Solving Project Scheduling Problems by Minimum Cut Computations

Posted: 12 Aug 2004

See all articles by Rolf H. Möhring

Rolf H. Möhring

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Andreas S. Schulz

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Frederik Stork

ILOG Deutschland GmbH

Marc Uetz

Maastricht University - Department of Economics

Abstract

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.

Keywords: Project scheduling, resource-constrained project scheduling, irregular costs, network optimization, linear programming relaxation

Suggested Citation

Möhring, Rolf H. and Schulz, Andreas S. and Stork, Frederik and Uetz, Marc, Solving Project Scheduling Problems by Minimum Cut Computations. Management Science Vol. 49, pp. 330-350, 2003. Available at SSRN: https://ssrn.com/abstract=561381

Rolf H. Möhring

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 6-1
Strasse des 17. Juni 136
Berlin, 10623
Germany
+49 30 314 24594 (Phone)
+49 30 314 25191 (Fax)

Andreas S. Schulz (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

E53-361
77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States
617-258-7340 (Phone)

Frederik Stork

ILOG Deutschland GmbH ( email )

Ober-Eschbacher Strasse 109
D-61352 Bad Homburg
Germany

Marc Uetz

Maastricht University - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

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