Skip to main content
SpringerLink
Log in

Project scheduling with irregular costs: complexity, approximability, and algorithms

  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract.

We address a generalization of the classical discrete time-cost tradeoff problem where the costs are irregular and depend on the starting and the completion times of the activities. We present a complete picture of the computational complexity and the approximability of this problem for several natural classes of precedence constraints. We prove that the problem is NP-hard and hard to approximate, even in case the precedence constraints form an interval order. For precedence constraints with bounded height, there is a complexity jump from height one to height two: For height one, the problem is polynomially solvable, whereas for height two, it is NP-hard and APX-hard. Finally, the problem is shown to be polynomially solvable if the precedence constraints have bounded width or are series parallel.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B. (1993) Network flows: Theory, algorithms, and applications. Prentice Hall, Upper Saddle River, NJ

    Google Scholar 

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

    Article  MATH  Google Scholar 

  3. Chang, G.J., Edmonds, J. (1985) The poset scheduling problem. Order 2: 113-118

    Google Scholar 

  4. De, P., Dunne, E.J., Gosh, J.B., Wells, C.E. (1995) The discrete time-cost tradeoff problem revisited. European Journal of Operational Research 81: 225-238

    Article  MATH  Google Scholar 

  5. De, P., Dunne, E.J., Gosh, J.B., Wells, C.E. (1997) Complexity of the discrete time-cost tradeoff problem for project networks. Operations Research 45: 302-306

    MATH  Google Scholar 

  6. Deineko, V.G., Woeginger, G.J. (2001) Hardness of approximation of the discrete time-cost tradeoff problem. Operations Research Letters 29: 207-210

    Article  MATH  Google Scholar 

  7. Demeulemeester, E.L., Herroelen, W.S. (2002) Project scheduling: A research handbook. Kluwer Academic Publishers

    Google Scholar 

  8. Dilworth, R.P. (1950) A decomposition theorem for partially ordered sets. Annals of Mathematics 51: 161-166

    MATH  Google Scholar 

  9. Frank, H., Frisch, I.T., van Slyke, R., Chou, W.S. (1970) Optimal design of centralized computer networks. Networks 1: 43-58

    MATH  Google Scholar 

  10. Garey, M.R., Johnson, D.S. (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco

    Google Scholar 

  11. Harvey, R.T., Patterson, J.H. (1979) An implicit enumeration algorithm for the time/cost tradeoff problem in project network analysis. Foundations of Control Engineering 4: 107-117

    Google Scholar 

  12. Håstad, J. (1997) Some optimal inapproximability results. Proceedings of the 29th ACM Symposium on the Theory of Computing (STOC’1997), pp. 1-10

  13. Håstad, J. (1999) Clique is hard to approximate within \(n^{1-\epsilon}\). Acta Mathematica 182: 105-142

    Google Scholar 

  14. Hindelang, T.J., Muth, J.F. (1979) A dynamic programming algorithm for decision CPM networks. Operations Research 27: 225-241

    MATH  Google Scholar 

  15. Kelley, J.E., Walker, M.R. (1959) Critical path planning and scheduling: An introduction. Mauchly Associates Inc., Ambler, PA

    Google Scholar 

  16. Maniezzo, V., Mingozzi, A. (1999) The project scheduling with irregular cost distribution. Operations Research Letters 25: 175-182

    Article  MATH  Google Scholar 

  17. Möhring, R.H. (1989) Computationally tractable classes of ordered sets. In: Rival, I. (ed.) Algorithms and order, pp. 105-193. Kluwer Academic Publishers

  18. Möhring, R.H., Schulz, A.S., Stork, F., Uetz, M. (2001) On project scheduling with with irregular starting time costs. Operations Research Letters 28: 149-154

    Article  Google Scholar 

  19. Robinson, D.R. (1975) A dynamic programming solution to cost-time tradeoff for CPM. Management Science 22: 158-166

    MATH  Google Scholar 

  20. Rothfarb, B., Frank, H., Rosenbaum, D.M., Steiglitz, K., Kleitman, D.J. (1970) Optimal design of offshore natural-gas pipeline systems. Operations Research 18: 992-1020

    Google Scholar 

  21. Skutella, M. (1998) Approximation algorithms for the discrete time-cost tradeoff problem. Mathematics of Operations Research 23: 909-929

    MATH  Google Scholar 

  22. Valdes, J., Tarjan, R.E., Lawler, E.L. (1982) The recognition of series-parallel digraphs. SIAM Journal on Computing 11: 298-313

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Quantitative Economies, University of Maastricht, P.O. Box 616, 6200, MD Maastricht, The Netherlands

    Alexander Grigoriev

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Alexander Grigoriev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerhard J. Woeginger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Grigoriev.

Additional information

Received: 2 February 2004, Published online: 29 October 2004

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigoriev, A., Woeginger, G.J. Project scheduling with irregular costs: complexity, approximability, and algorithms. Acta Informatica 41, 83–97 (2004). https://doi.org/10.1007/s00236-004-0150-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-004-0150-2

Keywords

Search

Navigation