Skip to main content
Log in

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

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S.M. Baroum and J.H. Patterson, The development of cash flow weight procedures for maximizing the net present value of a project, Journal of Operations Management 14 (1996) 209–227.

    Google Scholar 

  2. S.M. Baroum and J.H. Patterson, An exact solution procedure for maximizing the net present value of cash flows in a network, in: Project Scheduling-Recent Models, Algorithms and Applications, ed. J. W?glarz (Kluwer Akademic, 1999) pp. 107-134.

  3. J. B?a?ewicz, J.K. Lenstra and A.H.G. Rinnooy Kan, Scheduling subject to resource constraints: Classification and complexity, Discrete Applied Mathematics 5 (1983) 11–24.

    Google Scholar 

  4. P. Brucker, A. Drexl, R.H. Möhring, K. Neumann and E. Pesch, Resource-constrained project scheduling: Notation, classification, models, and methods, European Journal of Operational Research 112 (1999) 3–41.

    Google Scholar 

  5. B.V. Cherkassky and A.V. Goldberg, On implementing push-relabel method for the maximum flow problem, in: Proceedings of the 4th Conference on Integer Programming and Combinatorial Optimization, eds. E. Balas and J. Clausen, Lecture Notes in Computer Science, Vol. 920 (Springer, Berlin, 1995) pp. 157–171.

    Google Scholar 

  6. N. Christofides, R. Álvarez-Valdés and J.M. Tamarit, Project scheduling with resource constraints: A branch and bound approach, European Journal of Operational Research 29 (1987) 262–273.

    Google Scholar 

  7. B. De Reyck and W. Herroelen, An optimal procedure for the resource-constrained project scheduling problem with discounted cash flows and generalized precedence relations, Computers & Operations Research 25 (1998) 1–17.

    Google Scholar 

  8. R.H. Doersch and J.H. Patterson, Scheduling a project to maximize its present value: A zero-one programming approach, Management Science 23 (1977) 882–889.

    Google Scholar 

  9. A. Drexl and A. Kimms, Optimization guided lower and upper bounds for the resource investment problem, Working Paper 481, University of Kiel (1998)

  10. S.E. Elmaghraby and W.S. Herroelen, The scheduling of activities to maximize the net present value of projects, European Journal of Operational Research 49 (1990) 35–49.

    Google Scholar 

  11. M.L. Fisher, The lagrangian relaxation method for solving integer programming problems, Management Science 27 (1981) 1–18.

    Google Scholar 

  12. R.C. Grinold, The payment scheduling problem, Naval Research Logistics 19 (1972) 123–136.

    Google Scholar 

  13. M. Held, P. Wolfe and H.P. Crowder, Validation of subgradient optimization, Mathematical Programming 6 (1974) 62–88.

    Google Scholar 

  14. W.S. Herroelen, P. van Dommelen and E.L. Demeulemeester, Project network models with discounted cash flows: A guided tour through recent developments, European Journal of Operational Research 100 (1997) 97–121.

    Google Scholar 

  15. W.S. Herroelen and E. Gallens, Computational experience with an optimal procedure for the scheduling of activities to maximize the net present value of projects, European Journal of Operational Research 65 (1993) 274–277.

    Google Scholar 

  16. O. Icmeli and S.S. Erenguc, A tabu search procedure for the resource constrained project scheduling problem with discounted cash flows, Computers & Operations Research 21 (1994) 841–853.

    Google Scholar 

  17. O. Icmeli and S.S. Erenguc, A branch and bound procedure for the resource constrained project scheduling problem with discounted cash flows, Management Science 42 (1996) 1395–1408.

    Google Scholar 

  18. O. Icmeli, S.S. Erenguc and C.J. Zappe, Project scheduling problems: A survey, International Journal of Operations & Production Management 13 (1993) 80–91.

    Google Scholar 

  19. O. Icmeli Tukel and W.O. Rom, Analysis of the characteristics of projects in diverse industries, Journal of Operations Management 16 (1998) 43–61.

    Google Scholar 

  20. R. Kolisch and R. Padman, An integrated survey of project scheduling,Working Paper 463, University of Kiel (1997).

  21. R. Kolisch and A. Sprecher, PSPLIB-A project scheduling problem library, European Journal of Operational Research 96 (1997) 205–216.

    Google Scholar 

  22. R. Kolisch, A. Sprecher and A. Drexl, Characterization and generation of a general class of resource-constrained project scheduling problems, Management Science 41 (1995) 1693–1703.

    Google Scholar 

  23. R.H. Möhring, A.S. Schulz, F. Stork and M. Uetz, Resource constrained project scheduling: Computing lower bounds by solving minimum cut problems, in: Algorithms-ESA'99, Proceedings of the 7th Annual European Symposium on Algorithms, Prague, ed. J. Nešet?il, Lecture Notes in Computer Science, Vol. 1643 (Springer, Berlin, 1999) pp. 139–150.

    Google Scholar 

  24. K. Neumann and J. Zimmermann, Exact and heuristic procedures for net present value and resource levelling problems in project scheduling, Working Paper WIOR-538, University of Karlsruhe (1998).

  25. L. Özdamar and G. Ulusoy, A survey on the resource-constrained project scheduling problem, IIE Transactions 27 (1995) 574–586.

    Google Scholar 

  26. R. Padman and D.E. Smith-Daniels, Early-tardy cost trade-offs in resource constrained projects with cash flows: An optimization-guided heuristic approach, European Journal of Operational Research 64 (1993) 295–311.

    Google Scholar 

  27. R. Padman, D.E. Smith-Daniels and V.L. Smith-Daniels, Heuristic scheduling of resource-constrained projects with cash flows, Naval Research Logistics 44 (1997) 365–381.

    Google Scholar 

  28. J.P. Pinder and A.S. Marucheck, Using discounted cash flow heuristics to improve project net present value, Journal of Operations Management 14 (1996) 229–240.

    Google Scholar 

  29. A.H. Russell, Cash flows in networks, Management Science 16 (1970) 357–373.

    Google Scholar 

  30. R.A. Russell, A comparison of heuristics for scheduling projects with cash flows and resource restrictions, Management Science 32 (1986) 1291–1300.

    Google Scholar 

  31. C. Sepil, Comment on Elmaghraby and Herroelen's “The scheduling of activities to maximize the net present value of projects”, European Journal of Operational Research 73 (1994) 185–187.

    Google Scholar 

  32. D.E. Smith-Daniels and N.J. Aquilano, Using a late-start resource-constrained project schedule to improve project net present value, Decision Sciences 18 (1987) 617–630.

    Google Scholar 

  33. D.E. Smith-Daniels, R. Padman and V.L. Smith-Daniels, Heuristic scheduling of capital constrained projects, Journal of Operations Management 14 (1996) 241–254.

    Google Scholar 

  34. L.V. Tavares, Multicriteria scheduling of a railway renewal program, European Journal of Operational Research 25 (1986) 395–405.

    Google Scholar 

  35. L.V. Tavares, Optimal resource profiles for program scheduling, European Journal of Operational Research 29 (1987) 83–90.

    Google Scholar 

  36. K.K. Yang, F.B. Talbot and J.H. Patterson, Scheduling a project to maximize its net present value: An integer programming approach, European Journal of Operational Research 64 (1992) 188–198.

    Google Scholar 

  37. K.K. Yang, L.C. Tay and C.C. Sum, A comparison of stochastic scheduling rules for maximizing project net present value, European Journal of Operational Research 85 (1995) 327–339.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kimms, A. 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 102, 221–236 (2001). https://doi.org/10.1023/A:1010962300979

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010962300979

Navigation