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Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations

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  • Mahmoudi, Monirehalsadat
  • Zhou, Xuesong

Abstract

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state–space–time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space–time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers’ requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.

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  • Mahmoudi, Monirehalsadat & Zhou, Xuesong, 2016. "Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 19-42.
    • Handle: RePEc:eee:transb:v:89:y:2016:i:c:p:19-42
    DOI: 10.1016/j.trb.2016.03.009
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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. Marius Solomon & Alain Chalifour & Jacques Desrosiers & Jacques Boisvert, 1992. "An Application of Vehicle-Routing Methodology to Large-Scale Larvicide Control Programs," Interfaces, INFORMS, vol. 22(3), pages 88-99, June.
    3. Dumas, Yvan & Desrosiers, Jacques & Soumis, Francois, 1991. "The pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 54(1), pages 7-22, September.
    4. Thomas R. Sexton & Lawrence D. Bodin, 1985. "Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: I. Scheduling," Transportation Science, INFORMS, vol. 19(4), pages 378-410, November.
    5. Julien Bramel & David Simchi-Levi, 1995. "A Location Based Heuristic for General Routing Problems," Operations Research, INFORMS, vol. 43(4), pages 649-660, August.
    6. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Chris T., 2015. "The load-dependent vehicle routing problem and its pick-up and delivery extension," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 158-181.
    7. Marshall L. Fisher & Arnold J. Greenfield & R. Jaikumar & Joseph T. Lester, 1982. "A Computerized Vehicle Routing Application," Interfaces, INFORMS, vol. 12(4), pages 42-52, August.
    8. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2007. "An exact algorithm for a single-vehicle routing problem with time windows and multiple routes," European Journal of Operational Research, Elsevier, vol. 178(3), pages 755-766, May.
    9. Irina Ioachim & Jacques Desrosiers & Yvan Dumas & Marius M. Solomon & Daniel Villeneuve, 1995. "A Request Clustering Algorithm for Door-to-Door Handicapped Transportation," Transportation Science, INFORMS, vol. 29(1), pages 63-78, February.
    10. Quan Lu & Maged Dessouky, 2004. "An Exact Algorithm for the Multiple Vehicle Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 38(4), pages 503-514, November.
    11. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    12. Diana, Marco & Dessouky, Maged M., 2004. "A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 539-557, July.
    13. Rajendra S. Solanki & Frank Southworth, 1991. "An Execution Planning Algorithm for Military Airlift," Interfaces, INFORMS, vol. 21(4), pages 121-131, August.
    14. Walter J. Bell & Louis M. Dalberto & Marshall L. Fisher & Arnold J. Greenfield & R. Jaikumar & Pradeep Kedia & Robert G. Mack & Paul J. Prutzman, 1983. "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces, INFORMS, vol. 13(6), pages 4-23, December.
    15. Harilaos N. Psaraftis, 1980. "A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem," Transportation Science, INFORMS, vol. 14(2), pages 130-154, May.
    16. Marshall L. Fisher & Kurt O. Jörnsten & Oli B. G. Madsen, 1997. "Vehicle Routing with Time Windows: Two Optimization Algorithms," Operations Research, INFORMS, vol. 45(3), pages 488-492, June.
    17. Roberto Baldacci & Enrico Bartolini & Aristide Mingozzi, 2011. "An Exact Algorithm for the Pickup and Delivery Problem with Time Windows," Operations Research, INFORMS, vol. 59(2), pages 414-426, April.
    18. Harold K. Rappoport & Laurence S. Levy & Bruce L. Golden & Katherine J. Toussaint, 1992. "A Planning Heuristic for Military Airlift," Interfaces, INFORMS, vol. 22(3), pages 73-87, June.
    19. Hosni, Hadi & Naoum-Sawaya, Joe & Artail, Hassan, 2014. "The shared-taxi problem: Formulation and solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 303-318.
    20. Jaw, Jang-Jei & Odoni, Amedeo R. & Psaraftis, Harilaos N. & Wilson, Nigel H. M., 1986. "A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 243-257, June.
    21. Mitrovic-Minic, Snezana & Krishnamurti, Ramesh & Laporte, Gilbert, 2004. "Double-horizon based heuristics for the dynamic pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(8), pages 669-685, September.
    22. Furuhata, Masabumi & Dessouky, Maged & Ordóñez, Fernando & Brunet, Marc-Etienne & Wang, Xiaoqing & Koenig, Sven, 2013. "Ridesharing: The state-of-the-art and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 28-46.
    23. Jean-François Cordeau, 2006. "A Branch-and-Cut Algorithm for the Dial-a-Ride Problem," Operations Research, INFORMS, vol. 54(3), pages 573-586, June.
    24. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    25. Martin Savelsbergh & Marc Sol, 1998. "Drive: Dynamic Routing of Independent Vehicles," Operations Research, INFORMS, vol. 46(4), pages 474-490, August.
    26. Harilaos N. Psaraftis, 1983. "An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows," Transportation Science, INFORMS, vol. 17(3), pages 351-357, August.
    27. Thomas R. Sexton & Lawrence D. Bodin, 1985. "Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: II. Routing," Transportation Science, INFORMS, vol. 19(4), pages 411-435, November.
    28. Paolo Toth & Daniele Vigo, 1997. "Heuristic Algorithms for the Handicapped Persons Transportation Problem," Transportation Science, INFORMS, vol. 31(1), pages 60-71, February.
    29. Marielle Christiansen, 1999. "Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem," Transportation Science, INFORMS, vol. 33(1), pages 3-16, February.
    30. Paquette, Julie & Cordeau, Jean-François & Laporte, Gilbert & Pascoal, Marta M.B., 2013. "Combining multicriteria analysis and tabu search for dial-a-ride problems," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 1-16.
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