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Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW

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  1. Wang, Xiubin & Regan, Amelia C., 2002. "Local truckload pickup and delivery with hard time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 97-112, February.
  2. Julia Rieck & Jürgen Zimmermann, 2010. "A new mixed integer linear model for a rich vehicle routing problem with docking constraints," Annals of Operations Research, Springer, vol. 181(1), pages 337-358, December.
  3. Martinelli, Rafael & Pecin, Diego & Poggi, Marcus, 2014. "Efficient elementary and restricted non-elementary route pricing," European Journal of Operational Research, Elsevier, vol. 239(1), pages 102-111.
  4. Jiguang Wang & Yilun Zhang & Xinjie Xing & Yuanzhu Zhan & Wai Kin Victor Chan & Sunil Tiwari, 2024. "A data-driven system for cooperative-bus route planning based on generative adversarial network and metric learning," Annals of Operations Research, Springer, vol. 339(1), pages 427-453, August.
  5. Li, Siqiao & Zhu, Xiaoning & Shang, Pan & Li, Tianqi & Liu, Wenqian, 2023. "Optimizing a shared freight and passenger high-speed railway system: A multi-commodity flow formulation with Benders decomposition solution approach," Transportation Research Part B: Methodological, Elsevier, vol. 172(C), pages 1-31.
  6. Schulz, Arne & Pfeiffer, Christian, 2024. "Using fixed paths to improve branch-and-cut algorithms for precedence-constrained routing problems," European Journal of Operational Research, Elsevier, vol. 312(2), pages 456-472.
  7. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
  8. Iman Dayarian & Guy Desaulniers, 2019. "A Branch-Price-and-Cut Algorithm for a Production-Routing Problem with Short-Life-Span Products," Transportation Science, INFORMS, vol. 53(3), pages 829-849, May.
  9. Christian Tilk, 2016. "Branch-and-Price-and-Cut for the Vehicle Routing and Truck Driver Scheduling Problem," Working Papers 1616, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  10. Qie He & Stefan Irnich & Yongjia Song, 2018. "Branch-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Working Papers 1804, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  11. Ponboon, Sattrawut & Qureshi, Ali Gul & Taniguchi, Eiichi, 2016. "Branch-and-price algorithm for the location-routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 1-19.
  12. Ricardo Fukasawa & Qie He & Fernando Santos & Yongjia Song, 2018. "A Joint Vehicle Routing and Speed Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 694-709, November.
  13. Li, Jing-Quan & Mirchandani, Pitu B. & Borenstein, Denis, 2009. "Real-time vehicle rerouting problems with time windows," European Journal of Operational Research, Elsevier, vol. 194(3), pages 711-727, May.
  14. Dollevoet, T.A.B. & Pecin, D. & Spliet, R., 2020. "The path programming problem and a partial path relaxation," Econometric Institute Research Papers EI-2020-04, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  15. Miao Yu & Viswanath Nagarajan & Siqian Shen, 2022. "Improving Column Generation for Vehicle Routing Problems via Random Coloring and Parallelization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 953-973, March.
  16. Dayarian, Iman & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2015. "A column generation approach for a multi-attribute vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 888-906.
  17. Stefan Irnich & Daniel Villeneuve, 2006. "The Shortest-Path Problem with Resource Constraints and k -Cycle Elimination for k (ge) 3," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 391-406, August.
  18. Timo Hintsch & Stefan Irnich, 2018. "Exact Solution of the Soft-Clustered Vehicle Routing Problem," Working Papers 1813, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  19. Wang, Mengtong & Zhang, Canrong & Bell, Michael G.H. & Miao, Lixin, 2022. "A branch-and-price algorithm for location-routing problems with pick-up stations in the last-mile distribution system," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1258-1276.
  20. Bode, Claudia & Irnich, Stefan, 2014. "The shortest-path problem with resource constraints with (k,2)-loop elimination and its application to the capacitated arc-routing problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 415-426.
  21. Bettinelli, Andrea & Cacchiani, Valentina & Crainic, Teodor Gabriel & Vigo, Daniele, 2019. "A Branch-and-Cut-and-Price algorithm for the Multi-trip Separate Pickup and Delivery Problem with Time Windows at Customers and Facilities," European Journal of Operational Research, Elsevier, vol. 279(3), pages 824-839.
  22. Hernandez, Florent & Feillet, Dominique & Giroudeau, Rodolphe & Naud, Olivier, 2016. "Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 249(2), pages 551-559.
  23. Emilio Zamorano & Annika Becker & Raik Stolletz, 2018. "Task assignment with start time-dependent processing times for personnel at check-in counters," Journal of Scheduling, Springer, vol. 21(1), pages 93-109, February.
  24. Rasmussen, Matias Sevel & Justesen, Tor & Dohn, Anders & Larsen, Jesper, 2012. "The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies," European Journal of Operational Research, Elsevier, vol. 219(3), pages 598-610.
  25. Reihaneh, Mohammad & Ghoniem, Ahmed, 2019. "A branch-and-price algorithm for a vehicle routing with demand allocation problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 523-538.
  26. Range, Troels Martin, 2013. "Exploiting Set-Based Structures to Accelerate Dynamic Programming Algorithms for the Elementary Shortest Path Problem with Resource Constraints," Discussion Papers on Economics 17/2013, University of Southern Denmark, Department of Economics.
  27. Asvin Goel & Stefan Irnich, 2017. "An Exact Method for Vehicle Routing and Truck Driver Scheduling Problems," Transportation Science, INFORMS, vol. 51(2), pages 737-754, May.
  28. Zäpfel, Günther & Bögl, Michael, 2008. "Multi-period vehicle routing and crew scheduling with outsourcing options," International Journal of Production Economics, Elsevier, vol. 113(2), pages 980-996, June.
  29. Boschetti, Marco Antonio & Maniezzo, Vittorio & Strappaveccia, Francesco, 2017. "Route relaxations on GPU for vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 258(2), pages 456-466.
  30. Yao, Yu & Van Woensel, Tom & Veelenturf, Lucas P. & Mo, Pengli, 2021. "The consistent vehicle routing problem considering path consistency in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 21-44.
  31. Froger, Aurélien & Sadykov, Ruslan, 2023. "New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources," European Journal of Operational Research, Elsevier, vol. 306(1), pages 65-82.
  32. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
  33. Wang, Naiyu & Meng, Qiang & Zhang, Canrong, 2023. "A branch-price-and-cut algorithm for the local container drayage problem with controllable vehicle interference," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
  34. Diego Pecin & Claudio Contardo & Guy Desaulniers & Eduardo Uchoa, 2017. "New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 489-502, August.
  35. Shyam S. G. Perumal & Jesper Larsen & Richard M. Lusby & Morten Riis & Tue R. L. Christensen, 2022. "A column generation approach for the driver scheduling problem with staff cars," Public Transport, Springer, vol. 14(3), pages 705-738, October.
  36. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2018. "Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 52(2), pages 300-319, March.
  37. Natashia Boland & Mike Hewitt & Luke Marshall & Martin Savelsbergh, 2019. "The price of discretizing time: a study in service network design," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 195-216, June.
  38. Qinxiao Yu & Chun Cheng & Ning Zhu, 2022. "Robust Team Orienteering Problem with Decreasing Profits," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3215-3233, November.
  39. Guy Desaulniers & François Lessard & Ahmed Hadjar, 2008. "Tabu Search, Partial Elementarity, and Generalized k -Path Inequalities for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 42(3), pages 387-404, August.
  40. Charlotte Vilhelmsen & Richard M. Lusby & Jesper Larsen, 2017. "Tramp ship routing and scheduling with voyage separation requirements," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 913-943, October.
  41. Line Blander Reinhardt & Mads Kehlet Jepsen & David Pisinger, 2016. "The Edge Set Cost of the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 50(2), pages 694-707, May.
  42. Bhusiri, Narath & Qureshi, Ali Gul & Taniguchi, Eiichi, 2014. "The trade-off between fixed vehicle costs and time-dependent arrival penalties in a routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 1-22.
  43. Alberto Ceselli & Giovanni Righini & Matteo Salani, 2009. "A Column Generation Algorithm for a Rich Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 43(1), pages 56-69, February.
  44. Zhu, Xiaoyan & Wilhelm, Wilbert E., 2007. "Three-stage approaches for optimizing some variations of the resource constrained shortest-path sub-problem in a column generation context," European Journal of Operational Research, Elsevier, vol. 183(2), pages 564-577, December.
  45. Nigam, Ashutosh & Agarwal, Yogesh K., 2014. "Optimal relay node placement in delay constrained wireless sensor network design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 220-233.
  46. F. Errico & G. Desaulniers & M. Gendreau & W. Rei & L.-M. Rousseau, 2018. "The vehicle routing problem with hard time windows and stochastic service times," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 223-251, September.
  47. Jonathan F. Bard & Siwate Rojanasoonthon, 2006. "A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 24-44, February.
  48. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
  49. Wang, Mengtong & Miao, Lixin & Zhang, Canrong, 2021. "A branch-and-price algorithm for a green location routing problem with multi-type charging infrastructure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
  50. Yin, Yunqiang & Yang, Yongjian & Yu, Yugang & Wang, Dujuan & Cheng, T.C.E., 2023. "Robust vehicle routing with drones under uncertain demands and truck travel times in humanitarian logistics," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
  51. Guy Desaulniers & Diego Pecin & Claudio Contardo, 2019. "Selective pricing in branch-price-and-cut algorithms for vehicle routing," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 147-168, June.
  52. S. Ardizzoni & L. Consolini & M. Laurini & M. Locatelli, 2022. "Shortest path with acceleration constraints: complexity and approximation algorithms," Computational Optimization and Applications, Springer, vol. 83(2), pages 555-592, November.
  53. Les Foulds & Humberto Longo & Jean Martins, 2015. "A compact transformation of arc routing problems into node routing problems," Annals of Operations Research, Springer, vol. 226(1), pages 177-200, March.
  54. He, Ping & Jin, Jian Gang & Schulte, Frederik, 2024. "The flexible airport bus and last-mile ride-sharing problem: Math-heuristic and metaheuristic approaches," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
  55. Glize, Estèle & Roberti, Roberto & Jozefowiez, Nicolas & Ngueveu, Sandra Ulrich, 2020. "Exact methods for mono-objective and Bi-Objective Multi-Vehicle Covering Tour Problems," European Journal of Operational Research, Elsevier, vol. 283(3), pages 812-824.
  56. Bianchessi, N. & Mansini, R. & Speranza, M.G., 2014. "The distance constrained multiple vehicle traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 73-87.
  57. Stefan Irnich & Guy Desaulniers & Jacques Desrosiers & Ahmed Hadjar, 2010. "Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 297-313, May.
  58. Mads Jepsen & Bjørn Petersen & Simon Spoorendonk & David Pisinger, 2008. "Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows," Operations Research, INFORMS, vol. 56(2), pages 497-511, April.
  59. Qin, Hu & Su, E. & Wang, Yilun & Li, Jiliu, 2022. "Branch-and-price-and-cut for the electric vehicle relocation problem in one-way carsharing systems," Omega, Elsevier, vol. 109(C).
  60. Qie He & Stefan Irnich & Yongjia Song, 2019. "Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Transportation Science, INFORMS, vol. 53(5), pages 1409-1426, September.
  61. Theodore Athanasopoulos & Ioannis Minis, 2013. "Efficient techniques for the multi-period vehicle routing problem with time windows within a branch and price framework," Annals of Operations Research, Springer, vol. 206(1), pages 1-22, July.
  62. Christos Orlis & Nicola Bianchessi & Roberto Roberti & Wout Dullaert, 2020. "The Team Orienteering Problem with Overlaps: An Application in Cash Logistics," Transportation Science, INFORMS, vol. 54(2), pages 470-487, March.
  63. Guy Desaulniers & Daniel Villeneuve, 2000. "The Shortest Path Problem with Time Windows and Linear Waiting Costs," Transportation Science, INFORMS, vol. 34(3), pages 312-319, August.
  64. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2015. "Branch-and-Price for the Active-Passive Vehicle-Routing Problem," Working Papers 1513, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  65. Leonardo Lozano & Daniel Duque & Andrés L. Medaglia, 2016. "An Exact Algorithm for the Elementary Shortest Path Problem with Resource Constraints," Transportation Science, INFORMS, vol. 50(1), pages 348-357, February.
  66. Quoc Trung Bui & Yves Deville & Quang Dung Pham, 2016. "Exact methods for solving the elementary shortest and longest path problems," Annals of Operations Research, Springer, vol. 244(2), pages 313-348, September.
  67. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
  68. Jia, Menglei & Chen, Feng, 2023. "Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
  69. Zamorano, Emilio & Stolletz, Raik, 2017. "Branch-and-price approaches for the Multiperiod Technician Routing and Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 55-68.
  70. Gschwind, Timo, 2015. "A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 60-71.
  71. Li, Jiliu & Xu, Min & Sun, Peng, 2022. "Two-echelon capacitated vehicle routing problem with grouping constraints and simultaneous pickup and delivery," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 261-291.
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  73. Luigi Di Puglia Pugliese & Francesca Guerriero, 2012. "A computational study of solution approaches for the resource constrained elementary shortest path problem," Annals of Operations Research, Springer, vol. 201(1), pages 131-157, December.
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