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Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

Volume 4510 of the series Lecture Notes in Computer Science pp 214-228

A Continuous Multi-resources cumulative Constraint with Positive-Negative Resource Consumption-Production

  • Nicolas BeldiceanuAffiliated withÉcole des Mines de Nantes, LINA FRE CNRS 2729, 4 rue Alfred Kastler, La Chantrerie, BP 20722, 44307 Nantes Cedex 3
  • , Emmanuel PoderAffiliated withÉcole des Mines de Nantes, LINA FRE CNRS 2729, 4 rue Alfred Kastler, La Chantrerie, BP 20722, 44307 Nantes Cedex 3

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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 ·(logp + 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.