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Solving Project Scheduling Problems by Minimum Cut Computations

Author

Listed:
  • Rolf H. Möhring

    (Fakultät II, Institut für Mathematik, Technische Universität Berlin, Sekr. MA 6-1, Stra\beta e des 17. Juni 136, D-10623 Berlin, Germany)

  • Andreas S. Schulz

    (Sloan School of Management, E53-361, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139)

  • Frederik Stork

    (ILOG Deutschland GmbH, Ober-Eschbacher Stra\beta e 109, D-61352 Bad Homburg, Germany)

  • Marc Uetz

    (Faculty of Economics and Business Administration, Quantitative Economics, Universiteit Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

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 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.

Suggested Citation

  • Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:3:p:330-350
    DOI: 10.1287/mnsc.49.3.330.12737
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    References listed on IDEAS

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    1. Klein, Robert, 1999. "Computing lower bounds by destructive improvement - an application to resource-constrained project scheduling," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 10913, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Christofides, Nicos & Alvarez-Valdes, R. & Tamarit, J. M., 1987. "Project scheduling with resource constraints: A branch and bound approach," European Journal of Operational Research, Elsevier, vol. 29(3), pages 262-273, June.
    3. Ulrich Dorndorf & Erwin Pesch & Toàn Phan-Huy, 2000. "A Time-Oriented Branch-and-Bound Algorithm for Resource-Constrained Project Scheduling with Generalised Precedence Constraints," Management Science, INFORMS, vol. 46(10), pages 1365-1384, October.
    4. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    5. Brucker, Peter & Knust, Sigrid, 2000. "A linear programming and constraint propagation-based lower bound for the RCPSP," European Journal of Operational Research, Elsevier, vol. 127(2), pages 355-362, December.
    6. A. Kimms, 2001. "Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds," Annals of Operations Research, Springer, vol. 102(1), pages 221-236, February.
    7. J. M. W. Rhys, 1970. "A Selection Problem of Shared Fixed Costs and Network Flows," Management Science, INFORMS, vol. 17(3), pages 200-207, November.
    8. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    9. Aristide Mingozzi & Vittorio Maniezzo & Salvatore Ricciardelli & Lucio Bianco, 1998. "An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation," Management Science, INFORMS, vol. 44(5), pages 714-729, May.
    10. Kolisch, Rainer, 1996. "Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation," European Journal of Operational Research, Elsevier, vol. 90(2), pages 320-333, April.
    11. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    12. Klein, Robert & Scholl, Armin, 1999. "Computing lower bounds by destructive improvement: An application to resource-constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 112(2), pages 322-346, January.
    13. Kolisch, Rainer & Schwindt, Christoph & Sprecher, Arno, 1999. "Benchmark instances for project scheduling problems," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 9500, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    14. Kolisch, Rainer & Hartmann, Sönke, 1999. "Heuristic algorithms for the resource-constrained project scheduling problem: classification and computational analysis," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 10966, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    15. A Drexl & A Kimms, 2001. "Optimization guided lower and upper bounds for the resource investment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 340-351, March.
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