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Active and stable project scheduling

Author

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  • K. Neumann
  • H. Nübel
  • C. Schwindt

Abstract

The paper proposes a new classification of schedules for resource-constrained project scheduling problems with minimum and maximum time lags between project activities and regular and different types of nonregular objective functions. The feasible region of the scheduling problems represents a (generally disconnected) union of polytopes. In addition to the well-known concepts of active and semiactive schedules, pseudoactive and quasiactive as well as stable, semistable, pseudostable, and quasistable schedules are introduced. The (quasi-, pseudo-, semi-)active schedules are related to different types of left-shifts of sets of activities and correspond to minimal points of certain subsets of the feasible region. The (quasi-, pseudo-, semi-)stable schedules do not allow oppositely directed shifts and correspond to extreme points of certain subsets of the feasible region. The different sets of schedules contain optimal schedules for project scheduling problems which differ in their objective functions. The correspondence between those sets of schedules and vertices of specific polyhedral subsets of the feasible region can be exploited for analyzing schedule generation schemes which have been developed recently for finding solutions to the different classes of project scheduling problems. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:3:p:441-465
    DOI: 10.1007/s001860000092
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    Citations

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    Cited by:

    1. André Schnabel & Carolin Kellenbrink & Stefan Helber, 2018. "Profit-oriented scheduling of resource-constrained projects with flexible capacity constraints," Business Research, Springer;German Academic Association for Business Research, vol. 11(2), pages 329-356, September.
    2. Neumann, K. & Schwindt, C. & Zimmermann, J., 2003. "Order-based neighborhoods for project scheduling with nonregular objective functions," European Journal of Operational Research, Elsevier, vol. 149(2), pages 325-343, September.
    3. Heilmann, Roland, 2003. "A branch-and-bound procedure for the multi-mode resource-constrained project scheduling problem with minimum and maximum time lags," European Journal of Operational Research, Elsevier, vol. 144(2), pages 348-365, January.
    4. Thomas Selle & Jürgen Zimmermann, 2003. "A bidirectional heuristic for maximizing the net present value of large‐scale projects subject to limited resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(2), pages 130-148, March.
    5. Gehring, Marco & Volk, Rebekka & Schultmann, Frank, 2022. "On the integration of diverging material flows into resource‐constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1071-1087.
    6. Kreter, Stefan & Schutt, Andreas & Stuckey, Peter J. & Zimmermann, Jürgen, 2018. "Mixed-integer linear programming and constraint programming formulations for solving resource availability cost problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 472-486.
    7. Herroelen, Willy & Leus, Roel, 2004. "The construction of stable project baseline schedules," European Journal of Operational Research, Elsevier, vol. 156(3), pages 550-565, August.
    8. Neumann, K. & Zimmermann, J., 2000. "Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints," European Journal of Operational Research, Elsevier, vol. 127(2), pages 425-443, December.
    9. 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.
    10. Rieck, Julia & Zimmermann, Jürgen & Gather, Thorsten, 2012. "Mixed-integer linear programming for resource leveling problems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 27-37.

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