Abstract
Since opening a new flight connection or closing an existing flight has a great impact on the revenues of an airline, the generation of the flight schedule is one of the fundamental problems in airline planning processes.
In this paper we concentrate on a special case of the problem which arises at charter companies. In contrast to airlines operating on regular schedules, the market for charter airlines is well-known and the schedule is allowed to change completely from period to period. Thus, precise adjustments to the demands of the market have a great potential for minimizing operating costs.
We present a capacitated network design model and propose a combined branch-and-cut approach to solve this airline schedule generation problem. To tighten the linear relaxation bound, we add cutting planes which adjust the number of aircraft and the spill of passengers to the demand on each itinerary.
For real-world problems from a large European charter airline we obtain solutions within a very few percent of optimality with running times in the order of minutes on a customary personal computer for most of the data sets.
Similar content being viewed by others
References
A. Balakrishnan, T.L. Magnanti and R.T. Wong, A decomposition algorithm for local access telecommunications network expansion planning, Operations Research 43 (1995) 58–76.
C. Barnhart, E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh and P.H. Vance, Branch-and-price: column generation for solving huge integer programs, Operations Research 46 (1998) 316–329.
C. Barnhart and R.R. Schneur, Air network design for express shipment service, Operations Research 44(6) (1996) 852–863.
K. Büdenbender, T. Grünert and H.J. Sebastian, A tabu search algorithm for the direct flight network design problem, Transportation Science 34 (2000) 364–380.
S.-G. Chang and B. Gavish, Lower bounding procedures for multiperiod telecommunications network expansion problem, Operations Research 43(1) (1995) 43–57.
T. Christof, A. Löbel and M. Stoer, PORTA-POlyhedral Representation Transfomation Algorithm. www.zib.de/Optimization/Software/Porta/, 1998.
T.G. Crainic and G. Laporte, Planning models for freight transportation, European Journal of Operational Research 97 (1997) 409–438.
H. Crowder, E.L. Johnson and M.W. Padberg, Solving large scale zero-one linear programming problems, Operations Research 31 (1983) 803–834.
M.S. Daskin and N.D. Panayotopoulos, A Lagrangian relaxation approach to assigning aircraft to routes in hub and spoke networks, Transportation Science 23 (1989) 91–99.
G. Desaulniers, J. Desrosiers, Y. Dumas, M.M. Solomon and F. Soumis, Daily aircraft routing and scheduling, Management Science 43 (1997) 841–855.
G. Desaulniers, J. Desrosiers, I. Ioachim, M.M. Solomon, F. Soumis and D. Villeneuve, A unified framework for deterministic time constraint vehicle routing and crew scheduling problems, Les Cahiers de GERAD G-94-46 (1997).
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, 1979).
K. Holmberg and J. Hellstrand, Solving the uncapacitated network design problem by a Lagrangian heuristic and branch-and-bound, in: Operations Research Proceedings 1996, Selected Papers of the SOR' 96, eds. U. Zimmermann, U. Derigs, W. Gaul, R.H. Möhring, and K.P. Schuster (Springer, 1997).
K. Holmberg and D. Yuan, A Lagrangian heuristic based branch-and-bound approach for the capacitated network design problem, Operations Research 46 (1998) 247–259.
B.W. Lamar, Y. Sheffi and W.B. Powell, A capacity improvement lower bound for fixed charge network design problem, Operations Research 38(4) (1990) 704–710.
L.S. Lasdon, Optimization Theory for Large Systems (Collier-MaxMillan, New York, 1970).
T.L. Magnanti, P. Mirchandani and R. Vachani, Modeling and solving the two-facility capacitated network loading problem, Operations Research 43 (1995) 142–157.
T.L. Magnanti, P. Mireault and R.T. Wong, Tailoring Bender's decomposition for network design, Mathematical Programming Study 26 (1986) 112–154.
T.L. Magnanti and R.T. Wong, Network design and transportation planning: Models and algorithms, Transportation Science 18 (1984) 1–55.
M. Minoux, Network synthesis and optimum network design problems: Models, solution methods and applications, Network 19 (1989) 313–360.
A. Noltemeier, Modelle und Lösungsverfahren zur Generierung von Flugplänen, Ph.D. thesis, ZAIK/ZPR, University of Cologne, Germany (2000).
M.W. Padberg, T.J. van Roy and L.A. Wolsey, Valid linear inequalities for fixed charge problems, Operations Research 33 (1985) 842–861.
B. Rexing, C. Barnhart, T. Kniker, A. Jarrah and N. Krishnamoorthy, Airline fleet assignment with time windows, Transportation Science 34 (2000) 1–20.
D.M. Ryan and B.A. Foster, An integer programming approach to scheduling, in: Computer scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling, ed. A.Wren (North-Holland, Amsterdam, 1981) pp. 35–139.
M.W.P. Savelsbergh and G.L. Nemhauser. Functional Description of MINTO, a Mixed INTeger Optimizer, Version 3.0 (Georgia Institute of Technology, 1998).
V. Sridhar and J.S. Park, Benders-and-cut algorithm for fixed-charge capacitated network design problem, European Journal of Operational Research 125 (2000) 622–632.
Using the CPLEX Callable Library, Version 6.0, CPLEX Optimization, Inc., 1998.
T.J. van Roy and L.A. Wolsey, Valid inequalities for mixed 0-1 programs, Discrete Applied Mathematics 14 (1986) 199–213.
P.H. Vance, A. Atamtürk, C. Barnhart, E. Gelman, E.L. Johnson, A. Krishna, D. Mahidhara, G.L. Nemhauser and R. Rebello, A heuristic branch-and-price approach for the airline crew pairing problem (1997) (from author).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Erdmann, A., Nolte, A., Noltemeier, A. et al. Modeling and Solving an Airline Schedule Generation Problem. Annals of Operations Research 107, 117–142 (2001). https://doi.org/10.1023/A:1014998931654
Issue Date:
DOI: https://doi.org/10.1023/A:1014998931654