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An exact algorithm for an integrated project staffing problem with a homogeneous workforce

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Abstract

When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability. In resource scheduling problems important assumptions are made with respect to the resource requirements. As projects are typically labour intensive, the underlying (personnel) resource scheduling problems tend to be complex due to different rules and regulations. In this paper, we aim to integrate these two interrelated scheduling problems to minimise the overall cost. For that purpose, we propose an exact algorithm for the project staffing with resource scheduling constraints. Detailed computational experiments are presented to evaluate different branching rules and pruning strategies and to compare the proposed procedure with other optimisation techniques.

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Acknowledgments

We acknowledge the support for the postdoctoral research project fundings by the Fonds voor Wetenschappelijk Onderzoek (FWO), Vlaanderen, Belgium under contract number 3E009808T

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Authors and Affiliations

  1. Faculty of Economics and Business Administration, Ghent University, 9000, Ghent, Belgium

    Broos Maenhout & Mario Vanhoucke

  2. Vlerick Business School, 9000, Ghent, Belgium

    Mario Vanhoucke

  3. University College London, London, WC1E 6BT, UK

    Mario Vanhoucke

Authors
  1. Broos Maenhout
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  2. Mario Vanhoucke
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Corresponding author

Correspondence to Mario Vanhoucke.

Appendix

Appendix

1.1 List of Symbols

Activity and project scheduling characteristics

figure d

Personnel staffing characteristics

figure e

Auxiliary variables

figure f

Decision variables

figure g

1.2 Detailed results for the Project Branching Rules

In this Appendix, we represent the results for the various project branching rules that are discussed in Sect. 4.4.2. Tables 12, 13, 14, 15 and 16 display the results for project branching rules (a), (b), (c), (d) and (e), respectively. Table 13 presents the results for the start time branching rules (b1), (b2) and (b3) for various activity and time period selection rules. Rule (b2) considers only three time period selection rules, as the (chrono-)logical selection rule (LOG) is identical to the LOG rule applied to branching rule (b1). Rule (b3) uses the LP lower bound to determine the order in which the different start times for an activity are investigated. The time period selection rules FRA and CIN are less relevant if rule (b2) is used.

Table 12 Average results for the workload branching per activity with different selection criteria for problem instances with 10 activities (\(I_1 = 10\))
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Table 13 Average results for the start time branching with different selection criteria for problem instances with 10 activities (\(I_1 = 10\))
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Table 14 Average results for the activity set branching with different selection criteria for problem instances with 10 activities (\(I_1 = 10\))
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Table 15 Average results for the activity processing branching with different selection criteria for problem instances with 10 activities (\(I_1 = 10\))
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Table 16 Average results for the precedence relationship branching with different selection criteria for problem instances with 10 activities (\(I_1 = 10\))
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Maenhout, B., Vanhoucke, M. An exact algorithm for an integrated project staffing problem with a homogeneous workforce. J Sched 19, 107–133 (2016). https://doi.org/10.1007/s10951-015-0443-z

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