Many planning problems require that decisions are made now when data in the future is uncertain. Stochastic multi-stage linear programming (SMLP) provides a framework in which to model such problems. For problems up to a certain size, Benders Decomposition is a very efficient method for solving these. However, real life problems create SMLP problems which are too big to be solved by Benders Decomposition alone. Sampling techniques provide a way to estimate the true solution to such problems. An example of such a problem is the optimisation of hydro-electric generation from a system of linked reservoirs. Here the objective is to maximise the total value of the electricity generated. The decision maker only knows the hydrological state and inflow for the present time period, and the probability of future inflows and hydrological states.
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