In this paper we present a dual-time-scale formulation of dynamic user equilibrium (DUE) with demand evolution. Our formulation belongs to the problem class that Pang and Stewart (2008) refer to as differential variational inequalities. It combines the within-day time scale for which route and departure time choices fluctuate in continuous time with the day-to-day time scale for which demand evolves in discrete time steps. Our formulation is consistent with the often told story that drivers adjust their travel demands at the end of every day based on their congestion experience during one or more previous days. We show that analysis of the within-day assignment model is tremendously simplified by expressing dynamic user equilibrium as a differential variational inequality. We also show there is a class of day-to-day demand growth models that allow the dual-time-scale formulation to be decomposed by time-stepping to yield a sequence of continuous time, single-day, dynamic user equilibrium problems. To solve the single-day DUE problems arising during time-stepping, it is necessary to repeatedly solve a dynamic network loading problem. We observe that the network loading phase of DUE computation generally constitutes a differential algebraic equation (DAE) system, and we show that the DAE system for network loading based on the link delay model (LDM) of Friesz et al. (1993) may be approximated by a system of ordinary differential equations (ODEs). That system of ODEs, as we demonstrate, may be efficiently solved using traditional numerical methods for such problems. To compute an actual dynamic user equilibrium, we introduce a continuous time fixed-point algorithm and prove its convergence for effective path delay operators that allow a limited type of nonmonotone path delay. We show that our DUE algorithm is compatible with network loading based on the LDM and the cell transmission model (CTM) due to Daganzo (1995) . We provide a numerical example based on the much studied Sioux Falls network.

/pdf/approximate-network-loading-and-dual-time-scale-dynamic-user-2lnkjok15a.pdf

Approximate network loading and dual-time-scale dynamic user equilibrium

Although conceptual efforts have often suggested that the Internet harbors considerable possibilities to revolutionize political participation, empirical studies have often presented rather limited impacts in this regard. Nevertheless, novel online services such as Twitter are still pointed to as having potential to be employed by citizens and politicians alike. Utilizing state-of-the-art data collection methods, this study builds on the suggestions of previous research and gauges the degree to which EU parliamentarians make use of Twitter for so-called permanent campaigning. Specifically, the paper seeks to assess the degree to which Twitter use by European Parliament representatives can be described as being characterized by permanence—a concept related to the professionalization of political campaigns. Thus, by examining these uses outside of election periods, the study provides useful insights into the day-to-day uses of Twitter, contributing to the limited body of work focusing on the everyda...

https://www.tandfonline.com/doi/pdf/10.1080/19331681.2014.994158

The EU Parliament on Twitter—Assessing the Permanent Online Practices of Parliamentarians

This paper introduces a rolling horizon algorithm to plan the delivery of vehicles to automotive dealers by a heterogeneous fleet of auto-carriers. The problem consists in scheduling the deliveries over a multiple-day planning horizon during which requests for transportation arrive dynamically. In addition, the routing of the auto-carriers must take into account constraints related to the loading of the vehicles on the carriers. The objective is to minimize the sum of traveled distances, fixed costs for auto-carrier operation, service costs, and penalties for late deliveries. The problem is solved by a heuristic that first selects the vehicles to be delivered in the next few days and then optimizes the deliveries by an iterated local search procedure. A branch-and-bound search is used to check the feasibility of the loading. To handle the dynamic nature of the problem, the complete algorithm is applied repeatedly in a rolling horizon framework. Computational results on data from a major European logistics service provider show that the heuristic is fast and yields significant improvements compared to the sequential solution of independent daily problems.

/pdf/a-rolling-horizon-algorithm-for-auto-carrier-transportation-zpqlns2a3o.pdf

A rolling horizon algorithm for auto-carrier transportation

We study a real-world distribution problem arising in the automotive field in which cars, trucks, and other vehicles have to be loaded onto auto-carriers and then delivered to dealers. The solution of the problem involves both the computation of the routing of the auto-carriers along the road network and the determination of a feasible loading for each carrier. We solve the problem by means of an iterated local search algorithm that makes use of several inner local search strategies for the routing part and mathematical modeling and enumeration techniques for the loading part. Extensive computational results on real-world instances show that good savings on the total cost can be obtained within small computational efforts.

/pdf/optimization-of-a-real-world-auto-carrier-transportation-2o2qc4u0pt.pdf

Optimization of a Real-World Auto-Carrier Transportation Problem

The terms dynamic traffic assignment (DTA), dynamic user optimum (DUO) and dynamic user equilibrium (DUE) are interchangeable in the literature. They refer to a stable state on a road network in which, under the assumption of perfect information on traffic conditions and the assumption that every traveller chooses the least costly path to travel, no one can reduce his or her travel cost by changing his or her path unilaterally. This paper proposes an alternative definition of DUO on signalised road networks. In such a DUO state, the travel times or costs of used paths between the same origin-destination pair can be different because of the existence of signalised junctions. Usually, on signalised road networks, a DUE solution is sought to approximate such a DUO solution by assuming that the capacity of each approach at a signalised junction is equal to the saturation flow rate of the approach times the corresponding split. This paper discusses advantages and disadvantages of this approximation by comparing the DUE and DUO solutions of a DTA problem on a small signalised road network. It shows that such a DUE solution would not be a good approximation to a DUO solution.

An alternative definition of dynamic user optimum on signalised road networks

This paper studies an automotive distribution network with two transportation modes: railway and highway. Because lead-time influences the turnaround rate of expensive railcars and volume has a large impact on the total lead-time from a plant to a railway ramp, the paper considers quantity discounts in railway cost structures. This paper proposes a business scheme based on an integer linear program (ILP) to minimize the total distribution costs by making mode and ramp selection decisions. The numerical experiments based on randomly created instances show that the solutions obtained from the ILP significantly outperform the results of the simulated manual negotiation process used in practice. The two schemes lead to results that are not statistically different in payments to railways.

Mode selection for automotive distribution with quantity discounts

Effects of free-air temperature increase on grain yield and greenhouse gas emissions in a double rice cropping system

This paper studies the design of an automotive distribution network that has two transportation modes: railway and highway. In the automotive industry, a mode selection decision should be made for each plant-dealer pair. If railway is selected as the transportation mode for a pair, then the location of the ramp (automotive distribution center) also needs to be selected. Because lead-time influences the turnaround rate of expensive railcars for automotive distribution and because volume has a large impact on the total lead-time from a plant to a railway ramp, the paper considers quantity discounts in railway cost structures. In practice, multiple rounds of manual negotiations take place between automakers and railway companies to determine rates and finalize contracts. This paper proposes a business scheme that is based on an integer linear program (ILP) to minimize the total distribution costs by making mode and ramp selection decisions. The manual negotiation process is also simulated in this paper so that the ILP-based model can be compared to the simulated model. The numerical experiments based on randomly created instances show that the solutions obtained from the ILP significantly outperform the results of the simulated manual negotiation process. The real-world instances of the ILP can be solved by commercial optimization solvers in a small amount of time (several seconds). Another interesting finding is that with respect to payments to railways the ILP-based and the negotiation-based business schemes lead to results that are not statistically different. Therefore, the proposed ILP-based business scheme is incentive compatible and technically feasible for both automakers and railway companies.

Haiyuan Wang

Papers

Mode selection for automotive distribution with quantity discounts

Effects of free-air temperature increase on grain yield and greenhouse gas emissions in a double rice cropping system

Mode Selection for Automotive Distribution with Quantity Discounts

Differences in the functional properties and starch structures of early/late season rice between the early and late seasons