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Robust Capacity Planning Under Uncertainty

Author

Listed:
  • Dimitris Paraskevopoulos

    (The Management School, Imperial College, 53 Prince's Gate, London SW7 2PG, United Kingdom)

  • Elias Karakitsos

    (The Management School, Imperial College, 53 Prince's Gate, London SW7 2PG, United Kingdom)

  • Berc Rustem

    (Department of Computing, Imperial College, 180 Queen's Gate, SW7 2BZ, United Kingdom)

Abstract

The existence of uncertainty influences the investment, production and pricing decision of firms. Therefore, capacity expansion models need to take into account uncertainty. This uncertainty, may arise because of errors in the specification, statistical estimation of relationships and in the assumptions of exogenous variables. One such example is demand uncertainty. In this paper, a cautious capacity planning approach is described for solving problems in which robustness to likely errors is needed. The aim is to cast the problem in a deterministic framework and thereby avoid the complexities inherent in nonlinear stochastic formulations. We adopt a robust approach and minimize an augmented objective function that penalises the sensitivity of the objective function to various types of uncertainty. The robust or sensitivity approach is compared with Friedenfelds' equivalent deterministic demand method. Using numerical results from a large nonlinear programming capacity planning model, it is shown that as caution against demand uncertainty increases, the variance of the total objective function (profit) decreases. The cost of such robustness is a deterioration in the deterministic risky performance. This method is also applied to an industry simulation model in order to assess the effect of uncertainty in market demand on optimal capacity expansion and capacity utilisation.

Suggested Citation

  • Dimitris Paraskevopoulos & Elias Karakitsos & Berc Rustem, 1991. "Robust Capacity Planning Under Uncertainty," Management Science, INFORMS, vol. 37(7), pages 787-800, July.
  • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:7:p:787-800
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    File URL: http://dx.doi.org/10.1287/mnsc.37.7.787
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    1. repec:spr:infosf:v:13:y:2011:i:5:d:10.1007_s10796-010-9243-3 is not listed on IDEAS
    2. Jan A. Van Mieghem, 2003. "Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments," Manufacturing & Service Operations Management, INFORMS, vol. 5(4), pages 269-302, July.
    3. Yan, Shangyao & Tang, Ching-Hui, 2009. "Inter-city bus scheduling under variable market share and uncertain market demands," Omega, Elsevier, vol. 37(1), pages 178-192, February.
    4. Manuel Laguna, 1998. "Applying Robust Optimization to Capacity Expansion of One Location in Telecommunications with Demand Uncertainty," Management Science, INFORMS, vol. 44(11-Part-2), pages 101-110, November.
    5. Altendorfer, Klaus & Jodlbauer, Herbert, 2011. "Which utilization and service level lead to the maximum EVA?," International Journal of Production Economics, Elsevier, vol. 130(1), pages 16-26, March.
    6. Martínez-Costa, Carme & Mas-Machuca, Marta & Benedito, Ernest & Corominas, Albert, 2014. "A review of mathematical programming models for strategic capacity planning in manufacturing," International Journal of Production Economics, Elsevier, vol. 153(C), pages 66-85.
    7. Eberly, Janice C. & Van Mieghem, Jan A., 1997. "Multi-factor Dynamic Investment under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(2), pages 345-387, August.
    8. Mula, J. & Poler, R. & Garcia-Sabater, J.P. & Lario, F.C., 2006. "Models for production planning under uncertainty: A review," International Journal of Production Economics, Elsevier, vol. 103(1), pages 271-285, September.
    9. Hahn, G.J. & Kuhn, H., 2012. "Simultaneous investment, operations, and financial planning in supply chains: A value-based optimization approach," International Journal of Production Economics, Elsevier, vol. 140(2), pages 559-569.
    10. Darlington, J. & Pantelides, C. C. & Rustem, B. & Tanyi, B. A., 2000. "Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 121(2), pages 343-362, March.
    11. Yan, Shangyao & Tang, Ching-Hui, 2007. "A heuristic approach for airport gate assignments for stochastic flight delays," European Journal of Operational Research, Elsevier, vol. 180(2), pages 547-567, July.
    12. Pennings, Enrico & Natter, Martin, 2001. "Strategic diversification and capacity utilization," International Journal of Production Economics, Elsevier, vol. 72(3), pages 261-272, August.
    13. Vladimirou, Hercules & Zenios, Stavros A., 1997. "Stochastic linear programs with restricted recourse," European Journal of Operational Research, Elsevier, vol. 101(1), pages 177-192, August.
    14. Driouchi, Tarik & Bennett, David & Simpson, Gary, 2010. "A path-dependent contingent-claims approach to capacity investments," European Journal of Operational Research, Elsevier, vol. 201(1), pages 319-323, February.

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