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A note on decision rules for stochastic programs

✍ Scribed by David W. Walkup; Roger J.-B. Wets

Publisher
Elsevier Science
Year
1968
Tongue
English
Weight
341 KB
Volume
2
Category
Article
ISSN
0022-0000

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✦ Synopsis

In this note it will be shown that, in a sense to be made precise, 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. The proof relies on a basic property of linear programs established in . However, this result does not extend to stochastic programs with three or more stages. An example will be given of a simple inventory-type three-stage stochastic program with recourse for which the optimal second-stage decision rule is not piecewise linear. The example is then recast in the framework of the conditional probability E-model of chance-constrained programming given by Charnes and Kirby in [1],

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