Abstract
The Multiple Depot Crew Scheduling Problem (MD-CSP) appears in public transit systems (e.g., airline, bus and railway industry) and consists of determining the optimal duties for a set of crews (or vehicles) split among several depots in order to cover a set of timetabled trips satisfying a number of constraints. We consider the case in which every crew must return to the starting depot and limits are imposed on both the elapsed time and the working time of any duty. The MD-CSP is an extension of both the Multiple Depot Vehicle Scheduling Problem (MD-VSP) and the single depot Crew Scheduling Problem (CSP). The MD-CSP is formulated as a set partitioning problem with side constraints (SP), where each column corresponds to a feasible duty. In this paper we extend to the MD-CSP the exact method used by Bianco, Mingozzi and Ricciardelli (1994) for MD-VSP and that used by Mingozzi et al. (1999) for the CSP. We also introduce a new bounding procedure based on Lagrangian relaxation and column generation which can deal with the MD-CSP constraints. The computational results for both random and real-world test problems from the literature show that the new exact procedure outperforms, on the test problems used, other exact methods proposed in the literature for the MD-VSP and the CSP.
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References
Baldacci, R., E. Hadjiconstantinou, V. Maniezzo, and A. Mingozzi. (2002). “A New Method for Solving Capacitated Location Problems Based on a Set Partitioning Approach.” Computers and Operations Research 29, 365-386.
Barnhart, C., E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh, and P.H. Vance. (1994). “Branch-and-Price: Column Generation for Solving Huge Integer Programs.” In J.R. Birge and K.G. Murty (eds.), Mathematical Programming: State of the Art 1994. The University of Michigan, pp. 186-207.
Beasley, J.E. and B. Cao. (1996). “A Tree Search Algorithm for the Crew Scheduling Problem.” European Journal of Operational Research 94, 517-526.
Beasley, J.E. and B. Cao. (1998). “A Dynamic Programming Based Algorithm for the Crew Scheduling Problem.” Computers and Operations Research 25, 567-582.
Bianco, L., A. Mingozzi, and S. Ricciardelli. (1994). “A Set Partitioning Approach to the Multiple Depot Vehicle Scheduling Problem.” Optimization Methods and Software 3, 163-194.
Carpaneto, G., M. Dell'Amico, M. Fischetti, and P. Toth. (1989). “A Branch and Bound Algorithm for the Multiple Depot Vehicle Scheduling Problem.” Networks 19, 531-548.
Cranic, T.G. and J.M. Rousseau. (1987). “The Column Generation Principle and the Airline Crew Scheduling Problem.” INFOR 25, 136-151.
Dell'Amico, M., M. Fischetti, and P. Toth. (1993). “Heuristic Algorithms for the Multiple Depot Vehicle Scheduling Problem.” Management Science 39, 115-125.
Desrochers, M. and F. Soumis. (1989). “A Column Generation Approach to the Urban Transit Crew Scheduling Problem.” Transportation Science 23, 1-13.
Fischetti, M., S. Martello, P. Toth, and D. Vigo. (1998). “An LP-Based Heuristic Approach to the Crew Scheduling Problem.” In Proceedings TRISTAN III, San Juan, Puerto Rico.
Fischetti, M., A. Lodi, S. Martello, and P. Toth. (2001). “A Polyhedral Approach to the Simplified Crew Scheduling and Vehicle Scheduling Problems.” Management Science 47, 833-850.
Forbes,M.A., J.N. Holt, and A.M.Watts. (1994). “An Exact Algorithm for theMultiple Depot Bus Scheduling Problem.” European Journal of Operational Research 72(1), 115-124.
Hadjar, A., O. Marcotte, and F. Soumis. (2001). “A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem.” Technical Report, Les Cahiers du GERAD G-2001-25.
Lavoie, S., M. Minoux, and E. Odier. (1988). “A New Approach for Crew Pairing Problems by Column Generation with an Application to Air Transportation.” European Journal of Operational Research 35, 45-58.
Löbel, A. (1998a). “Optimal Vehicle Scheduling in Public Transit.” Ph.D. Dissertation, TU Berlin.
Löbel, A. (1998b). “Vehicle Scheduling in Public Transit and Lagrangian Pricing.” Management Science 44, 1637-1649.
Mingozzi, A., R. Baldacci, and S. Giorgi. (1999). “An Exact Method for the Vehicle Routing Problem with Backhauls.” Transportation Science 33, 315-329.
Mingozzi, A., M. Boschetti, S. Ricciardelli, and L. Bianco. (1999). “A Set Partitioning Approach to the Crew Scheduling Problem.” Operations Research 47, 873-888.
Mingozzi, A., N. Christofides, and E. Hadjiconstantinou. (1995). “An Exact Algorithm for the Vehicle Routing Problem Based on the Set Partitioning Formulation.” Technical Report, Department of Mathematics, University of Bologna, Italy.
Ribeiro, C.C. and F. Soumis. (1994). “A Column Generation Approach to the Multiple Depot Vehicle Scheduling Problem.” Operations Research 42, 41-52.
Yen, J.Y. (1971). “Finding the k-Shortest Loopless Paths in a Network.” Management Science 17, 712-716.
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Boschetti, M., Mingozzi, A. & Ricciardelli, S. An Exact Algorithm for the Simplified Multiple Depot Crew Scheduling Problem. Annals of Operations Research 127, 177–201 (2004). https://doi.org/10.1023/B:ANOR.0000019089.86834.91
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DOI: https://doi.org/10.1023/B:ANOR.0000019089.86834.91