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Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows
Abstract
In the pickup and delivery problem with time windows vehicle routes must be designed to satisfy a set of transportation requests, each involving a pickup and delivery location, under capacity, time window, and precedence constraints. This paper introduces a new branch-and-cut-and-price algorithm in which lower bounds are computed by solving through column generation the linear programming relaxation of a set partitioning formulation. Two pricing subproblems are considered in the column generation algorithm: an elementary and nonelementary shortest path problem. Valid inequalities are added dynamically to strengthen the relaxations. Some of the previously proposed inequalities for the pickup and delivery problem with time windows are also shown to be implied by the set partitioning formulation. Computational experiments indicate that the proposed algorithm outperforms a recent branch-and-cut algorithm.
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Cited by
A taxonomy for task allocation problems with temporal and ordering constraints
Nunes, E., Manner, M., Mitiche, H., & Gini, M. (2017) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2016.10.008 · Cited by 252
Congestion-aware system optimal route choice for shared autonomous vehicles
Levin, M. W. (2017) · Transportation Research Part C: Emerging Technologies · doi:10.1016/j.trc.2017.06.020 · Cited by 152
A survey of resource constrained shortest path problems: Exact solution approaches
Pugliese, L. D. P., & Guerriero, F. (2013) · Networks · doi:10.1002/net.21511 · Cited by 147
Hyland, M. F., & Mahmassani, H. S. (2017) · Transportation Research Record: Journal of the Transportation Research Board · doi:10.3141/2653-04 · Cited by 69
Vehicle routing problems with road‐network information: State of the art
Ben Ticha, H., Absi, N., Feillet, D., & Quilliot, A. (2018) · Networks · doi:10.1002/net.21808 · Cited by 51
Metadata
- Authors
- Ropke, S., & Cordeau, J.-F.
- Venue
- Transportation Science
- Published
- 2009-08
- Volume
- 43
- Issue
- 3
- Pages
- 267-286
- ISSN
- 0041-1655 (ISSN-L)
- 1526-5447
- OpenAlex
- W2119097848
- Cited by
- 487
- References
- 0
- FWCI
- 39.28
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ropke, S., & Cordeau, J.-F. (2009). Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows. Transportation Science. https://doi.org/10.1287/trsc.1090.0272
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