Skip to main content

A Lagrangian Relaxation Based Forward-Backward Improvement Heuristic for Maximising the Net Present Value of Resource-Constrained Projects

  • Conference paper
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2013)

Abstract

In this paper we propose a forward-backward improvement heuristic for the variant of resource-constrained project scheduling problem aiming to maximise the net present value of a project. It relies on the Lagrangian relaxation method to generate an initial set of schedules which are then improved by the iterative forward/backward scheduling technique. It greatly improves the performance of the Lagrangian relaxation based heuristics in the literature and is a strong competitor to the best meta-heuristics. We also embed this heuristic into a state-of-the-art CP solver. Experimentation carried out on a comprehensive set of test data indicates we compare favorably with the state of the art.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brucker, P., Drexl, A., Möhring, R., Neumann, K., Pesch, E.: Resource-constrained project scheduling: Notation, classification, models, and methods. European Journal of Operational Research 112(1), 3–41 (1999)

    Article  MATH  Google Scholar 

  2. Debels, D., Vanhoucke, M.: A decomposition-based genetic algorithm for the resource-constrained project-scheduling problem. Operations Research 55(3), 457–469 (2007)

    Article  MATH  Google Scholar 

  3. Gu, H.Y.: Computation of approximate alpha-points for large scale single machine scheduling problem. Computers & OR 35(10), 3262–3275 (2008)

    Article  MATH  Google Scholar 

  4. Gu, H., Stuckey, P.J., Wallace, M.G.: Maximising the net present value of large resource-constrained projects. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 767–781. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Gu, H., Xi, Y., Tao, J.: Randomized Lagrangian heuristic based on Nash equilibrium for large scale single machine scheduling problem. In: Proceedings of the 22nd IEEE International Symposium on Intelligent Control, pp. 464–468 (2007)

    Google Scholar 

  6. Hartmann, S., Kolisch, R.: Experimental evaluation of state-of-the-art heuristics for resource constrained project scheduling. European Journal of Operational Research 127, 394–407 (2000)

    Article  MATH  Google Scholar 

  7. Hartmann, S., Briskorn, D.: A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research 207(1), 1–14 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Herroelen, W.S., Demeulemeester, E.L., De Reyck, B.: A classification scheme for project scheduling. In: Weglarz, J. (ed.) Project Scheduling. International Series in Operations Research and Management Science, vol. 14, pp. 1–26. Kluwer Academic Publishers (1999)

    Google Scholar 

  9. Icmeli, O., Erengüç, S.S.: A branch and bound procedure for the resource constrained project scheduling problem with discounted cash flows. Management Science 42(10), 1395–1408 (1996)

    Article  MATH  Google Scholar 

  10. 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)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kolisch, R., Hartmann, S.: Experimental investigation of heuristics for resource-constrained project scheduling: An update. European Journal of Operational Research 174, 23–37 (2006)

    Article  MATH  Google Scholar 

  12. Li, K., Willis, R.: An iterative scheduling technique for resource-constrained project scheduling. European Journal of Operational Research 56, 370–379 (1992)

    Article  MATH  Google Scholar 

  13. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Inf. Proc. Let. 47(4), 173–180 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Möhring, R.H., Schulz, A.S., Stork, F., Uetz, M.: Solving project scheduling problems by minimum cut computations. Management Science 49(3), 330–350 (2003)

    Article  MATH  Google Scholar 

  15. Neumann, K., Zimmermann, J.: Exact and truncated branch-and-bound procedures for resource-constrained project scheduling with discounted cash flows and general temporal constraints. Central European Journal of Operations Research 10(4), 357–380 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Russell, A.H.: Cash flows in networks. Management Science 16(5), 357–373 (1970)

    Article  MATH  Google Scholar 

  18. Savelsbergh, M., Uma, R., Wein, J.: An experimental study of LP-based approximation algorithms for scheduling problems. INFORMS J. on Computing 17, 123–136 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Schutt, A., Chu, G., Stuckey, P.J., Wallace, M.G.: Maximising the net present value for resource-constrained project scheduling. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 362–378. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  20. Schutt, A., Feydy, T., Stuckey, P.J.: Explaining time-table-edge-finding propagation for the cumulative resource constraint. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 234–250. Springer, Heidelberg (2013)

    Google Scholar 

  21. Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Explaining the cumulative propagator. Constraints 16(3), 250–282 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sprecher, A., Kolisch, R., Drexl, A.: Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem. European Journal of Operational Research 80, 94–102 (1995)

    Article  MATH  Google Scholar 

  23. Vanhoucke, M.: A scatter search heuristic for maximising the net present value of a resource constrained project with fixed activity cash flows. International Journal of Production Research 48(7), 1983–2001 (2010)

    Article  MATH  Google Scholar 

  24. Vanhoucke, M., Demeulemeester, E.L., Herroelen, W.S.: On maximizing the net present value of a project under renewable resource constraints. Management Science 47, 1113–1121 (2001)

    Article  MATH  Google Scholar 

  25. Zhu, D., Padman, R.: A metaheuristic scheduling procedure for resource-constrained projects with cash flows. Naval Research Logistics 46, 912–927 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gu, H., Schutt, A., Stuckey, P.J. (2013). A Lagrangian Relaxation Based Forward-Backward Improvement Heuristic for Maximising the Net Present Value of Resource-Constrained Projects. In: Gomes, C., Sellmann, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2013. Lecture Notes in Computer Science, vol 7874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38171-3_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38171-3_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38170-6

  • Online ISBN: 978-3-642-38171-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics