An efficient computational approach for railway booking problems. (English) Zbl 1137.90327

Summary: This paper deals with the determination of seat allocations for a rail booking system. It is assumed that demand for each trip in the network can be divided into two segments, namely a full fare segment and a discounted fare segment. A constrained nonlinear integer programming model is formulated to deal with this problem. The purpose of this paper is to develop an efficient heuristic approach to develop the booking limits for all ticket types in the railway network. The solutions obtained by the heuristic approach are compared with those found by the Lingo software and the DICOPT solver. Numerical results show that the proposed heuristic approach only require a small number of CPU time to obtain superior solutions.


90B05 Inventory, storage, reservoirs
90B35 Deterministic scheduling theory in operations research
90C10 Integer programming
90C59 Approximation methods and heuristics in mathematical programming


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[1] Alstrup, J.; Boas, S.; Madsen, O. B.G.; Vidal, R. V.V., Booking policy for flights with two types of passengers, European Journal of Operational Research, 27, 274-288 (1986)
[2] Belobaba, P. P., Airline yield management: An overview of seat inventory control, Transportation Science, 21, 63-73 (1987)
[3] Belobaba, P. P., Application of a probabilistic decision model to airline seat inventory control, Operations Research, 37, 183-197 (1989)
[4] Brumelle, S. L.; McGill, J. I., Airline seat allocation with multiple nested fare classes, Operations Research, 41, 127-137 (1993) · Zbl 0775.90148
[5] Brumelle, S. L.; McGill, J. I.; Oum, T. H.; Sawaki, K.; Tretheway, M. W., Allocation of airline seats between stochastically dependent demands, Transportation Science, 24, 183-192 (1990)
[6] Burden, R. L.; Faires, J. D., Numerical Analysis (2001), Brooks/Cole: Brooks/Cole Pacific Grove, USA
[7] Clancimino, A.; Inzerillo, G.; Lucidi, S.; Palagi, L., A mathematical programming approach for the solution of the railway yield management problem, Transportation Science, 33, 168-181 (1999) · Zbl 1002.90529
[8] Curry, R. E., Optimal airline seat allocation with fare classes nested by origins and destination, Transportation Science, 24, 193-204 (1990)
[9] Gerchak, Y.; Parlar, M.; Yee, T., Optimal rationing policies and production quantities for products with Several Demand Classes, Canadian Journal of Administrative Science, 1, 161-176 (1985)
[10] Hersh, M.; Ladany, S. P., Optimal seat allocation for flights with one intermediate stop, Computers and Operations Research, 5, 31-37 (1978)
[11] Kennedy, J., Eberhart, R.C., 1995. Particle swarm optimization. In: Proceedings of the IEEE international Conference on Neural Networks 4, Perth, Australia 1942-1948.; Kennedy, J., Eberhart, R.C., 1995. Particle swarm optimization. In: Proceedings of the IEEE international Conference on Neural Networks 4, Perth, Australia 1942-1948.
[12] Koide, T.; Ishii, H., The hotel yield management with two types of room prices, overbooking and cancellations, International Journal of Production Economics, 417-428 (2005)
[13] Lee, T. L.; Hersh, M., A model for dynamic airline seat inventory control with multiple seat bookings, Transportation Science, 27, 252-265 (1993)
[14] McGill, I.; van Ryzin, G. J., Revenue management: Research overview and prospects, Transportation Science, 33, 233-256 (1999) · Zbl 1002.90032
[15] Robinson, L. W., Optimal and approximate control policies for airline booking with sequential nonmonotonic fare classes, Operations Research, 43, 2, 252-263 (1995) · Zbl 0832.90072
[16] Talluri, K. T.; van Ryzin, G. J., The Theory and Practice of Revenue Management (2004), Kluwer Academic Press: Kluwer Academic Press New York, NY · Zbl 1083.90024
[17] Weatherford, L. R.; Bodily, S. E., A taxonomy and research overview of perishable-asset revenue management: Yield management, overbooking, and pricing, Operations Research, 40, 831-844 (1992)
[18] Wollmer, R. D., An airline seat management model for a single leg route when lower fare classes book first, Operations Research, 40, 26-37 (1992) · Zbl 0825.90664
[19] You, P. S., Dynamic pricing in airline seat management for flights with multiple flight legs, Transportation Science, 33, 192-206 (1999) · Zbl 1002.90526
[20] You, P. S., Airline seat management with rejection-for-possible-upgrade decision, Transportation Research - Part B, 35, 507-524 (2001)
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