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A MinCumulative Resource Constraint

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13292))

Abstract

The cumulative constraint is the key to the success of Constraint Programming in solving scheduling problems with cumulative resources. It limits the maximum amount of a resource consumed by the tasks at any time point. However, there are few global constraints that ensure that a minimum amount of a resource is consumed at any time point. We introduce such a constraint, the MinCumulative. We show that filtering the constraint is NP-Hard and propose a checker and a filtering algorithm based on the fully elastic relaxation used for the cumulative constraint. We also show how to model MinCumulative using the SoftCumulative constraint. We present experiments comparing the different methods to solve MinCumulative using Constraint Programming.

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Notes

  1. 1.

    https://github.com/yanickouellet/min-cumulative-paper-public.

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Authors and Affiliations

  1. Université Laval, Québec, Canada

    Yanick Ouellet & Claude-Guy Quimper

Authors
  1. Yanick Ouellet
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  2. Claude-Guy Quimper
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Corresponding author

Correspondence to Claude-Guy Quimper .

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Editors and Affiliations

  1. UCLouvain, Louvain-la-Neuve, Belgium

    Pierre Schaus

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Ouellet, Y., Quimper, CG. (2022). A MinCumulative Resource Constraint. In: Schaus, P. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2022. Lecture Notes in Computer Science, vol 13292. Springer, Cham. https://doi.org/10.1007/978-3-031-08011-1_21

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  • DOI: https://doi.org/10.1007/978-3-031-08011-1_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08010-4

  • Online ISBN: 978-3-031-08011-1

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