Two-Stage Programming under Uncertainty with Discrete Distribution Function

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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.

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