Solving Airline Crew Scheduling Problems by Branch-and-Cut
AbstractThe crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline's fleets. The problem is especially important today since costs for flying personnel of major U.S. carriers have grown and now often exceed $1.3 billion a year and are the second largest item (next to fuel cost) of the total operating cost of major U.S. carriers. Thus even small percentage savings amount to substantial dollar amounts. We present a branch-and-cut approach to solving to proven optimality large set partitioning problems arising within the airline industry. We first provide some background related to this important application and then describe the approach for solving representative problems in this problem class. The branch-and-cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree-search algorithm that uses automatic reformulation procedures, heuristics and linear programming technology to assist in the solution. Numerical experiments are reported for a sample of 68 large-scale real-world crew scheduling problems. These problems include both pure set partitioning problems and set partitioning problems with side constraints. These "base constraints" represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality. An interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by INFORMS in its journal Management Science.
Volume (Year): 39 (1993)
Issue (Month): 6 (June)
zero-one programming; set partitioning; crew scheduling; polyhedral cuts; preprocessing; heuristics; automatic reformulation; branch-and-cut; scientific computation;
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Rönnberg, Elina & Larsson, Torbjörn, 2009. "Column generation in the integral simplex method," European Journal of Operational Research, Elsevier, vol. 192(1), pages 333-342, January.
- Desaulniers, G. & Desrosiers, J. & Dumas, Y. & Marc, S. & Rioux, B. & Solomon, M. M. & Soumis, F., 1997. "Crew pairing at Air France," European Journal of Operational Research, Elsevier, vol. 97(2), pages 245-259, March.
- Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
- Sriram, Chellappan & Haghani, Ali, 2003. "An optimization model for aircraft maintenance scheduling and re-assignment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(1), pages 29-48, January.
- Xia, Mu & Koehler, Gary J. & Whinston, Andrew B., 2004. "Pricing combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 154(1), pages 251-270, April.
- Kroon, L.G. & Fischetti, M., 2000. "Crew Scheduling for Netherlands Railways: "destination: customer"," ERIM Report Series Research in Management ERS-2000-56-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
- Liu, Jiyin & MacCarthy, B. L., 1997. "A global MILP model for FMS scheduling," European Journal of Operational Research, Elsevier, vol. 100(3), pages 441-453, August.
- Bjorndal, M. H. & Caprara, A. & Cowling, P. I. & Della Croce, F. & Lourenco, H. & Malucelli, F. & Orman, A. J. & Pisinger, D. & Rego, C. & Salazar, J. J., 1995. "Some thoughts on combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 83(2), pages 253-270, June.
- Wark, Peter & Holt, John & Ronnqvist, Mikael & Ryan, David, 1997. "Aircrew schedule generation using repeated matching," European Journal of Operational Research, Elsevier, vol. 102(1), pages 21-35, October.
- Abbink, E.J.W., 2008. "Solving large scale crew scheduling problems by using iterative partitioning," Econometric Institute Research Papers EI 2008-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Bredström, David & Jörnsten, Kurt & Rönnqvist, Mikael, 2007. "Searching for optimal integer solutions to set partitioning problems using column generation," Discussion Papers 2007/20, Department of Business and Management Science, Norwegian School of Economics.
- Beasley, J. E. & Cao, B., 1996. "A tree search algorithm for the crew scheduling problem," European Journal of Operational Research, Elsevier, vol. 94(3), pages 517-526, November.
- Darby-Dowman, K. & Fink, R. K. & Mitra, G. & Smith, J. W., 1995. "An intelligent system for US Coast Guard cutter scheduling," European Journal of Operational Research, Elsevier, vol. 87(3), pages 574-585, December.
- Yan, Shangyao & Chang, Jei-Chi, 2002. "Airline cockpit crew scheduling," European Journal of Operational Research, Elsevier, vol. 136(3), pages 501-511, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc).
If references are entirely missing, you can add them using this form.