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A Single Product Cycling Problem Under Brownian Motion Demand

Author

Listed:
  • R. G. Vickson

    (Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1)

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.

Suggested Citation

  • R. G. Vickson, 1986. "A Single Product Cycling Problem Under Brownian Motion Demand," Management Science, INFORMS, vol. 32(10), pages 1336-1345, October.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:10:p:1336-1345
    DOI: 10.1287/mnsc.32.10.1336
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    Cited by:

    1. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    2. Jingchen Wu & Xiuli Chao, 2014. "Optimal Control of a Brownian Production/Inventory System with Average Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 163-189, February.
    3. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    4. Germs, Remco & Foreest, Nicky D. van, 2014. "Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand," Research Report 14001-OPERA, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    6. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
    7. repec:dgr:rugsom:14001-opera is not listed on IDEAS
    8. Joaquin Gonzalez & Liliana Avelar Sosa & Gabriel Bravo & Oliverio Cruz-Mejia & Jose-Manuel Mejia-Muñoz, 2024. "Fog Computing and Industry 4.0 for Newsvendor Inventory Model Using Attention Mechanism and Gated Recurrent Unit," Logistics, MDPI, vol. 8(2), pages 1-14, June.

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