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Mixed-Integer Linear Programming Formulations

In: Handbook on Project Management and Scheduling Vol.1

Author

Listed:
  • Christian Artigues

    (Univ de Toulouse)

  • Oumar Koné

    (Université Nangui Abrogoua)

  • Pierre Lopez

    (Univ de Toulouse)

  • Marcel Mongeau

    (lab MAIAA, ENAC)

Abstract

In this chapter, (mixed-)integer linear programming formulations of the resource-constrained project scheduling problem are presented. Standard formulations from the literature and newly proposed formulations are classified according to their size in function of the input data. According to this classification, compact models (of polynomial size), pseudo-polynomial sized models, and formulations of exponential size are presented. A theoretical and experimental comparison of these formulations is then given. The complementarity of the formulations for different usages is finally discussed and directions for future work, such as hybridization with other methods, are given.

Suggested Citation

  • Christian Artigues & Oumar Koné & Pierre Lopez & Marcel Mongeau, 2015. "Mixed-Integer Linear Programming Formulations," International Handbooks on Information Systems, in: Christoph Schwindt & Jürgen Zimmermann (ed.), Handbook on Project Management and Scheduling Vol.1, edition 127, chapter 0, pages 17-41, Springer.
    • Handle: RePEc:spr:ihichp:978-3-319-05443-8_2
    DOI: 10.1007/978-3-319-05443-8_2
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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. Leila Hosseini & Shaojie Tang & Vijay Mookerjee & Chelliah Sriskandarajah, 2020. "A Switch in Time Saves the Dime: A Model to Reduce Rental Cost in Cloud Computing," Information Systems Research, INFORMS, vol. 31(3), pages 753-775, September.
    3. Brech, Claus-Henning & Ernst, Andreas & Kolisch, Rainer, 2019. "Scheduling medical residents’ training at university hospitals," European Journal of Operational Research, Elsevier, vol. 274(1), pages 253-266.
    4. Pamela C. Nolz, 2021. "Optimizing construction schedules and material deliveries in city logistics: a case study from the building industry," Flexible Services and Manufacturing Journal, Springer, vol. 33(3), pages 846-878, September.
    5. Kreter, Stefan & Rieck, Julia & Zimmermann, Jürgen, 2016. "Models and solution procedures for the resource-constrained project scheduling problem with general temporal constraints and calendars," European Journal of Operational Research, Elsevier, vol. 251(2), pages 387-403.
    6. Tsang, Man Yiu & Shehadeh, Karmel S., 2023. "Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times," European Journal of Operational Research, Elsevier, vol. 307(1), pages 48-63.
    7. Carvalho, Andréa Nunes & Oliveira, Fabricio & Scavarda, Luiz Felipe, 2015. "Tactical capacity planning in a real-world ETO industry case: An action research," International Journal of Production Economics, Elsevier, vol. 167(C), pages 187-203.
    8. Shehadeh, Karmel S. & Cohn, Amy E.M. & Epelman, Marina A., 2019. "Analysis of models for the Stochastic Outpatient Procedure Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 279(3), pages 721-731.
    9. Bersch, Christopher V. & Akkerman, Renzo & Kolisch, Rainer, 2021. "Strategic planning of new product introductions: Integrated planning of products and modules in the automotive industry," Omega, Elsevier, vol. 105(C).
    10. Klein, Nicklas & Gnägi, Mario & Trautmann, Norbert, 2024. "Mixed-integer linear programming for project scheduling under various resource constraints," European Journal of Operational Research, Elsevier, vol. 319(1), pages 79-88.
    11. Tom Rihm & Norbert Trautmann & Adrian Zimmermann, 2018. "MIP formulations for an application of project scheduling in human resource management," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 609-639, December.

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