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An exact algorithm to minimize the makespan in project scheduling with scarce resources and generalized precedence relations

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  • Bianco, Lucio
  • Caramia, Massimiliano
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    Abstract

    In this paper we propose an exact algorithm for the Resource Constrained Project Scheduling Problem (RCPSP) with generalized precedence relationships (GPRs) and minimum makespan objective. For the RCPSP with GPRs we give a new mathematical formulation and a branch and bound algorithm exploiting such a formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same mathematical formulation. We provide an extensive experimentation and a comparison with known lower bounds and competing exact algorithms drawn from the state of the art.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010964
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 219 (2012)
    Issue (Month): 1 ()
    Pages: 73-85

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    Handle: RePEc:eee:ejores:v:219:y:2012:i:1:p:73-85

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Branch and bound; Generalized precedence relationships; Lagrangian relaxation;

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    1. 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.
    2. Dorndorf, Ulrich, 2002. "Project scheduling with time windows: from theory to applications," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 3401, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. 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.
    4. 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.
    5. 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).
    6. De Reyck, Bert & Herroelen, willy, 1998. "A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations," European Journal of Operational Research, Elsevier, vol. 111(1), pages 152-174, November.
    7. Erik L. Demeulemeester & Willy S. Herroelen, 1997. "New Benchmark Results for the Resource-Constrained Project Scheduling Problem," Management Science, INFORMS, vol. 43(11), pages 1485-1492, November.
    8. 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.
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