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Optimal resource extraction with uncertain reserves

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  • Robert J. Lipshutz
  • Lawrence D. Stone

Abstract

We consider the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. We apply a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.

Suggested Citation

  • Robert J. Lipshutz & Lawrence D. Stone, 1992. "Optimal resource extraction with uncertain reserves," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 153-173, March.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:2:p:153-173
    DOI: 10.1002/1520-6750(199203)39:23.0.CO;2-8
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    References listed on IDEAS

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    1. Walter R. Stromquist & Lawrence D. Stone, 1981. "Constrained Optimization of Functionals with Search Theory Applications," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 518-529, November.
    2. Richard J. Gilbert, 1979. "Optimal Depletion of an Uncertain Stock," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(1), pages 47-57.
    3. Deshmukh, Sudhakar D & Pliska, Stanley R, 1980. "Optimal Consumption and Exploration of Nonrenewable Resources under Uncertainty," Econometrica, Econometric Society, vol. 48(1), pages 177-200, January.
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