Improved handling of uncertainty and robustness in set covering problems

This paper studies the emergency service facility location problem in an uncertain environment. The main focus is the integration of uncertainty regarding the covered area due to uncertain traveling times. Previous approaches only consider either probabilistic or fuzzy optimization to cope with uncertainty. However, in many real-world problems the required statistical parameters are not precisely known and the obtained solutions may reveal a non-adequate performance. We introduce a robust formulation of the uncertain/probabilistic set covering problem which combines the concepts of robust and probabilistic optimization by introducing ’Γ-robust α-covering’ constraints. This robust uncertain set covering problem can be stated as a compact mixed-integer linear programming model. Additionally, two noncompact integer linear model formulations are developed. As the strength of these formulations is not known a priori, we analyze the performance of these formulations in an extensive computational study. A case study highlights the benefits of our approach in comparison to a formulation neglecting these uncertainties. Keywords—Set Covering Problem, Robust Optimization, Emergency Medical Services, Cutting plane algorithm