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Lower Bounds and Exact Solution Approaches

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Book cover Handbook on Project Management and Scheduling Vol.1

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

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Abstract

Generalized precedence relations are temporal constraints in which the starting/finishing times of a pair of activities have to be separated by at least or at most an amount of time denoted as time lag (minimum time lag and maximum time lag, respectively). This chapter is devoted to project scheduling with generalized precedence relations with and without resource constraints. Attention is focused on lower bounds and exact algorithms. In presenting existing results on these topics, we concentrate on recent results obtained by ourselves. The mathematical models and the algorithms presented here are supported by extensive computational results.

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Notes

  1. 1.

    Given resource k, let r k min be the maximum usage of this resource by a single activity, that is \(r_{k}^{\mathit{min}} =\max _{i\in V }r_{\mathit{ik}}\). Let r k max denote the peak demand of resource k in the earliest start schedule with infinite resource capacity. The resource strength of resource k is thus defined as \(RS_{k} = \frac{R_{k}-r_{k}^{\mathit{min}}} {r_{k}^{\mathit{max}}-r_{k}^{\mathit{min}}}\) (Kolish et al. 1995).

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Authors and Affiliations

  1. Department of Enterprise Engineering, University of Rome “Tor Vergata”, Roma, Italy

    Lucio Bianco & Massimiliano Caramia

Authors
  1. Lucio Bianco
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  2. Massimiliano Caramia
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Correspondence to Lucio Bianco .

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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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Bianco, L., Caramia, M. (2015). Lower Bounds and Exact Solution Approaches. 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_5

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