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Lower Bounds on the Minimum Project Duration

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Handbook on Project Management and Scheduling Vol.1

Part of the book series: International Handbooks on Information Systems ((INFOSYS))

Abstract

In this chapter methods to calculate lower bounds on the minimum project duration (i.e. the makespan C max ) of the basic resource-constrained project scheduling problem \(\mathit{PS}\,\mid \,\mathit{prec}\,\mid \,C_{\mathit{max}}\) are presented. We distinguish between constructive and destructive lower bounds.

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References

  • Artigues C, Demassey S, Néron E (2010) Resource-constrained project scheduling: models, algorithms, extensions and applications. Wiley, Hoboken

    Google Scholar 

  • Baar T, Brucker P, Knust S (1999) Tabu search algorithms and lower bounds for the resource-constrained project scheduling problem. In: Voss S, Martello S, Osman I, Roucairol C (eds) Meta-heuristics: advances and trends in local search paradigms for optimization. Kluwer, Boston, pp 1–18

    Chapter  Google Scholar 

  • Baptiste P, Demassey S (2004) Tight LP bounds for resource constrained project scheduling. OR Spectr 26(2):251–262

    Article  Google Scholar 

  • Baptiste P, Le Pape C, Nuijten W (2001) Constraint-based scheduling: applying constraint programming to scheduling problems. International series in operations research & management science, vol 39. Kluwer, Boston

    Google Scholar 

  • Bianco L, Caramia M (2011) A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations. Comput Oper Res 38(1):14–20

    Article  Google Scholar 

  • Brucker P, Knust S (2000) A linear programming and constraint propagation-based lower bound for the RCPSP. Eur J Oper Res 127(2):355–362

    Article  Google Scholar 

  • Brucker P, Knust S (2003) Lower bounds for resource-constrained project scheduling problems. Eur J Oper Res 149(2):302–313

    Article  Google Scholar 

  • Brucker P, Knust S (2012) Complex scheduling. Springer, Berlin

    Book  Google Scholar 

  • Carlier J, Néron E (2000) A new LP-based lower bound for the cumulative scheduling problem. Eur J Oper Res 127(2):363–382

    Article  Google Scholar 

  • Damay J, Quilliot A, Sanlaville E (2007) Linear programming based algorithms for preemptive and non-preemptive RCPSP. Eur J Oper Res 182(3):1012–1022

    Article  Google Scholar 

  • Demeulemeester E (1992) Optimal algorithms for various classes of multiple resource constrained project scheduling problems. Ph.D. dissertation, Katholieke Universiteit Leuven, Leuven, Belgium

    Google Scholar 

  • Dorndorf U, Huy TP, Pesch E (1999) A survey of interval capacity consistency tests for time-and resource-constrained scheduling. In: Wȩglarz J (ed) Project scheduling. Kluwer, Boston, pp 213–238

    Chapter  Google Scholar 

  • Klein R, Scholl A (1999) Computing lower bounds by destructive improvement: an application to resource-constrained project scheduling. Eur J Oper Res 112(2):322–346

    Article  Google Scholar 

  • Kolisch R, Sprecher A (1997) PSPLIB - a project scheduling problem library: OR software - ORSEP operations research software exchange program. Eur J Oper Res 96(1):205–216. http://www.om-db.wi.tum.de/psplib/

  • Mingozzi A, Maniezzo V, Ricciardelli S, Bianco L (1998) An exact algorithm for project scheduling with resource constraints based on a new mathematical formulation. Manage Sci 44(5):714–729

    Article  Google Scholar 

  • Möhring R, Schulz A, Stork F, Uetz M (2003) Solving project scheduling problems by minimum cut computations. Manage Sci 49(3):330–350

    Article  Google Scholar 

  • Néron E, Artigues C, Baptiste P, Carlier J, Damay J, Demassey S, Laborie P (2006) Lower bounds for resource constrained project scheduling problem. In: Perspectives in modern project scheduling. Springer, New York, pp 167–204

    Google Scholar 

  • Schutt A, Feydy T, Stuckey P, Wallace M (2011) Explaining the cumulative propagator. Constraints 16(3):250–282

    Article  Google Scholar 

  • Stinson J, Davis E, Khumawala B (1978) Multiple resource-constrained scheduling using branch and bound. AIIE Trans 10(3):252–259

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Osnabrück, Osnabrück, Germany

    Sigrid Knust

Authors
  1. Sigrid Knust
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Correspondence to Sigrid Knust .

Editor information

Editors and Affiliations

  1. Institute of Management and Economics, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Christoph Schwindt

  2. Institute of Management and Economics, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Jürgen Zimmermann

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Knust, S. (2015). Lower Bounds on the Minimum Project Duration. In: Schwindt, C., Zimmermann, J. (eds) Handbook on Project Management and Scheduling Vol.1. International Handbooks on Information Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-05443-8_3

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