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Optimal cutoff strategies in capacity expansion problems

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  • Michael Monticino
  • James Weisinger

Abstract

Capacity expansion refers to the process of adding facilities or manpower to meet increasing demand. Typical capacity expansion decisions are characterized by uncertain demand forecasts and uncertainty in the eventual cost of expansion projects. This article models capacity expansion within the framework of piecewise deterministic Markov processes and investigates the problem of controlling investment in a succession of same type projects in order to meet increasing demand with minimum cost. In particular, we investigate the optimality of a class of investment strategies called cutoff strategies. These strategies have the property that there exists some undercapacity level M such that the strategy invests at the maximum available rate at all levels above M and does not invest at any level below M. Cutoff strategies are appealing because they are straightforward to implement. We determine conditions on the undercapacity penalty function that ensure the existence of optimal cutoff strategies when the cost of completing a project is exponentially distributed. A by‐product of the proof is an algorithm for determining the optimal strategy and its cost. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • Michael Monticino & James Weisinger, 1995. "Optimal cutoff strategies in capacity expansion problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(7), pages 1021-1039, October.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:7:p:1021-1039
    DOI: 10.1002/1520-6750(199510)42:73.0.CO;2-N
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    1. P. Massé & R. Gibrat, 1957. "Application of Linear Programming to Investments in the Electric Power Industry," Management Science, INFORMS, vol. 3(2), pages 149-166, January.
    2. 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.
    3. Charles R. Scherer & Leland Joe, 1977. "Electric Power System Planning with Explicit Stochastic Reserves Constraint," Management Science, INFORMS, vol. 23(9), pages 978-985, May.
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    1. Salles, J. L. F. & do Val, J. B. R., 2001. "An impulse control problem of a production model with interruptions to follow stochastic demand," European Journal of Operational Research, Elsevier, vol. 132(1), pages 123-145, July.

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