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.Keywords: Vehicle routing problem with pickup and delivery with time windows; Lagrangian relaxation; Timedependent least-cost path problem; Forward dynamic programming; Ride-sharing service optimization.
1 IntroductionAs population and personal travel activities continue to increase, traffic congestion has remained as one of the major concerns for transportation system agencies with tight resource constraints. The next generation of transportation system initiatives aims to integrate various demand management strategies and traffic control measures to actively achieve mobility, environment, and sustainability goals. A number of approaches hold promises of reducing the undesirable effects of traffic congestion due to driving-alone trips, to name a few, demand-responsive transit services, dynamic ride-sharing, and intermodal traffic corridor management.The optimized and coordinated ride-sharing services provided by transportation network companies (TNC) can efficiently utilize limited vehicle and driver resources while satisfying time-sensitive origin-to-destination transportation service requests. In a city with numerous travelers with different purposes, each traveler has his own traveling schedule. Instead of using his own car, the traveler can (by the aid of ride-sharing) bid and call a car just a few minutes before leaving his origin, or preschedule a car a day prior to his departure. The on-demand transportation system provides a traveler with a short waiting time even if he resides in a high-demand area. Currently, several realtime ride-sharing or, more precisely, app-based transportation network and taxi companies, such as Uber and Lyft are serving passengers in many metropolitan areas. In the ...
Recently, automation, shared use, and electrification are viewed as the ''three revolutions'' in the future transportation sector, and the traditional scheduled public transit system will be greatly enhanced with flexible services and autonomous vehicle scheduling capabilities. Many emerging scheduled transportation applications include the fully automatic operation system in urban rail transit, joint line planning, and timetabling for high-speed rail as well as emerging self-driving vehicle dispatching. The vehicle routing problem (VRP) holds promise for seeking an optimal set of vehicle routes and schedules to meet customers' requirements and plays a vital role in optimizing services for feature scheduled transportation systems. Due to the difficulty of finding optimal solutions for large-scale instances, enormous research efforts have been dedicated to developing efficient algorithms, while our paper presents a unique perspective based on a timedependent and state-dependent path searching framework. An open-source and light-weight VRP with pickup and delivery with time windows (VRPPDTW) modeling package, namely VRPLite, has been developed in this research to provide a high-quality and computationally efficient solution engine for transportation on demand applications. This paper describes the space-time-state
In this study, to incorporate realistic discrete stochastic capacity distribution over a large number of sampling days or scenarios (say 30 to 100 days), we propose a multi-scenario based optimization model with different types of traveler knowledge in an advanced traveler information provision environment. The proposed method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions (and related reliability measure) across a large number of different sampling days. Using a gap function framework or describing the mixed user equilibrium under different information availability over a long-term steady state, a nonlinear programming model is formulated to describe the route choice behavior of the perfect information (PI) and expected travel time (ETT) user classes under stochastic day-dependent travel time. Driven by a computationally efficient algorithm suitable for large-scale networks, the model was implemented in a standard optimization solver and an open-source simulation package and further applied to medium-scale networks to examine the effectiveness of dynamic traveler information under realistic stochastic capacity conditions.
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