Skip to main content

Solving Airline-fleet Scheduling Problems with Mixed-integer Programming

  • Chapter
Operational Research in Industry

Abstract

This chapter discusses the solution of real-life airline fleet scheduling problems of a large European airline, and aims to minimize the number of aircraft needed to serve a given set of flights. There is certain Nfreedom to schedule the flights expressed as a time window per each flight within which the flight has to depart. This is the strategy of some European carriers, which first fix the number of flights per connection together with the time window and the fleet for each flight according to the expected number of passengers. In a second step they schedule the flights within their given departure time windows. This problem of scheduling the flights and simultaneously generating aircraft rotations will be called the fleet scheduling problem. (For more details on the planning process see Suhl, 1995)

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Baker, E.K., L.D. Bodin and M. Fisher (1995) ‘The Development and Implementation of a Heuristic Set Covering Based System for Air Crew Scheduling’, Transportation Policy Decision Making, 3, 95–110.

    Google Scholar 

  • Bodin, L, B. Golden, A. Assad and M. Ball (1983) ‘Routing and Scheduling of Vehicles and Crews’, Computers and Operations Research, 10, 63–211.

    Article  Google Scholar 

  • Brearley, A.L., G. Mitra and H.P. Williams (1975) Analysis of Mathematical Programming Problems Prior to Applying the Simplex Algorithm’, Mathematical Programming, 8, 54–83.

    Article  Google Scholar 

  • Christofides, N., A. Mingozzi and P. Toth (1979) The Vehicle Routing Problem, Combinatorial Optimization, Chapter 11, (New York: Wiley, 1979).

    Google Scholar 

  • Crowder, H., E.L. Johnson and M.W. Padberg (1983) ‘Solving Largescale Zero–one Linear Programming Problems’, Operations Research. 31, 803–34.

    Article  Google Scholar 

  • Desrosiers, J., F. Soumis and M. Desrochers (1984) ‘Routing with Time Windows by Column Generation’, Networks, 14, 545–65.

    Article  Google Scholar 

  • Desrosiers, J., Y. Dumas, M. Desrochers, F. Soumis, B. Sanso and P. Trudeau (1991) ‘A Breakthrough in Airline Crew Scheduling’, GERAD Report, G-91-11, Montreal.

    Google Scholar 

  • Dietrich, B.L. and L.F. Escudero (1990) ‘Coefficient Reduction for Knapsack Constraints in 0–1 Programs with VUBs’, Operations Research Letters, 9, 9–14.

    Article  Google Scholar 

  • Dietrich, B.L., L.F. Escudero and F. Chance (1993) ‘Efficient Reformulation for 0–1 Programs - Methods and Computational Results’, Discrete Applied Mathematics, 42, 147–75.

    Article  Google Scholar 

  • Gertsbach, J. and Y. Gurevich (1997) ‘Constructing an Optimal Fleet for a Transportation Schedule’, Transportation Science, 11, 20–36.

    Article  Google Scholar 

  • Guignard, M. and K. Spielberg (1981) ‘Logical Reduction Methods in Zeroone Programming (Minimal Preferred Variables)’, Operations Research, 29, 49–74.

    Article  Google Scholar 

  • Hoffman, K. and M.W. Padberg (1991) ‘Improving LP-representations of Zero–one Linear Programs for Branch-and-cut’, ORSA Journal on Computing, 3, 121–34.

    Article  Google Scholar 

  • Johnson, E.L., M.M. Kostreva and U.H. Suhl (1988) ‘Solving 0–1 Integer Programming Problems Arising from Large-scale Planning Models’, Operations Research, 35, 803–19.

    Google Scholar 

  • Johnson, E.L. (1989) ‘Modeling and Strong Linear Programs for Mixed Integer Programming’, in S.W. Wallace (ed.), Algorithms and Model Formulation in Mathematical Programming (Berlin: Springer Verlag), 1–44.

    Chapter  Google Scholar 

  • Levin, A. (1971) ‘Scheduling and Fleet Routing Models for Transportation Systems’, Transportation Science, 5, 232–55.

    Article  Google Scholar 

  • Savelsbergh, M.W.P. (1994) ‘Preprocessing and Probing Techniques for Mixed Integer Programming Problems’, ORSA Journal on Computing, 6, 445–54.

    Article  Google Scholar 

  • Suhl, L.M. (1995) Computer-Aided Scheduling (Wiesbaden: Gabler Verlag Edition Wissenschaft.

    Book  Google Scholar 

  • Suhl, U.H. (1985) ‘Solving Large-scale Mixed Integer Programs with Fixed Charge Variables’, Mathematical Programming, 32, 165–82.

    Article  Google Scholar 

  • Suhl, U.H. (1994) ‘MOPS - Mathematical Optimization System’, European Journal of Operational Research, 72, 312–22.

    Article  Google Scholar 

  • Suhl, U.H. and H. Hilbert (1998) A Branch-and-Cut Algorithm for Solving Generalized Multiperiod Steiner Problems in Graphs’, Networks, 31,4, 273- 82.

    Article  Google Scholar 

  • Suhl, U.H. and R. Szymanski (1994) ‘Supernode Processing of Mixed-Integer Models’, Computational Optimization and Applications, 3, 317–31.

    Article  Google Scholar 

  • Wolsey, L.A. (1989) ‘Tight Formulations for Mixed Integer Programming: A Survey’, Mathematical Programming, 45, 173–91.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Copyright information

© 1999 Uwe H. Suhl and Leena M. Suhl

About this chapter

Cite this chapter

Suhl, U.H., Suhl, L.M. (1999). Solving Airline-fleet Scheduling Problems with Mixed-integer Programming. In: Ciriani, T.A., Gliozzi, S., Johnson, E.L., Tadei, R. (eds) Operational Research in Industry. Palgrave Macmillan, London. https://doi.org/10.1057/9780230372924_7

Download citation

Publish with us

Policies and ethics