Klein Haneveld, Willem K.

Stougie, L

van der Vlerk, Maarten H.

English

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 algorithm

ARTS repository - University of Groningen

Simple Integer Recourse Models:Convexity and Convex Approximations

https://pure.rug.nl/ws/files/2984125/04A21.pdf

Simple Integer Recourse Models:Convexity and Convex Approximations

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ARTS repository - University of Groningen