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arXiv · 2509.21758

Approximating value functions via corner Benders' cuts

Matheus J. Ota·Ricardo Fukasawa·Aleksandr M. Kazachkov
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Abstract

We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation and a row generation scheme that handles the redundant inequalities. Via a known connection between arc-flow and path-flow formulations, we show that our method can recover the linear programming bound of a Dantzig-Wolfe formulation using multiple cuts in the projected space. In computational experiments, our generic technique enhances the performance of a problem-specific state-of-the-art algorithm for the vehicle routing problem with stochastic demands, a well-studied variant of the classic capacitated vehicle routing problem that accounts for customer demand uncertainty.

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Matheus J. Ota, Ricardo Fukasawa, Aleksandr M. Kazachkov. 2025-09-26. Approximating value functions via corner Benders' cuts. https://arxiv.org/abs/2509.21758

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