AIRLINE CREW SCHEDULING USING SET PARTITIONING AND COLUMN GENERATION: A REPORT ON BARNHART ET AL. (2003) WITH AN INDIAN CONTEXT
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Anil Surendra Modi School of Commerce, NMIMS Deemed-to-be University, Mumbai, India
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Abstract
Airline crew pay depends on rules that limit who may fly which flight, and a weak crew plan is costly to fix once flights are running. The regulator's inquiry into the cancellation of 2,507 IndiGo flights in three days of December 2025 pointed to over-optimised rosters with thin buffers. This report studies the chapter "Airline Crew Scheduling" by Barnhart, Cohn, Johnson, Klabjan, Nemhauser and Vance (2003) and sets it out as an operations research case study. The chapter models crew pairing as a set partitioning problem and solves it by column generation and branch-and-price. It then extends the models to crew assignment, recovery from disruption and robust planning. We re-work the chapter's seven-flight example and check it by enumeration and a linear programming solver. Only one set of pairings covers every flight exactly once, at 9 hours of pay for 7 hours of flying. The linear programming bound is 8 without the crewbase constraints and 9 with them. We also tabulate the results quoted in the chapter, such as a fall in the gap to the flying-time bound from 10 to 15 per cent to 1 to 2 per cent, and relate them to the Indian case. The chapter is strongest on method and weakest on open data and on rules outside the United States.
Keywords
airline crew scheduling; crew pairing; set partitioning; column generation; branch-and-price; robust scheduling; flight duty time limitations
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Double-Blind Peer Review
License:
CC BY-NC 4.0
Volume/Issue:
Volume 02, Issue 10
Review Rounds:
2
Article Type:
Research Article
Publication Date:
Oct 06 2026
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Doshi, P., Shah, N., Kayal, N., Dewoolkar, N. & Bagania, N. (2026). Airline Crew Scheduling Using Set Partitioning and Column Generation: A Report on Barnhart et al. (2003) with an Indian Context. International Journal of Science, Strategic Management and Technology, 02(10), 1-9. https://doi.org/10.55041/ijsmt.v2i10.008
Doshi, Paarsh, et al.. "Airline Crew Scheduling Using Set Partitioning and Column Generation: A Report on Barnhart et al. (2003) with an Indian Context." International Journal of Science, Strategic Management and Technology, vol. 02, no. 10, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijsmt.v2i10.008.
Doshi, Paarsh,Nihar Shah,Nilay Kayal,Nidhish Dewoolkar, and Nitya Bagania. "Airline Crew Scheduling Using Set Partitioning and Column Generation: A Report on Barnhart et al. (2003) with an Indian Context." International Journal of Science, Strategic Management and Technology 02, no. 10 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijsmt.v2i10.008.
References
Anbil, R., Barnhart, C., Johnson, E., & Hatay, L. (1994). A column generation technique for the long-haul crew assignment problem. In T. Ciriani & R. Leachman (Eds.), Optimization in industry II (pp. 7-24). John Wiley & Sons.
Anbil, R., Gelman, E., Patty, B., & Tanga, R. (1991). Recent advances in crew pairing optimization at American Airlines. Interfaces, 21, 62-74.
Anbil, R., Johnson, E., & Tanga, R. (1992). A global approach to crew pairing optimization. IBM Systems Journal, 31, 71-78.
Andersson, E., Housos, E., Kohl, N., & Wedelin, D. (1998). Crew pairing optimization. In G. Yu (Ed.), Operations research in the airline industry (pp. 228-258). Kluwer Academic Publishers.
Barahona, F., & Anbil, R. (1999). On some difficult linear programs coming from set partitioning (Technical Report RC-21410). T. J. Watson Research Center.
Barnhart, C., Cohn, A. M., Johnson, E. L., Klabjan, D., Nemhauser, G. L., & Vance, P. H. (2003). Airline crew scheduling. In R. W. Hall (Ed.), Handbook of transportation science (2nd ed., pp. 517-560). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48058-1_14
Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., & Vance, P. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46, 316-329.
Bixby, R., Gregory, J., Lustig, I., Marsten, R., & Shanno, D. (1992). Very large-scale linear programming: A case study in combining interior point and simplex methods. Operations Research, 40, 885-897.
Anbil, R., Gelman, E., Patty, B., & Tanga, R. (1991). Recent advances in crew pairing optimization at American Airlines. Interfaces, 21, 62-74.
Anbil, R., Johnson, E., & Tanga, R. (1992). A global approach to crew pairing optimization. IBM Systems Journal, 31, 71-78.
Andersson, E., Housos, E., Kohl, N., & Wedelin, D. (1998). Crew pairing optimization. In G. Yu (Ed.), Operations research in the airline industry (pp. 228-258). Kluwer Academic Publishers.
Barahona, F., & Anbil, R. (1999). On some difficult linear programs coming from set partitioning (Technical Report RC-21410). T. J. Watson Research Center.
Barnhart, C., Cohn, A. M., Johnson, E. L., Klabjan, D., Nemhauser, G. L., & Vance, P. H. (2003). Airline crew scheduling. In R. W. Hall (Ed.), Handbook of transportation science (2nd ed., pp. 517-560). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48058-1_14
Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., & Vance, P. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46, 316-329.
Bixby, R., Gregory, J., Lustig, I., Marsten, R., & Shanno, D. (1992). Very large-scale linear programming: A case study in combining interior point and simplex methods. Operations Research, 40, 885-897.
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