Skip to main content
Log in

An algorithm for large scale 0–1 integer programming with application to airline crew scheduling

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

Abstract

We present an approximation algorithm for solving large 0–1 integer programming problems whereA is 0–1 and whereb is integer. The method can be viewed as a dual coordinate search for solving the LP-relaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems that have appeared in the literature.

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. E.H.L. Aarts and J.H.M. Korst,Simulated Annealing and Boltzmann Machines (Wiley, 1989).

  2. J.P. Arabeyre, J. Fearnley, F.C. Steiger and W. Teather, The Airline Crew scheduling problem: A survey, Transp. Sci. 3(1969)140–163.

    Google Scholar 

  3. D. Avis, A note on some computationally difficult set covering problems, Math. Progr. 18(1980)138–145.

    Google Scholar 

  4. E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics and subgradient optimization: a computational study, Math. Progr. Study 12(1980)37–60.

    Google Scholar 

  5. U. Bertele and F. Brioschi,Nonserial Dynamic Programming (Academic Press, 1972).

  6. V. Chvatal, A greedy-heuristic for the set-covering problem, Math. Oper. Res. 4(1979)233–235.

    Google Scholar 

  7. CPLEX Reference Manual (CPLEX Optimization Inc., 1992).

  8. J. Derosiers, Y. Dumas, M.M. Solomon and F. Soumis, Time constrained routing and scheduling, in:Handbooks in Operations Research and Management Science, volume onNetworks (North-Holland, 1993), to be published.

  9. M.M. Etschmaier and D.F. Mathaisel, Airline scheduling: an overview, Transp. Sci. 19(1985)127–138.

    Google Scholar 

  10. T.A. Feo and M.G.C. Resende, A probabilistic heuristic for a computational difficult set covering problem, Oper. Res. Lett. 8(1989)67–71.

    Google Scholar 

  11. D.R. Fulkerson, G.L. Nemhauser and L.E. Trotter, Jr., Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems, Math. Progr. Study 7(1974)72–81.

    Google Scholar 

  12. M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, 1979).

  13. T.C. Hu,Integer Programming and Network Flows (Addison-Wesley, 1969).

  14. N. Karmarkar, M.G.C. Resende and K.G. Ramakrishnan, An interior point algorithm to solve computationally difficult set covering problems, Math. Progr. 52(1991)597–618.

    Google Scholar 

  15. S. Lavoie, M. Minoux and E. Odier, A new approach for crew pairing problems with an application to air transportation, Euro. J. Oper. Res. 35(1988)45–58.

    Google Scholar 

  16. G.L. Nemhauser and L.A. Wolsey,Integer and Combinational Optimization (Wiley, 1988).

  17. A. Schrijver,Theory of Linear and Integer Programming (Wiley, 1986).

  18. M. Syslo, N. Deo and J.S. Kowalik,Discrete Optimization Algorithms (Prentice-Hall, 1983).

  19. D. Wedelin, Probabilistic networks and combinatorial optimization, Technical report 49, Department of Computing Science, Chalmers University of Technology (1989).

  20. D. Wedelin, Probabilistic inference, combinatorial optimization and the discovery of causal structure from data, Ph.D Thesis, Department of Computing Science, Chalmers University of Technology (1993).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wedelin, D. An algorithm for large scale 0–1 integer programming with application to airline crew scheduling. Ann Oper Res 57, 283–301 (1995). https://doi.org/10.1007/BF02099703

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02099703

Keywords

Navigation