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An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation

Author

Listed:
  • Aristide Mingozzi

    (Department of Mathematics, University of Bologna, Bologna, Italy)

  • Vittorio Maniezzo

    (Department of Mathematics, University of Bologna, Bologna, Italy)

  • Salvatore Ricciardelli

    (Department of Electrical Engineering, University Tor Vergata, Rome, Italy)

  • Lucio Bianco

    (Department of Electrical Engineering, University Tor Vergata, Rome, Italy)

Abstract

In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem that requires an exponential number of variables, corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints. Different relaxations of the above formulation are used to derive new lower bounds, which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by Stinson et al. (1978). A tree search algorithm, based on the above formulation, that uses new lower bounds and dominance criteria is also presented. Computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:5:p:714-729
    DOI: 10.1287/mnsc.44.5.714
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    References listed on IDEAS

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    1. Oguz, Osman & Bala, Hasan, 1994. "A comparative study of computational procedures for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 72(2), pages 406-416, January.
    2. A. Alan B. Pritsker & Lawrence J. Waiters & Philip M. Wolfe, 1969. "Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach," Management Science, INFORMS, vol. 16(1), pages 93-108, September.
    3. 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.
    4. Marshall L. Fisher, 1973. "Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I," Operations Research, INFORMS, vol. 21(5), pages 1114-1127, October.
    5. Edward W. Davis & James H. Patterson, 1975. "A Comparison of Heuristic and Optimum Solutions in Resource-Constrained Project Scheduling," Management Science, INFORMS, vol. 21(8), pages 944-955, April.
    6. Erik Demeulemeester & Willy Herroelen, 1992. "A Branch-and-Bound Procedure for the Multiple Resource-Constrained Project Scheduling Problem," Management Science, INFORMS, vol. 38(12), pages 1803-1818, December.
    7. Dale F. Cooper, 1976. "Heuristics for Scheduling Resource-Constrained Projects: An Experimental Investigation," Management Science, INFORMS, vol. 22(11), pages 1186-1194, July.
    8. James H. Patterson & Walter D. Huber, 1974. "A Horizon-Varying, Zero-One Approach to Project Scheduling," Management Science, INFORMS, vol. 20(6), pages 990-998, February.
    9. Rainer Kolisch & Arno Sprecher & Andreas Drexl, 1995. "Characterization and Generation of a General Class of Resource-Constrained Project Scheduling Problems," Management Science, INFORMS, vol. 41(10), pages 1693-1703, October.
    10. Boctor, Fayer F., 1990. "Some efficient multi-heuristic procedures for resource-constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 49(1), pages 3-13, November.
    11. Edward W. Davis & George E. Heidorn, 1971. "An Algorithm for Optimal Project Scheduling under Multiple Resource Constraints," Management Science, INFORMS, vol. 17(12), pages 803-816, August.
    12. Arne Thesen, 1976. "Heuristic Scheduling of Activities under Resource and Precedence Restrictions," Management Science, INFORMS, vol. 23(4), pages 412-422, December.
    13. F. Brian Talbot & James H. Patterson, 1978. "An Efficient Integer Programming Algorithm with Network Cuts for Solving Resource-Constrained Scheduling Problems," Management Science, INFORMS, vol. 24(11), pages 1163-1174, July.
    14. James H. Patterson, 1984. "A Comparison of Exact Approaches for Solving the Multiple Constrained Resource, Project Scheduling Problem," Management Science, INFORMS, vol. 30(7), pages 854-867, July.
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