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Two-Stage Programming under Uncertainty with Discrete Distribution Function

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  • M. El Agizy

    (Mobil Oil Corporation, New York, New York)

Abstract

This paper establishes the relation between two approaches for solving two-stage programming under uncertainty with discrete distribution function. To accomplish this we use optimality conditions and a simple change in variables. We also review, as special cases, a transportation problem and a production-inventory model. For the transportation model we show that any of the corresponding deterministic equivalent linear programs represents a directed network. For the inventory problem we show that the demand constraints can be eliminated in the equivalent linear program. Finally, a stochastic Leontief production model is introduced. Under reasonable assumptions, we establish that its solution can be obtained by solving a certainty Leontief program. Also, we show that the optimal selection of alternative substitute activities is independent of the demand distribution.

Suggested Citation

  • M. El Agizy, 1967. "Two-Stage Programming under Uncertainty with Discrete Distribution Function," Operations Research, INFORMS, vol. 15(1), pages 55-70, February.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:1:p:55-70
    DOI: 10.1287/opre.15.1.55
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    Cited by:

    1. Feinerman, E. & Yaron, D., 1983. "Economics of Irrigation Water Mixing Within A Farm Framework," Working Papers 232610, Hebrew University of Jerusalem, Center for Agricultural Economic Research.

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