Scenario-Based Robust Optimization for Two-Stage Decision Making Under Binary Uncertainty

This paper addresses problems of two-stage optimization under binary uncertainty. We define a scenario-based robust optimization (ScRO) formulation that combines principles of stochastic optimization (by constructing probabilistic scenarios) and robust optimization (by protecting against adversarial perturbations within discrete uncertainty sets). To solve it, we develop a sparse row generation algorithm that iterates between a master problem (which provides a lower bound based on minimal uncertainty sets) and a history-based subproblem (which generates an upper bound and updates minimal uncertainty sets). We generate scenarios and uncertainty sets from element-wise probabilities using a deviation likelihood method or from historical samples using a sample clustering approach. Using public data sets, results suggest that (i) our ScRO formulation outperforms benchmarks based on deterministic, stochastic, and robust optimization; (ii) our deviation likelihood and sample clustering approaches outperform scenario generation baselines; and (iii) our sparse row generation algorithm outperforms off-the-shelf implementation and state-of-the-art cutting plane benchmarks. An application to a real-world ambulance dispatch case study suggests that the proposed modeling and algorithmic approach can reduce the number of late responses by more than 25%. Funding: K. Wang’s research was supported by the National Natural Science Foundation of China [Grants 72322002, 52221005, and 52220105001]