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Resource-Constrained Project Scheduling:Computing Lower Bounds by Solving Minimum Cut Problems

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Algorithms - ESA’ 99 (ESA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1643))

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Abstract

We present a novel approach to compute Lagrangian lower bounds on the objective function value of a wide class of resource-constrained project scheduling problems. The basis is a polynomial-time algorithm to solve the following scheduling problem: Given a set of activities with start-time dependent costs and temporal constraints in the form of time windows, find a feasible schedule of minimum total cost. In fact, we show that any instance of this problem can be solved by a minimum cut computation in a certain directed graph.

We then discuss the performance of the proposed Lagrangian approach when applied to various types of resource-constrained project scheduling problems. An extensive computational study based on different established test beds in project scheduling shows that it can significantly improve upon the quality of other comparably fast computable lower bounds.

Research partially supported by the Bundesministerium für Bildung,Wissenschaft, Forschung und Technologie (bmb+f), grant No. 03-MO7TU1-3.

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Author information

Authors and Affiliations

  1. Technische Universität Berlin, Fachbereich Mathematik, Sekr. MA 6-1, Straße des 17. Juni 136, 10623, Berlin, Germany

    Rolf H. Möhring, Frederik Stork & Marc Uetz

  2. MIT, Sloan School of Management and Operations Research Center, E53-361, 30Wadsworth St, Cambridge, MA, 02139

    Andreas S. Schulz

Authors
  1. Rolf H. Möhring
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  2. Andreas S. Schulz
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  3. Frederik Stork
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  4. Marc Uetz
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and DIMATIA Centre, Charles University, Malostranská nám. 25, CZ-11800, Prague 1, Czech Republic

    Jaroslav Nešetřil

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© 1999 Springer-Verlag Berlin Heidelberg

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Möhring, R.H., Schulz, A.S., Stork, F., Uetz, M. (1999). Resource-Constrained Project Scheduling:Computing Lower Bounds by Solving Minimum Cut Problems. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_13

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  • DOI: https://doi.org/10.1007/3-540-48481-7_13

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  • Print ISBN: 978-3-540-66251-8

  • Online ISBN: 978-3-540-48481-3

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