Clearing Systems and ( s, S ) Inventory Systems with Nonlinear Costs and Positive Lead Times

Shaler Stidham
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Shaler Stidham: North Carolina State University, Raleigh, North Carolina

Operations Research, 1986, vol. 34, issue 2, 276-280

Abstract: Stochastic clearing systems model many different applications, including certain bulk server queues, shuttle buses, and buffers in communication systems. We extend the characterization of the optimal parameters of a generalized stochastic clearing system (Stidham, S., Jr. 1977. Cost models for stochastic clearing systems. Opns. Res. 25 100–127.) from piece-wise linear to general convex cost-rate functions, and discuss applications to continuous-review and periodic-review ( s , S ) inventory models with nonlinear holding and storage costs and/or nonzero lead times. As in Stidham, we show that log-concavity of the sojourn function associated with the input process guarantees that the necessary conditions are also sufficient for optimality of the clearing parameters, which correspond to s and S in inventory examples. Our conditions are weaker and our model more general than those found in the previous literature on ( s , S ) inventory models.

Keywords: 362 (s; S) stochastic models in inventory/production; 686 batch service queues; 696 optimization in queues (search for similar items in EconPapers)
Date: 1986
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Citations: View citations in EconPapers (7)

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