From Classification to Optimization: A Scenario-based Robust Optimization Approach

Abstract

This paper addresses data-driven decision-making problems under categorical uncertainty. Consider a two-stage optimization problem with first-stage planning and second-stage routing decisions, under uncertainty regarding which customers to visit. Classification models can estimate the probability of each customer visit from covariates but how to embed these predictions into the optimization? We propose a scenario-based robust optimization approach that combines stochastic programming (by constructing probabilistic scenarios), robust optimization (by protecting against adversarial perturbations within discrete uncertainty sets), and data-driven optimization (by defining scenarios and uncertainty sets from classification outputs). We develop a cutting-plane algorithm that converges to the optimum in a finite number of iterations for a general class of problems. Using public datasets, results suggest that (i) our scenario-based robust optimization approach outperforms benchmarks based on deterministic, stochastic and robust optimization; (ii) data-driven opti- mization outperforms benchmarks that ignore covariate information; and (iii) our cutting-plane algorithm outperforms direct implementation by returning better solutions in shorter computational times.