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The aggregation closure is polyhedral for packing and covering integer programs

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Abstract

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta studied the concept of aggregation cuts for packing and covering integer programs. The aggregation closure is the intersection of all aggregation cuts. Bodur et al. studied the strength of this closure, but left open the question of whether the aggregation closure is polyhedral. In this paper, we answer this question in the positive, i.e., we show that the aggregation closure is polyhedral. Finally, we demonstrate that a generalization, the k-aggregation closure, is also polyhedral for all k.

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Acknowledgements

We would like to thank Ricardo Fukasawa for informing us that an independent proof of polyhedrality for aggregation closures, by Alberto Del Pia, Jeff Linderoth, and Haoran Zhu, was the subject of a poster at the Mixed Integer Programming Workshop, 2019. We also would like to thank Haoran Zhu for pointing us to the question about the polyhedrality of k-aggregation closures. We are very grateful to two anonymous referees for their detailed and careful feedback, which helped us to improve the paper.

Funding

Funding was provided by the Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada (Grant Nos. RGPIN-2018-04335, RGPIN-2020-04346, DGECR-2020-00265).

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Kanstantsin Pashkovich, Laurent Poirrier & Haripriya Pulyassary

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  1. Kanstantsin Pashkovich
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  2. Laurent Poirrier
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  3. Haripriya Pulyassary
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Correspondence to Kanstantsin Pashkovich.

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Pashkovich, K., Poirrier, L. & Pulyassary, H. The aggregation closure is polyhedral for packing and covering integer programs. Math. Program. 195, 1135–1147 (2022). https://doi.org/10.1007/s10107-021-01723-1

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