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PreprintCC BY 4.0HAL

Affine Decision Rules for Robust Optimization with Decision-Dependent Information Discovery

  • Ugur Karabas
  • Henri Lefebvre
  • Michael Poss
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Abstract

We study robust optimization problems with decision-dependent information discovery under polyhedral uncertainty and continuous recourse. We first establish structural properties of the resulting min-max-min problem, including existence of solutions and a condition under which information discovery has no value. Then, we develop a heuristic approach that combines affine decision rules with scenario generation and show that its adversarial separation problem is NP-hard. Additionally, we introduce a sampling procedure to estimate solution quality without solving the overall problem to global optimality. Numerical experiments on knapsack and facility-location instances show that the method outperforms a K-adaptability approach recently proposed in the literature in terms of computation time while achieving comparable solution quality. Our approach is applicable to polyhedral uncertainty sets that can be expressed as Ξ = σ + -σ -: (σ + , σ -) ∈ Θ with a downward monotone polytope Θ.

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Cite

BibTeXRIS
BibTeX
@misc{karabas2026affine,
  title = {{Affine Decision Rules for Robust Optimization with Decision-Dependent Information Discovery}},
  author = {Ugur Karabas and Henri Lefebvre and Michael Poss},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05784143v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Affine Decision Rules for Robust Optimization with Decision-Dependent Information Discovery
AU  - Ugur Karabas
AU  - Henri Lefebvre
AU  - Michael Poss
PY  - 2026
DA  - 2026/10/07
PB  - HAL
UR  - https://hal.science/hal-05784143v1
AB  - We study robust optimization problems with decision-dependent information discovery under polyhedral uncertainty and continuous recourse. We first establish structural properties of the resulting min-max-min problem, including existence of solutions and a condition under which information discovery has no value. Then, we develop a heuristic approach that combines affine decision rules with scenario generation and show that its adversarial separation problem is NP-hard. Additionally, we introduce a sampling procedure to estimate solution quality without solving the overall problem to global optimality. Numerical experiments on knapsack and facility-location instances show that the method outperforms a K-adaptability approach recently proposed in the literature in terms of computation time while achieving comparable solution quality. Our approach is applicable to polyhedral uncertainty sets that can be expressed as Ξ = σ + -σ -: (σ + , σ -) ∈ Θ with a downward monotone polytope Θ.
ER  -