A Single Product Cycling Problem Under Brownian Motion Demand

R. G. Vickson
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R. G. Vickson: Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Management Science, 1986, vol. 32, issue 10, 1336-1345

Abstract: This paper treats a continuous review, single product stochastic cycling problem with demand modelled as a Brownian motion process. A broad class of production policies is admitted: they may be nonstationary, non-Markovian, or, in fact, almost arbitrary. Control theory is used to show that, within this wide class of policies, a simple, stationary, two-number policy is optimal for the average cost minimization problem. This policy switches production on when it is currently off and net inventory reaches a low critical level, or switches it off when it is on and net inventory reaches a high critical level. Simple methods are developed for obtaining the optimal critical levels numerically. Examples are developed comparing the results with those given by Graves and Keilson for a different demand process having the same mean and variance per unit time.

Keywords: Brownian motion; single product; stochastic scheduling (search for similar items in EconPapers)
Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:32:y:1986:i:10:p:1336-1345

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