TY - JOUR
T1 - Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows
T2 - A dynamic programming approach based on state-space-time network representations
AU - Mahmoudi, Monirehalsadat
AU - Zhou, Xuesong
N1 - Funding Information:
This paper is partially supported by National Science Foundation —United States under Grant No. CMMI 1,538,105 “Collaborative Research: Improving Spatial Observability of Dynamic Traffic Systems through Active Mobile Sensor Networks and Crowdsourced Data”, a US University Transportation Center project titled “scheduling and managing self-driving cars for enhanced transportation system mobility and safety”, and project RCS2015K006 sponsored by State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China. We thank Prof. Hani S. Mahmassani at Northwestern University, Prof. Pitu Mirchandani at Arizona State University, and Dr. Lingyun Meng at Beijing Jiaotong University for their valuable comments. We would also like to thank our colleague, Jeffrey Taylor at the University of Utah for his help throughout the project. The work presented in this paper remains the sole responsibility of the authors.
Publisher Copyright:
© 2016 Elsevier Ltd.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - 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.
AB - 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.
KW - Forward dynamic programming
KW - Lagrangian relaxation
KW - Ride-sharing service optimization
KW - Time-dependent least-cost path problem
KW - Vehicle routing problem with pickup and delivery with time windows
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U2 - 10.1016/j.trb.2016.03.009
DO - 10.1016/j.trb.2016.03.009
M3 - Article
AN - SCOPUS:84962840749
SN - 0191-2615
VL - 89
SP - 19
EP - 42
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
ER -