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Surveillance problems: Wiener processes

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  • Gordon R. Antelman
  • I. Richard Savage

Abstract

This paper extends the results presented by I. R. Savage in a previous paper [8]. That paper studied economically optimal policies for inspecting and repairing production processes which behave as Poisson processes. Similar results are presented here for production processes which behave as Wiener processes. With continuous surveillance, methods are presented which permit the computation of exactly optimal strategies and the optimal income per unit of time. With costly surveillance, a functional equation is presented. The solution of this equation would yield the optimal strategy. Explicit solutions do not seem feasible but many qualitative properties of the solutions are found. The most interesting of these says, roughly (see Proposition 12 for exact statement), that the time between inspections decreases as the observed quality decreases.

Suggested Citation

  • Gordon R. Antelman & I. Richard Savage, 1965. "Surveillance problems: Wiener processes," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(1), pages 35-55, March.
    • Handle: RePEc:wly:navlog:v:12:y:1965:i:1:p:35-55
    DOI: 10.1002/nav.3800120103
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    Cited by:

    1. Xing, Shiqi & Batabyal, Amitrajeet, 2019. "A Safe Minimum Standard, an Elasticity of Substitution, and the Cleanup of the Ganges in Varanasi," MPRA Paper 93846, University Library of Munich, Germany, revised 15 Mar 2019.
    2. Jonathan E. Helm & Mariel S. Lavieri & Mark P. Van Oyen & Joshua D. Stein & David C. Musch, 2015. "Dynamic Forecasting and Control Algorithms of Glaucoma Progression for Clinician Decision Support," Operations Research, INFORMS, vol. 63(5), pages 979-999, October.
    3. Amitrajeet Batabyal & Peter Nijkamp, 2005. "Alternate strategies for managing resistance to antibiotics and pesticides," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 7(1), pages 39-51, March.
    4. Amitrajeet A. Batabyal & Gregory J. DeAngelo, 2008. "A Dynamic And Stochastic Analysis Of Fertilizer Use In Swidden Agriculture," World Scientific Book Chapters, in: Dynamic And Stochastic Approaches To The Environment And Economic Development, chapter 4, pages 67-78, World Scientific Publishing Co. Pte. Ltd..
    5. Tiziano De Angelis & Jhanvi Garg & Quan Zhou, 2022. "A quickest detection problem with false negatives," Papers 2210.01844, arXiv.org.

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