Christina Büsing

Christina Büsing, Fabio D'Andreagiovanni

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. The critical aim of our work is to close the knowledge gap about the adoption of a multi-band uncertainty set in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, which have been interested in getting a better modeling of arbitrary distributions, built on historical data of the uncertainty affecting the considered real-world problems. In this paper, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.

Christina Büsing, Fabio D'Andreagiovanni

The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling resolution by partitioning the band into multiple sub-bands is advisable. The critical aim of our work is to close the knowledge gap on the adoption of multi-band uncertainty in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, interested in getting a better modeling of arbitrary shaped distributions, built on historical data about the uncertainty affecting the considered real-world problems.

Tabea Brandt, Christina Büsing, Johanna Leweke et al.

Developing algorithms for real-life problems that perform well in practice highly depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult. This is especially true for any patient related optimization problems, e.g., for patient-to-room assignment, due to data privacy policies. Furthermore, obtained real-life data usually cannot be published which prohibits reproducibility of results by other researchers. Therefore, often artificially generated instances are used. In this paper, we present combinatorial insights about the feasibility of instances for the patient-to-room assignment problem (PRA). We use these insights to develop a configurable instance generator for PRA with an easy-to-use graphical user interface. Configurability is in this case especially important as we observed in an extensive analysis of real-life data that, e.g., the probability distribution for patients' age and length of stay depends on the respective ward.