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I'm trying to recall a theorem that I was taught in grad school, but can't remember the name of the theorem. We were learning about different methods to solve unit committment and economic dispatch models for electric power grids. The TA showed us a theorem that proved that stochastic methods that incorporate the uncertainty inherent in variable renewable power generation will produce better results than purely deterministic models. Anyone have any idea what that theorem is called?

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*In the following, we assume minimization.

$$VSS = EEV - SP \geq 0$$

holds, where SP is the objective of stochastic problem and the EEV is "expected value of the expected value solution". The former is the value of objective function by solving the stochastic programming problem. The latter fixes the first-stage variables to that yield by "expected value problem (EV)", i.e., stochastic parameters in the stochastic programming problem are replaced with their expected value. VSS - value of stochastic solution, represents the value of solving the stochastic problem rather than a deterministic counterpart.

References:

[1] Birge, J. R. (1982). The value of the stochastic solution in stochastic linear programs with fixed recourse. Mathematical Programming, 24(1), 314–325. https://doi.org/10.1007/BF01585113

[2] Madansky, A. (1960). Inequalities for stochastic linear programming problems. Management Science, 6(2), 197–204. https://doi.org/10.1287/mnsc.6.2.197

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