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Optimization guided lower and upper bounds for the resource investment problem

Author

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  • A Drexl

    (Christian-Albrechts-Universität zu Kiel)

  • A Kimms

    (Christian-Albrechts-Universität zu Kiel)

Abstract

The resource investment problem deals with the issue of providing resources to a project such that a given deadline can be met. The objective is to make the resources available in the cheapest possible way. For each resource, expenses depend on the maximum amount required during the course of the project. In this paper we develop two lower bounds for this NP-hard problem using Lagrangean relaxation and column generation techniques, respectively. Both procedures are capable of yielding feasible solutions as well. Hence, we also have two optimization guided heuristics. A computational study consisting of a set of 3210 instances compares both approaches and allows insight into the performance.

Suggested Citation

  • A Drexl & A Kimms, 2001. "Optimization guided lower and upper bounds for the resource investment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 340-351, March.
    • Handle: RePEc:pal:jorsoc:v:52:y:2001:i:3:d:10.1057_palgrave.jors.2601099
    DOI: 10.1057/palgrave.jors.2601099
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    Citations

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    Cited by:

    1. Zhu, Xia & Ruiz, Rubén & Li, Shiyu & Li, Xiaoping, 2017. "An effective heuristic for project scheduling with resource availability cost," European Journal of Operational Research, Elsevier, vol. 257(3), pages 746-762.
    2. Coughlan, Eamonn T. & Lübbecke, Marco E. & Schulz, Jens, 2015. "A branch-price-and-cut algorithm for multi-mode resource leveling," European Journal of Operational Research, Elsevier, vol. 245(1), pages 70-80.
    3. 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.
    4. Moehring, Rolf & Uetz, Marc & Stork, Frederik & Schulz, Andreas S., 2002. "Solving Project Scheduling Problems by Minimum Cut," Working papers 4231-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Patrick Gerhards, 2020. "The multi-mode resource investment problem: a benchmark library and a computational study of lower and upper bounds," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(4), pages 901-933, December.
    6. Karen Puttkammer & Rainer Kleber & Tobias Schulz & Karl Inderfurth, 2011. "Simultane Maschinenbelegungs- und Personaleinsatzplanung in KMUs anhand eines Fallbeispiels aus der Druckereibranche," FEMM Working Papers 110010, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    7. Shadrokh, Shahram & Kianfar, Fereydoon, 2007. "A genetic algorithm for resource investment project scheduling problem, tardiness permitted with penalty," European Journal of Operational Research, Elsevier, vol. 181(1), pages 86-101, August.
    8. Rodrigues, Sávio B. & Yamashita, Denise S., 2010. "An exact algorithm for minimizing resource availability costs in project scheduling," European Journal of Operational Research, Elsevier, vol. 206(3), pages 562-568, November.
    9. Drótos, Márton & Kis, Tamás, 2011. "Resource leveling in a machine environment," European Journal of Operational Research, Elsevier, vol. 212(1), pages 12-21, July.
    10. Kerem Bülbül & Philip Kaminsky & Candace Yano, 2004. "Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 407-445, April.
    11. 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.
    12. Yamashita, Denise Sato & Armentano, Vinicius Amaral & Laguna, Manuel, 2006. "Scatter search for project scheduling with resource availability cost," European Journal of Operational Research, Elsevier, vol. 169(2), pages 623-637, March.
    13. Hartmann, Sönke & Briskorn, Dirk, 2008. "A survey of variants and extensions of the resource-constrained project scheduling problem," Working Paper Series 02/2008, Hamburg School of Business Administration (HSBA).
    14. Wolff, Pascal & Emde, Simon & Pfohl, Hans-Christian, 2021. "Internal resource requirements: The better performance metric for truck scheduling?," Omega, Elsevier, vol. 103(C).
    15. Aria Shahsavar & Nima Zoraghi & Babak Abbasi, 2018. "Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects," Operational Research, Springer, vol. 18(2), pages 315-342, July.
    16. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    17. Masoud Arjmand & Amir Abbas Najafi & Majid Ebrahimzadeh, 2020. "Evolutionary algorithms for multi-objective stochastic resource availability cost problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 935-985, September.
    18. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    19. Briskorn, Dirk & Davari, Morteza & Matuschke, Jannik, 2021. "Single-machine scheduling with an external resource," European Journal of Operational Research, Elsevier, vol. 293(2), pages 457-468.
    20. Cédric Verbeeck & Vincent Peteghem & Mario Vanhoucke & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "A metaheuristic solution approach for the time-constrained project scheduling problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 353-371, March.
    21. Qingyou Yan & Qian Zhang & Xin Zou, 2016. "A Cost Optimization Model for Multiresource Leveling Problem without Project Duration Constraint," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, July.

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