ROADEF 2026>
Interpreting Decisions in Two-Stage Stochastic Programs
Adrien Belfer  1@  , Luce Brotcorne  2  , Henri Lefebvre  3  , Marius Roland  1  
1 : CRIStAL
Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
2 : CRIStAL
Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
3 : Trier University, Department of Mathematics, 54296 Trier

This work studies how to interpret optimal decisions in Two-Stage Stochastic Programs (TSSPs), where uncertainty is modeled through a scenario set with associated probabilities. Although TSSPs are widely used in fields such as energy, logistics, and finance, their solutions can be hard to understand when many scenarios interact in complex ways. To address this, we introduce a new explanatory framework called XPL. The idea is to adjust the scenario probabilities within an admissible set so that an alternative, user-preferred first-stage decision becomes optimal. The model is formulated as a bilevel optimization problem integrating constraints on allowable probability changes, desired decisions, and a user-defined measure of desirability. This approach connects to counterfactual explanations, inverse optimization, and sensitivity analysis. We discuss single-level reformulations, solution methods relying on decomposition techniques, and practical applications for decision makers. Computational experiments on literature benchmark instances highlight the feasibility of the approach.


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