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.
Keywords Simple integer recourse - Convexity - Convex approximation
Research of the third author has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.