Simple Integer Recourse Models: Convexity and Convex Approximations
AbstractWe consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective function is convex. This result is also stated in terms of random variables. Next, we present a class of convex approximations of the objective function, which are obtained by perturbing the distributions of the right-hand side parameters. We derive a uniform bound on the absolute error of the approximation. Finally, we give a representation of convex simple integer recourse problems as continuous simple recourse problems, so that they can be solved by existing special purpose algorithms
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Bibliographic InfoPaper provided by University of Groningen, Research Institute SOM (Systems, Organisations and Management) in its series Research Report with number 04A21.
Date of creation: 2004
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-12-12 (All new papers)
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- Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods, EconWPA 0201001, EconWPA, revised 13 Nov 2003.
- Vlerk, Maarten H. van der, 2004. "Convex approximations for a class of mixed-integer recourse models," Research Report, University of Groningen, Research Institute SOM (Systems, Organisations and Management) 04A28, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
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