Dual-Clustering Constraint Generation for Two-Stage Stochastic Programs

P. Díaz-Cachinero, R. Gázquez, R. Mínguez

Two-stage stochastic programming models decision-making under uncertainty when first-stage decisions precede random outcomes and fixed recourse follows. For large scenario sets under risk aversion, Conditional Value-at-Risk (CVaR) is commonly used. We propose a single-loop algorithm combining dual clustering, grouping scenarios with identical optimal second-stage dual solutions, and constraint generation, adding only the hyperplanes needed to represent CVaR. The method converges under mild conditions and stops when the reduced model matches the CVaR of the full scenario set within tolerance. We illustrate the approach on a stochastic capacitated facility location problem and benchmark it against Benders adaptive-cuts methods using instances from the OR-Library. Results show substantial speed-ups, up to several orders of magnitude, while preserving solution quality.

Keywords: Stochastic programming, location problems, linear programming, risk measures, Conditional value-at-risk

GT GELOCA IV: Stochastic optimization and fairness in location and routing
September 4, 2026  3:30 PM
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