W. K. Klein Haneveld, University of Groningen
Abstract:
Simple Recourse is the name of a class of stochastic linear programming problems where deviations from goals are penalized individually and linearly. In particular, when only the right-hand sides are random such problems are relatively easy to solve. The only nonlinearity comes from a number of one-dimensional expected shortage and expected surplus functions. From a mathematical point of view, these functions are just integrals of tails of the cumulative distribution functions, and their study has independent interest. Starting with a discussion of these functions, I organize a guided tour in the world where they are relevant. The choice of subjects and the way they are dealt with is biased, since it reflects old and recent interests of the guide over the last 30 years. For instance, subjects like multiple-simple recourse, integrated chance constraints and adjustments for integer decision variables will be discussed as well as aspects of production-inventory control and projectplanning seen from the perspective of Simple Recourse. But also concepts as conjugate duality and stochastic dominance will be touched where it is appropriate. In this expository lecture I try to convince the audience that the world of Simple Recourse is larger and more interesting than the terminology seems to suggest.