Abstract
For real life bus and train driver scheduling instances, the number of columns in terms of the set covering/partitioning ILP model could run into billions making the problem very difficult. Column generation approaches have the drawback that the sub-problems for generating the columns would be computationally expensive in such situations. This paper proposes a hybrid solution method, called PowerSolver, of using an iterative heuristic to derive a series of small refined sub-problem instances fed into an existing efficient set covering ILP based solver. In each iteration, the minimum set of relief opportunities that guarantees a solution no worse than the current best is retained. Controlled by a user-defined strategy, a small number of the banned relief opportunities would be reactivated and some soft constraints may be relaxed before the new sub-problem instance is solved. PowerSolver is proving successful by many transport operators who are now routinely using it. Test results from some large scale real-life exercises will be reported.
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Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. (1998). Branch-and-price: column generation for solving huge integer programs. Operations Research, 46, 316–329.
Caprara, A., Fischetti, M., Toth, P., Vigo, D., & Luigi Guida, P. (1997). Algorithms for railway crew management. Mathematical Programming, 79, 125–141.
Chicago Workshop. (1975). Preprints of the international workshop on automated techniques for scheduling of vehicle operators for urban public transportation services.
Daduna, J. R., & Wren, A. (Eds.). (1988). Computer-aided transit scheduling. Proceedings of the fourth international workshop on computer-aided scheduling of public transport. Berlin: Springer.
Daduna, J. R., Branco, I., & Paixáo, J. M. P. (Eds.). (1995). Computer-aided transit scheduling. Proceedings of the sixth international workshop on computer-aided scheduling of public transport. Berlin: Springer.
Desrochers, M., & Rousseau, J.-M. (Eds.). (1992). Computer-aided transit scheduling. Proceedings of the fifth international workshop on computer-aided scheduling of public transport. Berlin: Springer.
Desrochers, M., & Soumis, F. (1989). A column generation approach to the urban transit crew scheduling problem. Transportation Science, 23, 1–13.
Desrochers, M., Gilbert, J., Sauve, M., & Soumis, F. (1992). CREW-OPT: subproblem modelling in a column generation approach to urban crew scheduling. In M. Desrochers et al. (Eds.), Computer-aided transit scheduling (pp. 395–406). Berlin: Springer.
Fores, S., Proll, L., & Wren, A. (2002). TRACS II: a hybrid IP/heuristic driver scheduling system for public transport. Journal of the Operational Research Society, 53, 1093–1100.
Hoffman, K. L., & Padberg, M. (1993). Solving airline crew scheduling problems by branch-and-cut. Management Science, 39(6), 657–682.
Kwan, A. S. K., Kwan, R. S. K., Parker, M. E., & Wren, A. (1996). Producing train driver shifts by computer, In J. Allan et al. (Eds.), Computer in railways V, Volume 1: Railway systems and management (pp. 421–435). Computational Mechanics Publications.
Kwan, R. S. K. (2004). Bus and train driver scheduling. In J.Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models, and performance analysis (Chapter 51, pp. 1–20). CRC Press.
Kwan, R. S. K., & Wren, A. (1996). Hybrid genetic algorithms for bus driver scheduling. In L. Bianco & P. Toth (Eds.), Advanced methods in transportation analysis (pp. 609–619). Berlin: Springer.
Kwan, R. S. K., Kwan, A. S. K., & Wren, A. (2001). Evolutionary driver scheduling with relief chains. Evolutionary Computation, 9, 445–460.
Layfield, C. J., Smith, B. M., & Wren, A. (1999). Bus relief opportunity selection using constraint programming. In Proceedings of first international conference on the practical applications of constraint technologies and logic programming (pp. 537–552). Blackpool: The Practical Application Company.
Li, J., & Kwan, R. S. K. (2003). A fuzzy genetic algorithm for driver scheduling. European Journal of Operational Research, 147, 334–344.
Rousseau, J.-M. (Ed.). (1985). Computer scheduling of public transport 2. Proceedings of the third international workshop on computer-aided scheduling of public transport. Amsterdam: North-Holland.
Smith, B. M., & Wren, A. (1988). A bus crew scheduling system using a set covering formulation. Transportation Research, 22A, 97–108.
Voss, S., & Daduna, J. R. (Eds.). (2001). Computer-aided scheduling of public transport. Proceedings of the eighth international conference on computer-aided scheduling of public transport (CASPT 2000). Berlin: Springer.
Wilson, N. H. M. (Ed.). (1999). Computer-aided transit scheduling. Proceedings of the seventh international workshop on computer-aided scheduling of public transport. Berlin: Springer.
Wren, A. (Ed.). (1981a). Computer scheduling of public transport. Proceedings of the second international workshop on computer-aided scheduling of public transport. Amsterdam: North-Holland.
Wren, A. (1981b). General review of the use of computers in scheduling buses and their crews. In A. Wren (Ed.), Computer scheduling of public transport (pp. 3–16). Amsterdam: North-Holland.
Wren, A., & Rousseau, J.-M. (1995). Bus driver scheduling—an overview. In J. R. Daduna, I. Branco & J. M. P. Paixao (Eds.), Computer-aided transit scheduling (pp. 173–187). Berlin: Springer.
Wren, A., Fores, S., Kwan, A. S. K., Kwan, R. S. K., Parker, M. E., & Proll, L. (2003). A flexible system for scheduling drivers. Journal of Scheduling, 6, 437–455.
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Kwan, R.S.K., Kwan, A. Effective search space control for large and/or complex driver scheduling problems. Ann Oper Res 155, 417–435 (2007). https://doi.org/10.1007/s10479-007-0203-3
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DOI: https://doi.org/10.1007/s10479-007-0203-3