Construction method in parametric programming

We consider a linear programming problem, with two parameters in the objective function, and present an algorithm for finding the decomposition of the parameter space into maximal polyhedral areas in which particular basic solutions are optimal. Special attention is paid to fill up areas of degenerate solutions

Simple integer recourse models : convexity and convex approximations

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