A branch-and-cut algorithm for scheduling of projects with variable-intensity activities

Authors:
Tamás Kis
Affiliations:
Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende utca 13-17, 1111, Budapest, Hungary
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

In this paper we study a resource constrained project scheduling problem in which the resource usage of each activity may vary over time proportionally to its varying intensity. We formalize the problem by means of a mixed integer-linear program, prove that feasible solution existence is NP-complete in the strong sense and propose a branch-and-cut algorithm for finding optimal solutions. To this end, we provide a complete description of the polytope of feasible intensity assignments to two variable-intensity activities connected by a precedence constraint along with a fast separation algorithm. A computational evaluation confirms the effectiveness of our method on various benchmark instances.