Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing. Recently, a large-scale study highlighted some of the benefits of car pooling but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride-sharing that (i) scales to large numbers of passengers and trips and (ii) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff between fleet size, capacity, waiting time, travel delay, and operational costs for low- to medium-capacity vehicles, such as taxis and van shuttles. The algorithm is validated with ∼3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multivehicle, multitask assignment problems.

https://www.pnas.org/content/pnas/114/3/462.full.pdf

On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment

Dynamic Traffic Assignment (DTA) has evolved substantially since the pioneering work of Merchant and Nemhauser. Numerous formulations and solutions approaches have been introduced ranging from mathematical programming, to variational inequality, optimal control, and simulation-based. The aim of this special issue is to document the main existing DTA approaches for future reference. This opening paper will summarize the current understanding of DTA, review the existing literature, make the connection to the approaches presented in this special issue, and attempt to hypothesize about the future.

Foundations of dynamic traffic assignment : the past, the present and the future

Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes. In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand. The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.

Emergency Logistics Planning in Natural Disasters

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

/pdf/route-planning-in-transportation-networks-k0typz8i4k.pdf

Route Planning in Transportation Networks

http://www.iro.umontreal.ca/~potvin/soumia2.pdf

Vehicle dispatching with time-dependent travel times

Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.

A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem

An algorithm is introduced that calculates the time-dependent shortest paths from all nodes in a network to a given destination node for every time step over a given time horizon in a network with time-dependent arc costs. Unlike other time-dependent algorithms, this approach can handle networks where the travel cost is not necessarily the travel time itself. The algorithm is based on the general Bellman's principle of optimality. It descretizes the horizon of interest into small time intervals. Starting from the destination node, it calculates the paths operating backwards. A proof of the correctness of the proposed algorithm is presented. The algorithm is efficiently implemented and coded on a CRAY Y/MP-8 supercomputer and tested on a large actual street network as well as several random networks. The motivation for this study was the need to compute time-dependent shortest paths in a real-time environment in connection with intelligent vehicle highway systems. The suitability of the proposed algorithm for such applications is demonstrated.

Time dependent, shortest-path algorithm for real-time intelligent vehicle highway system applications

An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays

This paper is concerned with the stochastic shortest path problem with recourse when limited forms of spatial and temporal arc cost dependencies are accounted for. Recourse is defined as the opportunity for a decision maker to reevaluate his or her remaining path when en-route information is available. Formulations with recourse typically provide opportunities for corrective actions when information becomes available; information here is modeled as arc cost dependencies, defined as spatial and temporal. System properties are stated and proved and solution algorithms are developed for limited cases of spatial and temporal arc cost dependencies. The numerical results verify some of the theoretical insights and demonstrate the applicability of the introduced algorithms.

Athanasios K. Ziliaskopoulos

Papers

Foundations of dynamic traffic assignment : the past, the present and the future

A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem

Time dependent, shortest-path algorithm for real-time intelligent vehicle highway system applications

An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays

On the online shortest path problem with limited arc cost dependencies