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A constructive branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

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  • Kai Watermeyer

    (Clausthal University of Technology)

  • Jürgen Zimmermann

    (Clausthal University of Technology)

Abstract

This paper deals with the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints with the objective to minimize the project duration. The consideration of partially renewable resources allows to integrate the decision about the availability of a resource for a specific time period into the scheduling process. Together with general temporal constraints, which permit to establish minimum and maximum time lags between activities, even more aspects of real-life projects can be taken into account. We present a branch-and-bound algorithm for the stated problem that is based on a serial schedule-generation scheme. For the first time it is shown how a dominance criterion can be applied on the associated generation scheme to reduce the start times in each scheduling step. To improve the performance of the solution procedure, we integrate consistency tests and lower bounds from the literature and devise new pruning techniques. In a comprehensive experimental performance analysis we compare our exact solution procedure with all available branch-and-bound algorithms for partially renewable resources. Additionally, we investigate a directly derived priority rule-based approximation method from our new enumeration scheme. The results of the computational study demonstrate the efficiency of our branch-and-bound algorithm and reveal that the derived approximation method is only suited to solve small- and medium-sized instances.

Suggested Citation

  • Kai Watermeyer & Jürgen Zimmermann, 2023. "A constructive branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints," Journal of Scheduling, Springer, vol. 26(1), pages 95-111, February.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:1:d:10.1007_s10951-022-00735-9
    DOI: 10.1007/s10951-022-00735-9
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    References listed on IDEAS

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    1. Ramon Alvarez-Valdes & Jose Manuel Tamarit & Fulgencia Villa, 2015. "Partially Renewable Resources," International Handbooks on Information Systems, in: Christoph Schwindt & Jürgen Zimmermann (ed.), Handbook on Project Management and Scheduling Vol.1, edition 127, chapter 0, pages 203-227, Springer.
    2. Brucker, Peter & Knust, Sigrid, 2003. "Lower bounds for resource-constrained project scheduling problems," European Journal of Operational Research, Elsevier, vol. 149(2), pages 302-313, September.
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    5. Kai Watermeyer & Jürgen Zimmermann, 2020. "A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 427-460, June.
    6. Böttcher, Jan & Drexl, A. & Kolisch, R. & Salewski, F., 1999. "Project scheduling under partially renewable resource constraints," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 345, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    7. Kolisch, Rainer, 1996. "Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation," European Journal of Operational Research, Elsevier, vol. 90(2), pages 320-333, April.
    8. K. Neumann & H. Nübel & C. Schwindt, 2000. "Active and stable project scheduling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 441-465, December.
    9. Alvarez-Valdes, R. & Crespo, E. & Tamarit, J.M. & Villa, F., 2008. "GRASP and path relinking for project scheduling under partially renewable resources," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1153-1170, September.
    10. Jan Böttcher & Andreas Drexl & Rainer Kolisch & Frank Salewski, 1999. "Project Scheduling Under Partially Renewable Resource Constraints," Management Science, INFORMS, vol. 45(4), pages 543-559, April.
    11. F. Brian Talbot & James H. Patterson, 1978. "An Efficient Integer Programming Algorithm with Network Cuts for Solving Resource-Constrained Scheduling Problems," Management Science, INFORMS, vol. 24(11), pages 1163-1174, July.
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    Cited by:

    1. Mareike Karnebogen & Jürgen Zimmermann, 2024. "Generation schemes for the resource-constrained project scheduling problem with partially renewable resources and generalized precedence constraints," Annals of Operations Research, Springer, vol. 338(1), pages 173-192, July.

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