|edoc-Server der Humboldt-Universität zu Berlin|
Willem K. Klein Haneveld, University of Groningen|
Leen Stougie, Technical University Eindhoven
Maarten H. van der Vlerk, University of Groningen
|Title:||Simple Integer Recourse Models – Convexity and Convex Approximations|
|Date of Acceptance:||10.01.2005|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-10046346)|
|Keywords (eng):||Simple integer recourse, convexity, convex approximation|
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|We 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 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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