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A steepest ascent approach to maximizing the net present value of projects

Author

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  • Christoph Schwindt
  • Jürgen Zimmermann

Abstract

We study the scheduling of projects subject to general temporal constraints between activities such that the project net present value is maximized. The proposed algorithm is based on a first-order steepest ascent approach, where the steepest ascent directions are normalized by the supremum norm. In each iteration, the procedure ascends from a vertex of the feasible region to some non-adjacent vertex, which leads to a considerable speed-up compared to standard line-search. In an experimental performance analysis, we compare previous solution methods from literature to the algorithm presented in this paper. On the basis of two randomly generated test sets, the efficiency of the steepest ascent approach is demonstrated. Problem instances with up to 1000 activities can be solved in less than one second on a personal computer. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Christoph Schwindt & Jürgen Zimmermann, 2001. "A steepest ascent approach to maximizing the net present value of projects," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 435-450, July.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:3:p:435-450
    DOI: 10.1007/s001860100129
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    Citations

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    Cited by:

    1. Leyman, Pieter & Vanhoucke, Mario, 2017. "Capital- and resource-constrained project scheduling with net present value optimization," European Journal of Operational Research, Elsevier, vol. 256(3), pages 757-776.
    2. 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.
    3. Peymankar, Mahboobeh & Davari, Morteza & Ranjbar, Mohammad, 2021. "Maximizing the expected net present value in a project with uncertain cash flows," European Journal of Operational Research, Elsevier, vol. 294(2), pages 442-452.
    4. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2024. "Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies," European Journal of Operational Research, Elsevier, vol. 317(1), pages 16-24.
    5. Domingo A. Tarzia, 2016. "Properties of the financial break-even point in a simple investment project as a function of the discount rate," Papers 1611.03740, arXiv.org.
    6. Domingo Alberto Tarzia, 2016. "Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate," Journal of Economic and Financial Studies (JEFS), LAR Center Press, vol. 4(2), pages 31-45, April.
    7. 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.
    8. Vanhoucke, M., 2006. "A scatter search procedure for maximizing the net present value of a project under renewable resource constraints," Vlerick Leuven Gent Management School Working Paper Series 2006-40, Vlerick Leuven Gent Management School.
    9. M. Vanhoucke, 2006. "An efficient hybrid search algorithm for various optimization problems," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/365, Ghent University, Faculty of Economics and Business Administration.
    10. Creemers, Stefan, 2018. "Maximizing the expected net present value of a project with phase-type distributed activity durations: An efficient globally optimal solution procedure," European Journal of Operational Research, Elsevier, vol. 267(1), pages 16-22.
    11. Wiesemann, Wolfram & Kuhn, Daniel & Rustem, Berç, 2010. "Maximizing the net present value of a project under uncertainty," European Journal of Operational Research, Elsevier, vol. 202(2), pages 356-367, April.
    12. 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.
    13. Thomas Schmitt & Bruce Faaland, 2004. "Scheduling recurrent construction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1102-1128, December.
    14. 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.
    15. 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.
    16. Wenhui Zhao & Nicholas G. Hall & Zhixin Liu, 2020. "Project Evaluation and Selection with Task Failures," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 428-446, February.

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