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Inequalities for Stochastic Linear Programming Problems

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  • Albert Madansky

    (The RAND Corporation)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.6.2.197
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 6 (1960)
    Issue (Month): 2 (January)
    Pages: 197-204

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    Handle: RePEc:inm:ormnsc:v:6:y:1960:i:2:p:197-204

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    Cited by:
    1. 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, vol. 15(1), pages 48-64, July.
    2. 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.
    3. 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.
    4. 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, vol. 107(C), pages 1-9.

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