Approximating value functions via corner Benders' cuts
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.
Cite
@article{arxiv.2509.21758,
title = {Approximating value functions via corner Benders' cuts},
author = {Matheus J. Ota and Ricardo Fukasawa and Aleksandr M. Kazachkov},
journal= {arXiv preprint arXiv:2509.21758},
year = {2025}
}