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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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