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Inequalities for Stochastic Linear Programming Problems

Author

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  • Albert Madansky

    (The RAND Corporation)

Abstract

Consider a linear-programming problem in which the "right-hand side" is a random vector whose expected value is known and where the expected value of the objective function is to be minimized. An approximate solution is often found by replacing the "right-hand side" by its expected value and solving the resulting linear programming problem. In this paper conditions are given for the equality of the expected value of the objective function for the optimal solution and the value of the objective function for the approximate solution; bounds on these values are also given. In addition, the relation between this problem and a related problem, where one makes an observation on the "right-hand side" and solves the (nonstochastic) linear programming problem based on this observation, is discussed.

Suggested Citation

  • Albert Madansky, 1960. "Inequalities for Stochastic Linear Programming Problems," Management Science, INFORMS, vol. 6(2), pages 197-204, January.
  • Handle: RePEc:inm:ormnsc:v:6:y:1960:i:2:p:197-204
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    File URL: http://dx.doi.org/10.1287/mnsc.6.2.197
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    References listed on IDEAS

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    1. M. E. Salveson, 1956. "A Problem in Optimal Machine Loading," Management Science, INFORMS, vol. 2(3), pages 232-260, April.
    2. M. Beckman & R. Muth, 1956. "An Inventory Policy for a Case of Lagged Delivery," Management Science, INFORMS, vol. 2(2), pages 145-155, January.
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    Cited by:

    1. Mestre, Ana Maria & Oliveira, Mónica Duarte & Barbosa-Póvoa, Ana Paula, 2015. "Location–allocation approaches for hospital network planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 240(3), pages 791-806.
    2. Zhuang, Jifang & Gabriel, Steven A., 2008. "A complementarity model for solving stochastic natural gas market equilibria," Energy Economics, Elsevier, vol. 30(1), pages 113-147, January.
    3. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    4. Munoz, F.D. & Hobbs, B.F. & Watson, J.-P., 2016. "New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints," European Journal of Operational Research, Elsevier, vol. 248(3), pages 888-898.
    5. Crean, Jason & Parton, Kevin & Mullen, John & Jones, Randall, 2013. "Representing climatic uncertainty in agricultural models – an application of state-contingent theory," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 57(3), September.
    6. Douglas T. Gardner & J. Scott Rogers, 1999. "Planning Electric Power Systems Under Demand Uncertainty with Different Technology Lead Times," Management Science, INFORMS, pages 1289-1306.
    7. Bistline, John E., 2015. "Electric sector capacity planning under uncertainty: Climate policy and natural gas in the US," Energy Economics, Elsevier, vol. 51(C), pages 236-251.
    8. Laureano Escudero & Araceli Garín & María Merino & Gloria Pérez, 2007. "The value of the stochastic solution in multistage problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 48-64, July.
    9. Jirutitijaroen, Panida & Kim, Sujin & Kittithreerapronchai, Oran & Prina, José, 2013. "An optimization model for natural gas supply portfolios of a power generation company," Applied Energy, Elsevier, pages 1-9.
    10. de Boer, Sanne V. & Freling, Richard & Piersma, Nanda, 2002. "Mathematical programming for network revenue management revisited," European Journal of Operational Research, Elsevier, vol. 137(1), pages 72-92, February.

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