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Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds

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  • A. Kimms

Abstract

Resource-constrained project scheduling under a net present value objective attracts growing interest. Because this is an NP-hard problem, it is unlikely that optimum solutions can be computed for large instances within reasonable computation time. Thus, heuristics have become a popular research field. Up to now, however, upper bounds are not well researched. Therefore, most researchers evaluate their heuristics on the basis of a best known lower bound, but it is unclear how good the performance really is. With this contribution we close this gap and derive tight upper bounds on the basis of a Lagrangian relaxation of the resource constraints. We also use this approach as a basis for a heuristic and show that our heuristic as well as the cash flow weight heuristic proposed by Baroum and Patterson yield solutions very close to the optimum result. Furthermore, we discuss the proper choice of a test-bed and emphasize that discount rates must be carefully chosen to give realistic instances. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • A. Kimms, 2001. "Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds," Annals of Operations Research, Springer, vol. 102(1), pages 221-236, February.
    • Handle: RePEc:spr:annopr:v:102:y:2001:i:1:p:221-236:10.1023/a:1010962300979
    DOI: 10.1023/A:1010962300979
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    Citations

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    Cited by:

    1. 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.
    2. Hartmann, Sönke, 2011. "Project scheduling with resource capacities and requests varying with time," Working Paper Series 01/2011, Hamburg School of Business Administration (HSBA).
    3. 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.
    4. Chen, Jiaqiong & Askin, Ronald G., 2009. "Project selection, scheduling and resource allocation with time dependent returns," European Journal of Operational Research, Elsevier, vol. 193(1), pages 23-34, February.
    5. Alessandro Hill & Andrea J. Brickey & Italo Cipriano & Marcos Goycoolea & Alexandra Newman, 2022. "Optimization Strategies for Resource-Constrained Project Scheduling Problems in Underground Mining," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3042-3058, November.
    6. 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).
    7. Homberger, Jörg & Fink, Andreas, 2017. "Generic negotiation mechanisms with side payments – Design, analysis and application for decentralized resource-constrained multi-project scheduling problems," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1001-1012.
    8. 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.
    9. 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.
    10. He, Zhengwen & Xu, Yu, 2008. "Multi-mode project payment scheduling problems with bonus-penalty structure," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1191-1207, September.
    11. He, Zhengwen & Wang, Nengmin & Jia, Tao & Xu, Yu, 2009. "Simulated annealing and tabu search for multi-mode project payment scheduling," European Journal of Operational Research, Elsevier, vol. 198(3), pages 688-696, November.
    12. Mika, Marek & Waligora, Grzegorz & Weglarz, Jan, 2005. "Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models," European Journal of Operational Research, Elsevier, vol. 164(3), pages 639-668, August.
    13. Nursel Kavlak & Gündüz Ulusoy & Funda Sivrikaya Şerifoğlu & Ş. İlker Birbil, 2009. "Client‐contractor bargaining on net present value in project scheduling with limited resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 93-112, March.

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