Abstract
Abstract : It is shown that a two-stage stochastic program with recourse with right-hand sides random (i.e., a two-stage programming under uncertainty problem) has optimal decision rules which are continuous and piecewise linear. However, this result does not extend to programs with three or more stages. An example is given of a simple inventory-type three-stage stochastic program with recourse for which the the optimal second-stage decision rule is not piecewise linear. The example is also recast in the framework of the conditional probability E-model of chance-constrained programming showing that the Charnes- Kirby theorem on the existence of piecewise linear decision rules for such programs is invalid for more than two stages.
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