Vehicle routing in reverse logistics for recycling end-of-life consumer electronic goods in South Korea

This paper presents a vehicle routing approach for the transport of end-of-life consumer electronic goods for recycling in South Korea. The objective is to minimize the distance of transportation of end-of-life goods collected by local authorities and major manufacturers’ distribution centers to four regional recycling centers located. A vehicle routing problem is constructed for each regional center, and a Tabu search is applied to solve it. Computational results using field data show that the method outperforms existing approaches to reverse logistics.     

A route-based solution algorithm for dynamic user equilibrium assignments

The aim of this study is to establish a method to calculate good quality user equilibrium assignments under time varying conditions. For this purpose, it introduces a dynamic network loading method that can maintain correct flow propagation as well as flow conservation, and it shows a novel route-based solution algorithm. This novel algorithm turns out to be convenient and logically plausible compared to the conventional [Frank, M., Wolfe, P., 1956. An algorithm for quadratic programming. Naval Research Logistics Quarterly 3, 95–110] algorithm, because the former does not require evaluation of an objective function and it finds solutions maintaining correct flow propagation in the time-varying network conditions. The application of novel dynamic network loading method and solution algorithm to test networks shows that we can find high quality dynamic user equilibrium assignment. This is illustrated in an example network using the deterministic queuing model for a link performance function and associating costs and flows in a predictive way in discrete time.     

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.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Optimal solution to the vehicle routing problem by adopting a meta-heuristic algorithm

The delivery service provided by large-scale retailers continues to grow as online sales occupy an increasingly large share of the market. This study aims to tease out efficient vehicle scheduling times as well as optimal delivery routes by applying meta-heuristic algorithms. Monthly data on existing routes were obtained from a branch of Korea’s leading large-scale online retailer. The first task was to examine the status of existing routes by comparing delivery routes created using Dijkstra’s algorithm with existing delivery routes and their vehicle scheduling. The second task was to identify optimal delivery routes through a comparative analysis of the genetic algorithm and Tabu search algorithm, known for its superior applicability amongst other meta-heuristic algorithms. These findings demonstrate that the optimal vehicle routing problem not only has the potential to reduce distribution costs for operators and expedite delivery for consumers, but also the added social benefit of reduced carbon emissions.     

A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagation constraints, we show that the continuous-time dynamic user equilibrium problem can be formulated as an infinite dimensional mixed complementarity model. The continuous-time model can be further discretized as a finite dimensional non-linear complementarity problem (NCP). The proposed discrete-time model captures the exact flow propagation constraints that were usually approximated in previous studies. By associating link inflow at the beginning of a time interval to travel times at the end of the interval, the resulting discrete-time model is predictive rather than reactive. The solution existence and compactness condition for the proposed model is established under mild assumptions. The model is solved by an iterative algorithm with a relaxed NCP solved at each iteration. Numerical examples are provided to illustrate the proposed model and solution approach. We particularly show why predictive DUE is preferable to reactive DUE from an algorithmic perspective.     

The existence of an equilibrium solution to the traffic assignment problem when there are junction interactions

We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.     

Logistic modeling of the equilibrium speed-density relationship

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed-density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.     

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.     

More paradoxes in the equilibrium assignment problem

The sensitivity of travel costs to changes in input flows in the Wardrop equilibrium problem is studied. Examples are given showing that both origin to destination and global travel costs may decrease as a result of an increase in input flows. Other examples show that, in the two-mode equilibrium assignment problem transit origin to destination travel costs may decrease as a result of an increase in automobile input flows.     

A bottom-up solution for the multi-facility optimal pavement resurfacing problem

Transportation infrastructure management has been a subject of growing economic importance in recent years due to the magnitude of agency expenditures. Increasingly sophisticated methods have been developed to model pavement deterioration and solve for optimal management strategies. However, it is unclear whether these more complex methods are providing more useful results. This paper presents a simple approach for optimizing the frequency and intensity of resurfacing for multiple highway facilities. It builds upon existing optimization methods for the single-facility, continuous-state, continuous-time problem and corresponding results, which include a threshold structure for optimal solutions. This threshold structure allows for mathematical simplifications and for a straightforward optimization approach to be applied to the multi-facility case. The approach is bottom-up rather than top-down, preserving facility-specific features to develop informative budget allocation results. Application of the approach in a case study indicates that solutions are likely to be robust to deterioration model uncertainty, which is consistent with previous facility-level findings. In addition, the methodology is shown to be robust to the form of the deterioration model.     

A modified Frank-Wolfe algorithm for solving the traffic assignment problem

This paper presents a very simple modification of the Frank-Wolfe algorithm for the solution of the traffic assignment problem. It is shown that the modified algorithm can be implemented without much increase in computational effort over the original one. Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the modification.     

废旧家电逆向物流回收处理模式分析

在国内外逆向物流理论研究基础上,结合我国废旧家电市场现状进行分析,得出第三方逆向物流是解决目前我国废旧家电行业问题的一种有效途径。运用层次分析法对第三方废旧家电逆向物流服务商进行甄选,并且构建了一套由第三方废旧家电逆向物流服务商参与的系统模型,利用线性规划方法描述了再利用逆向物流网络的构建,并结合具体案例利用软件LINGO分析了模型的有效性。     

A reverse causal-effect modeling approach for signal control of an oversaturated intersection

A novel approach is presented in which signalized intersections are treated as normal highway bottlenecks for improved computational efficiency. It is unique in two ways. First, it treats the signalized intersections as common freeway bottlenecks by a reversed cause and effect modeling approach. Both traffic arrivals and departures are modeled by smooth continuous functions of time as if there were no interruptions to traffic flows from signals. The use of smooth continuous functions for departure curves instead of commonly used step functions makes it easy to apply differential calculus in optimization and future extension to a system of intersections. Second, a dynamic linear programming (LP) model is then developed to maximize the total vehicular output from the intersection during the entire period of congestion subject to prevailing capacity and other operational constraints. The continuous optimal departure flow rate (the effect) is then converted to signal timing parameters (the cause) that can be readily implemented. Two numerical examples are presented to demonstrate the properties of the proposed algorithm and examine its performance.     

The corridor problem: Preliminary results on the no-toll equilibrium

Consider a traffic corridor that connects a continuum of residential locations to a point central business district, and that is subject to flow congestion. The population density function along the corridor is exogenous, and except for location vehicles are identical. All vehicles travel along the corridor from home to work in the morning rush hour, and have the same work start-time but may arrive early. The two components of costs are travel time costs and schedule delay (time early) costs. Determining equilibrium and optimum traffic flow patterns for this continuous model, and possible extensions, is termed “The Corridor Problem”. Equilibria must satisfy the trip-timing condition, that at each location no vehicle can experience a lower trip price by departing at a different time. This paper investigates the no-toll equilibrium of the basic Corridor Problem.     

An alternative formulation of the simultaneous route and departure-time choice equilibrium problem

Traditional (static) network equilibrium models have always been formulated in a route-based fashion rather than a vehicle-based fashion. That is, the decision variables have been the number of vehicles using each route rather than the route choices of each vehicle. Given the success of this approach, it is not surprising that recent “dynamic” network equilibrium models have been formulated in a similar way. That is, the decision variables in these models are usually the route-specific departure rates over time. In this paper, we develop a vehicle-based equilibrium model of simultaneous route and departure-time choice and discuss the possible advantages of this approach. We then describe a heuristic for solving this model and demonstrate its effectiveness on several small examples.     

An algorithm for solving asymmetric equilibrium problems with a continuous cost-flow function

The paper gives two user objective functions for the asymmetric assignment problem, and an algorithm of descent type. The algorithm produces a sequence of flows which converges to the set of equilibria if the cost-flow function is continuous.     

Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models

The purpose of this paper is to examine the scaling effect and overlapping problem in a route choice context using the logit-based stochastic user equilibrium (SUE) principle to explicitly account for the congestion effect. Numerical experiments are performed on nine models: the deterministic user equilibrium model, the multinomial logit SUE model with and without scaling, the C-logit SUE model with and without scaling, the path-size logit SUE model with and without scaling, and the paired combinatorial logit SUE model with and without scaling. Sensitivity analysis is conducted to examine the effects of route sets, congestion levels, dispersion intensities, and network asymmetries. A real transportation network in the City of Winnipeg, Canada is also used to compare the network equilibrium flow allocations of different SUE models. The results of the sensitivity analysis and the Winnipeg network reveal that both scaling effect and overlapping problem can have a significant impact on the network equilibrium flow allocations.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

On the convergence of iterative methods for the distribution balancing problem

A general distribution balancing problem, specified by the given outflows and inflows and the factorial form of its solution, is formulated. Solution uniqueness and boundedness is discussed—primarily in graph theoretical terms. An entropy maximisation problem, subject to general linear constraints, is transformed into an unconstrained optimisation problem by application of standard duality theory, and a relevant general convergence theorem for iterative solution methods is given. The optimum solution in a special case is identified with the flow solution. When expressed in flow variables, the dual objective has a unique and bounded optimum solution and is an appropriate unifying concept for measuring the rate of convergence of different solution methods. By regarding the balancing procedure as an iterative optimisation method, a new and simple proof of its convergence is given, together with some asymptotic results, which are also compared with those of Newton's method. It is pointed out that there are two different forms of Newton's method, according to the choice of variables—untransformed or transformed— in the original distribution balancing problem. When Newton's method is applied to the whole system of equations simultaneously, the trajectory of iterates is observed to depend on this variable choice. For the transformed variables it is noticed that the convergence with the balancing procedure is quicker than with Newton's method applied to the outflow- and inflow- equations, alternately. To guarantee global convergence with Newton's method and to increase the rate a supplementary linear search routine is recommended.