Convex approximations for simple integer recourse models by perturbing the underlying distributions Willem K. Klein Haneveld * , Leen Stougie ² and Maarten H. van der Vlerk ‡ 23rd May 1997 Abstract We present a class of convex approximations of the expected value func- tion of a simple recourse problem with fixed technology matrix and integer second-stage variables. These approximations are obtained by perturbing the distributions of the right-hand side parameters. The resulting distributions are special instances of the class of distributions that yield convex expected value functions. A complete characterization of this class was given in a previous paper. We derive a uniform bound on the error of the approximation. Moreover, we give a representation of the resulting convex approximating problems as continuous simple recourse problems with a known discrete distribution, so that they can be solved by existing special purpose algorithms. Keywords: Simple integer recourse, convex, perturbation * Department of Econometrics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands, e-mail: W.K.Klein.Haneveld@eco.rug.nl ² Institute for Actuarial Sciences, Econometrics, and Operations Research, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands, e-mail: leen@fee.uva.nl ‡ Department of Econometrics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands, e-mail: M.H.van.der.Vlerk@eco.rug.nl. Research partially funded by NWO/ESR. 1