Simple Integer Recourse Models

Willem K. Klein Haneveld; Leen Stougie; Maarten H. van der Vlerk

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SPEPS Preprint

Author(s):	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
Submission Date:	08.09.2004
Series Title:	Stochastic Programming E-Print Series (SPEPS)
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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Abstract (eng):

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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