A continuous multi-resources cumulative constraint with positive-negative resource consumption-production

Beldiceanu, N.;Poder, E.
(2007) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. 4th International Conference, CPAIOR 2007 — Location: Brussels, Belgium (23.May.2007)

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  • Beldiceanu, N.
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  • Poder, E.
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Abstract
This article first introduces an extension of the classical cumulative constraint: each task is no more a rectangle but rather a sequence of contiguous trapezoid sub-tasks with variable duration and heights. The resource function is no more constant but is a positive or negative piecewise linear function of time. Finally-a task is no more pre-assigned to one resource, but to a task corresponds a set of possible resource assignments. In this context, this article provides an O(p ldr (log p+q)) for computing all the cumulated resource profiles where q is the number of resources and p is the total number of trapezoid sub-tasks of all the tasks.
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Beldiceanu, N., & Poder, E. (2007). A continuous multi-resources cumulative constraint with positive-negative resource consumption-production. In Van Hentenryck, P.; Wolsey, L.; (ed.), Integration of AI and OR Techniques in Constraint Programming forCombinatorial Optimization Problems. Proceedings 4th InternationalConference, CPAIOR 2007 (p. p. 214-228). Springer-verlag. https://hdl.handle.net/2078.5/223338