Simple integer recourse models : convexity and convex approximations

W.K. Klein Haneveld, L. Stougie, M.H. Vlerk, van der

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)
1 Downloads (Pure)


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 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.
Original languageEnglish
Pages (from-to)435-473
JournalMathematical Programming
Issue number2-3
Publication statusPublished - 2006


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