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

•Model vehicle routing with real-world transportation networks and time-dependent link travel time.•Develop an efficient dynamic programming algorithm based on state–space–time networks.•Model pickup and delivery time window constraints using multi-dimensional network flow program.•Synchronize vehic...

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Vydáno v:Transportation research. Part B: methodological Ročník 89; s. 19 - 42
Hlavní autoři: Mahmoudi, Monirehalsadat, Zhou, Xuesong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.07.2016
Témata:
Algorithms
Forward dynamic programming
Lagrangian relaxation
Mathematical models
Optimization
Ride-sharing service optimization
Route planning
Route selection
Time-dependent least-cost path problem
Transportation networks
Vehicle routing problem with pickup and delivery with time windows
Vehicles
Windows (intervals)
USA, Illinois, Chicago
Forward dynamic programming
Time-dependent least-cost path problem
Lagrangian relaxation
Ride-sharing service optimization
Vehicle routing problem with pickup and delivery with time windows
ISSN:0191-2615, 1879-2367
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Shrnutí:•Model vehicle routing with real-world transportation networks and time-dependent link travel time.•Develop an efficient dynamic programming algorithm based on state–space–time networks.•Model pickup and delivery time window constraints using multi-dimensional network flow program.•Synchronize vehicle routing and determine request pricing within Lagrangian relaxation framework. 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. [Display omitted]
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ISSN:0191-2615
1879-2367
DOI:10.1016/j.trb.2016.03.009