approximate linear programming (ALP) to compute nearly optimal average cost for multiclass queueing network control problems. ALP works directly with the LP form of the optimality equations, but approximates the di¤erential cost by a linear form. We use quadratics, piece-wise quadratic value functions from… (More)

Most analyses of make-to-stock production control assume that either all orders are eventually met (complete backordering) or that no customers are willing to wait (lost sales). We consider a more nuanced model of customer behavior, where the fraction of potential customers who place orders depends on the current backlog, and hence the lead time. A… (More)

Approximate linear programming (ALP) has been shown to provide useful bounds on optimal average cost for multiclass queueing network control problems. Approximation architectures can be chosen so that a manageable number of variables gives moderate accuracy; however, the number of constraints grows exponentially in the number of queues. We use column… (More)

Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in… (More)

- Cheng-Hung Wu, Mark E. Lewis, Michael H. Veatch
- IEEE Trans. Automat. Contr.
- 2006

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… (More)

- Michael H. Veatch
- IEEE Trans. Automat. Contr.
- 2001

In Hajek's arrival routing problem, customers are routed to one of n queues to minimize average holding cost. Interarrival and service times are exponentially distributed. We solve the associated. The optimal uid policy tells us the asymptotic slopes of the switching surfaces in the original problem when the queues are large. If these slopes are nonzero,… (More)

- Michael H. Veatch, Michael C. Caramanis
- IEEE Trans. Automat. Contr.
- 1999

We consider the control of a production facility consisting of a single workstation with multiple failure modes and part types using a continuous flow control model. Technical issues concerning the convexity and differentiability of the differential cost function are investigated. It is proven that under an optimal control policy the differential cost is C1… (More)