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Capacity Expansion Under Stochastic Demands

Author

Listed:
  • James C. Bean

    (The University of Michigan, Ann Arbor, Michigan)

  • Julia L. Higle

    (The University of Arizona, Tucson, Arizona)

  • Robert L. Smith

    (The University of Michigan, Ann Arbor, Michigan)

Abstract

We consider the problem of optimally meeting a stochastically growing demand for capacity over an infinite horizon. Under the assumption that demand for product follows either a nonlinear Brownian motion or a non-Markovian birth and death process, we show that this stochastic problem can be transformed into an equivalent deterministic problem. Consistent with earlier work by A. Manne, the equivalent problem is formed by replacing the stochastic demand by its deterministic trend and discounting all costs by a new interest rate that is smaller than the original, in approximate proportion to the uncertainty in the demand.

Suggested Citation

  • James C. Bean & Julia L. Higle & Robert L. Smith, 1992. "Capacity Expansion Under Stochastic Demands," Operations Research, INFORMS, vol. 40(3-supplem), pages 210-216, June.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:3-supplement-2:p:s210-s216
    DOI: 10.1287/opre.40.3.S210
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