Solving Project Scheduling Problems by Minimum Cut Computations Solving Project Scheduling Problems by Minimum Cut Computations †

In project scheduling, a set of precedence-constrained jobs has to be scheduled so as to minimize a given objective. In resource-constrained project scheduling, the jobs additionally compete for scarce resources. Due to its universality, the latter problem has a variety of applications in manufacturing, production planning, project management, and elsewhere. It is one of the most intractable problems in operations research, and has therefore become a popular playground for the latest optimization techniques, including virtually all local search paradigms. We show that a somewhat more classical mathematical programming approach leads to both competitive feasible solutions and strong lower bounds, within quite reasonable computation times. The basic ingredients of our approach are the Lagrangian relaxation of a time-indexed integer programming formulation and relaxation-based list scheduling, enriched with a useful idea from recent approximation algorithms for machine scheduling problems. The efficiency of the algorithm results from the insight that the relaxed problem can be solved by computing a minimum cut in an appropriately defined directed graph. Our computational study covers different types of resource-constrained project scheduling problems, based on several, notoriously hard test sets, including practical problem instances from chemical production planning. †An extended abstract of this work appeared in the Proceedings of the 7th Annual European Symposium on Algorithms (Möhring, Schulz, Stork, and Uetz 1999). Technische Universität Berlin, Fakultät II, Institut für Mathematik, Sekr. MA 6-1, Straße des 17. Juni 136, D10623 Berlin, Germany. Email: [email protected] Massachusetts Institute of Technology, Sloan School of Management, E53-361, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. Email: [email protected] ‡ILOG Deutschland GmbH, Ober-Eschbacher Straße 109, D-61352 Bad Homburg, Germany. Email: [email protected] §Universiteit Maastricht, Faculty of Economics and Business Administration, Quantitative Economics, P.O. Box 616, 6200 MD Maastricht, The Netherlands. Email: [email protected]