An algorithm for the combined distribution and assignment problem

Much interest has recently been shown in the combination of the distribution and assignment models. In this paper we adopt a generalized Benders' decomposition to solve this combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows. The master problem which is generated is used to show that the combined problem can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function. An algorithm for solving the master problem is discussed, and some computational results presented.     

The dual of the traffic assignment problem with elastic demands

This article is concerned with the dual of the traffic assignment problem, and of the combined generation, distribution, and assignment problem. The duals, and duality relations, for the arc-chain and node-arc formulations of the problem are derived using only the Kuhn-Tucker conditions for convex programs. This has the advantage of being more familiar to most readers than the conjugate function presentation which has been used elsewhere.     

Network representation,continuum approximations and a solution to the spatial aggregation problem of traffic assignment

This paper complements the preceding one, which showed how one could modify equilibrium traffic assignment algorithms for networks with many centroids. In this one it is shown how one can substitute centroids by zones with continuous population densities. The technique, which is mathematically guaranteed to approximate a flow pattern in accordance with Wardrop's user equilibrium criterion, requires some geometrical calculations which can be handled off-line. With the suggested approach, it is possible to represent the spatial distribution of trip ends more realistically and this allows traffic assignment models to capture the effects of short and intrazonal trips in a way previously impossible. The method is shown to be computationally feasible.     

Walking infrastructure design assessment by continuous space dynamic assignment modeling

For the planning and design of walking infrastructure, characterized by the fact that the pedestrians can choose their paths freely in two‐dimensional space, applicability of traditional discrete network models is limited. This contribution puts forward an approach for user‐optimal dynamic assignment in continuous time and space for analyzing for instance walking infrastructure in a two‐dimensional space. Contrary to network‐based approaches, the theory allows the traffic units to choose from an infinite non‐countable set of paths through the considered space. The approach first determines the continuous paths using a path choice model. Then, origin‐destination flows are assigned and traffic conditions are calculated. The approach to determine a user‐optimal assignment is heuristic and consists of a sequence of all‐or‐nothing assignments. An application example is presented, showing dynamic user equilibrium traffic flows through a realistic transfer station. The example is aimed at illustrating the dynamic aspects of the modeling approach, such as anticipation on expected flow conditions, and predicted behavior upon catching or missing a connection.     

Reserve capacity model based on variable demand for land-use development control

In this paper, the concept of reserve capacity has been extended to zone level to measure the land-use development potentiality of each trip generation zone. Bi-level programing models are proposed to determine the signal setting of individual intersections for maximizing possible increase in total travel demand and the corresponding reserve capacity for each zone. The change of the origin–destination pattern with the variation of upper level decision variables is presented through the combined distribution/assignment model under user equilibrium conditions. Both singly constrained and doubly constrained combined models are considered for different trip purposes and data information. Furthermore, we have introduced the continuous network design problem by increasing road capacity and examined its effect on the land-use development potentiality of trip generation zone. A numerical example is presented to illustrate the application of the models and how a genetic algorithm is applied to solve the problem.     

An equivalent optimization problem for combined multiclass distribution,assignment and modal split which obviates symmetry restrictions

This paper presents a model for combined multiclass trip distribution, trip assignment and modal split. Although this model is based on an equivalent optimization problem, it avoids the symmetry restrictions heretofore always associated with such approaches to multiclass trip assignment. This is accomplished by expressing Wardrop's first principle as a set of nonlinear constraints in standard mathematical programming form. An algorithm is proposed, each iteration of which requires solving a nonlinear program with linear constraints.     

Trip assignment to radial major roads

The problem of flow-dependent trip assignment is considered for a city with a small number of radial major roads. CBD-based work trips are assigned to these radial major roads on the basis that each commuter seeks to minimise his individual travel time. A system of differential equations is derived for the spatial pattern of trip assignment in a model city with a continuous distribution of home locations and a ring-radial road network. This system is then solved for the special case of a uniform distribution of home locations.     

An equilibrium algorithm for the spatial aggregation problem of traffic assignment

Present traffic assignment methods require that all possible origins and destinations of trips taking place within a study area be represented as if they were taking place to and from a small set of points or centroids. Each centroid is supposed to represent the location of all trip-ends within a given zone, and this necessarily misrepresents points located at the edges of the zone.In order to alleviate this problem (which we refer to as the spatial aggregation problem) one could use smaller zones and more centroids, but existing traffic assignment algorithms cannot efficiently handle many centroids.This paper introduces an algorithm procedure which is designed to handle a substantially larger number of centroids. In the paper that follows, the technique is further developed to take into account a continuous distribution of population.     

Spatial allocation on a network with congestion

This article formalizes the land use design problem as a discrete-convex programming problem integrating within a quadratic assignment framework a realistic representation of transportation behavior (automobile congestion and variable demand for travel) as modelled by a combined trip distribution trip assignment model. Hill-climbing algorithms are proposed to solve the resulting optimization problem. Their performance is compared and evaluated on a set of test problems.     

A hybrid-choice latent-class model for the analysis of the effects of weather on cycling demand

In this paper we analyze demand for cycling using a discrete choice model with latent variables and a discrete heterogeneity distribution for the taste parameters. More specifically, we use a hybrid choice model where latent variables not only enter into utility but also inform assignment to latent classes. Using a discrete choice experiment we analyze the effects of weather (temperature, rain, and snow), cycling time, slope, cycling facilities (bike lanes), and traffic on cycling decisions by members of Cornell University (in an area with cold and snowy winters and hilly topography). We show that cyclists can be separated into two segments based on a latent factor that summarizes cycling skills and experience. Specifically, cyclists with more skills and experience are less affected by adverse weather conditions. By deriving the median of the ratio of the marginal rate of substitution for the two classes, we show that rain deters cyclists with lower skills from bicycling 2.5 times more strongly than those with better cycling skills. The median effects also show that snow is almost 4 times more deterrent to the class of less experienced cyclists. We also model the effect of external restrictions (accidents, crime, mechanical problems) and physical condition as latent factors affecting cycling choices.     

Continuous equilibrium network design models

It is known that the network design problem with the assumption of user optimal flows can be modeled as a 0–1 mixed integer programming problem. Instead, we formulate the network design problem with continuous investment variables subject to equilibrium assignment as a nonlinear optimization problem. We show that this optimization problem is equivalent to an unconstrained problem which we solve by direct search techniques. For convex investment cost functions, the performance of both Powell's method and the method of Hooke and Jeeves is approximately the same with respect to computational requirements for a 24 node, 76 arc network. For the case of concave investment functions, Hooke and Jeeves was superior. The solution to the concave continuous model was very similar to that of the 0–1 model. Furthermore, the required solution time was far less than that required by the corresponding discrete model of the same network. The advantages and disadvantages of the continuous approach as well as the computational requirements are discussed.     

Development of an indicator to assess the spatial fit of discrete choice models

Discrete choice models are increasingly implemented using geographical data. When this is the case, it may not be sufficient to project market shares accurately, but also to correctly replicate the spatial pattern of choices. Analysts might then be interested in assessing the results of a model’s fit relative to the spatial distribution of the observed responses. While canonical approaches exist for the exploratory spatial analysis of continuous variables, similar tools have not been widely implemented for discrete choice models, where the variable of interest is categorical. For this reason, despite recent progress with spatial models for discrete outcomes, there is still not a simple and intuitive tool to assess the quality of the spatial fit of a discrete choice model. The objective of this paper is to introduce a new indicator of spatial fit that can be applied to the results of discrete choice models. Utility of the indicator is explored by means of numerical experiments and then demonstrated by means of a case study of vehicle ownership in Montreal, Canada.     

A note on trip matrix estimation from link traffic count data

In this note, a simple network equilibrium based approach for estimating a trip matrix using link traffic count data is proposed. In essence a combined distribution and assignment model is formulated in which the link flow data serve to furnish an estimate for the sum of the integrals of the link cost functions. A comparison of this model with others proposed previously is made.     

Modeling techniques for periodic vehicle routing problems

This paper presents a continuous approximation model for the period vehicle routing problem with service choice (PVRP-SC). The PVRP-SC is a variant of the period vehicle routing problem in which the visit frequency to nodes is a decision of the model. This variation can result in more efficient vehicle tours and/or greater service benefit to customers. We present a continuous approximation model to facilitate strategic and tactical planning of periodic distribution systems and evaluate the value of service choice. Further, results from the continuous model can provide guidelines for constructing solutions to the discrete PVRP-SC.     

Jobs-housing imbalance, spatial correlation, and excess commuting

In this paper, we use continuous urban structure instead of zonal model, try to calculate unbiased excess commuting with joint distribution of homes and workplaces developed by Vaughan (1974), and describe the relationship between urban structure and commuting distance explicitly and theoretically for generalized home-workplace assignment pattern. We simplify the quadrivariate distribution model to a model with three important parameters: the spread of homes, the spread of workplaces, and the spatial correlation of homes and workplaces. Then we show that excess commuting and capacity utilization are expressed by the imbalance and the spatial correlation of jobs-housing structure in a theoretical context, moreover it explicitly evaluates targeting US and Japanese/Korean cities.     

Modelling the dynamics between tour-based mode choices and tour-timing choices in daily activity scheduling

Transportation - The paper presents a dynamic discrete–continuous modelling approach to capture individuals’ tour-based mode choices and continuous time expenditure choices tradeoffs in...     

Modeling and solving discrete network design problem with stochastic user equilibrium

In this paper, we address the discrete network design problem, which determines the addition of new roads to existing transportation network to optimize the transportation system performance. Road users are assumed to follow the traffic assignment principle of stochastic user equilibrium. A mixed‐integer nonlinear nonconvex problem is developed to model this discrete network design problem with stochastic user equilibrium. The original problem is relaxed into a convex mixed‐integer nonlinear program, whose solution provides a lower bound of the original problem. The relaxed problem is then embedded into two proposed global optimization solution algorithms to obtain the global optimal solution of the problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Equity based land‐use and transportation problem

Due to additional trip production by land use development, the O‐D travel costs between some O‐D pairs may also change intuitively. This leads to positive and negative impacts on network users traveling between different O‐D pairs. Therefore the equity issue about the benefit distribution gained from the land‐use development problem is raised. This paper proposes an Equity based Land‐Use Transportation Problem (ELUTP) which is intended to examine the benefit distribution among the network users and the resulting equity associated with land‐use development problem in terms of the change of equilibrium O‐D travel cost. In the resulting bi‐level programming model, the upper level sub‐problem maximizes traffic production incorporating equity constraints, while the lower level sub‐problem is a combined trip distribution/assignment user equilibrium problem. Genetic algorithm based method is applied to test the models using an example network.     

A continuous approximation model for time definite many-to-many transportation

Time definite freight transportation carriers provide very reliable scheduled services between origin and destination terminals. They seek to reduce transportation costs through consolidation of shipments at hubs, but are restricted by the high levels of service to provide less circuitous routings. This paper develops a continuous approximation model for time definite transportation from many origins to many destinations. We consider a transportation carrier serving a fixed geographic region in which demand is modeled as a continuous distribution and time definite service levels are imposed by limiting the maximum travel distance via the hub network. Analytical expressions are developed for the optimal number of hubs, hub locations, and transportation costs. Computational results for an analogous discrete demand model are presented to illustrate the behavior observed with the continuous approximation models.     

Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective

This study proposes a formulation of the within-day dynamic stochastic traffic assignment problem. Considering the stochastic nature of route choice behavior, we treat the solution to the assignment problem as the conditional joint distribution of route traffic, given that the network is in dynamic stochastic user equilibrium. We acquire the conditional joint probability distribution using Bayes’ theorem. A Metropolis–Hastings sampling scheme is developed to estimate the characteristics (e.g., mean and variance) of the route traffic. The proposed formulation has no special requirements for the traffic flow models and user behavior models, and so is easily implemented.