ManWo Ng

A Hybrid Bilevel Model for the Optimal Shelter Assignment in Emergency Evacuations

: The rise in natural and man-made disasters in recent years has led to an increased interest in emergency evacuation planning. Athough the vast majority of the existing evacuation planning models assumes system optimal (cooperative) behavior, recent research has shown that during large evacuations people tend to exhibit selfish (noncooperative) behavior. This article presents a hybrid bilevel model that balances both behavioral assumptions (in the upper level, shelter assignment occurs in a system optimal fashion, whereas evacuees are free to choose how to reach their assigned shelters in the lower level), hence providing a model that is more in line with the current state-of-the-knowledge of human behavior during disasters. The proposed model is solved using a simulated annealing algorithm. A hypothetical evacuation scenario in Sioux Falls, South Dakota, illustrates the proposed model. We demonstrate that the resulting evacuation strategies can be significantly different from conventional system optimal evacuation plans.

Distribution-free vessel deployment for liner shipping

One important problem faced by the liner shipping industry is the fleet deployment problem. In this problem, the number and type of vessels to be assigned to the various shipping routes need to be determined, in such a way that profit is maximized, while at the same time ensuring that (most of the time) sufficient vessel capacity exists to meet shipping demand. Thus far, the standard assumption has been that complete probability distributions can be readily specified to model the uncertainty in shipping demand. In this paper, it is argued that such distributions are hard, if not impossible, to obtain in practice. To relax this oftentimes restrictive assumption, a new distribution-free optimization model is proposed that only requires the specification of the mean, standard deviation and an upper bound on the shipping demand. The proposed model possesses a number of attractive properties: (1) It can be seen as a generalization of an existing variation of the liner fleet deployment model. (2) It remains a mixed integer linear program and (3) The model has a very intuitive interpretation. A numerical case study is provided to illustrate the model.

Reliable System-Optimal Network Design: Convex Mean–Variance Model with Implicit Chance Constraints

It is critical to account for uncertainty in the design of transportation networks. Various models assuming both user-optimal and system-optimal behavior (as a computationally viable proxy for the more realistic user-optimal design problem) have been proposed. Most of these models do not provide any form of probabilistic guarantee for the obtained capacity expansion decisions. However, for system reliability, it is often useful to know how likely it is that the total system travel time would deviate from a certain value if the prescribed solutions from a specific model are implemented. A new mean-variance type of system-optimal network design model with probabilistic guarantees on systemwide travel time is proposed. The proposed model has several unique features. First, uncertainty in the link performance function is considered. This uncertainty is a result of capacity uncertainty as well as fundamental uncertainty about the functional form of the link performance function itself. Second, instead of imposing an explicit chance constraint–which in general would lead to nonconvexity–probabilistic guarantees on the obtained system travel time are obtained implicitly. More specific, the model yields a one-sided confidence interval for the total systemwide travel time that has an a priori specified confidence level. Finally, it is not necessary to specify an explicit probability distribution to model the uncertainty. Instead, the proposed model is distribution free in that any symmetric probability distribution suffices. Numerical results are presented and discussed.

A Dynamic Route Choice Model Considering Uncertain Capacities

: The standard assumption in (dynamic) traffic assignment models is that route choice is solely determined by a (perceived) deterministic travel time. However, recently, there is a growing interest in (dynamic) equilibrium route choice models in which travelers not only select their paths based on an estimated deterministic travel time, but also based on travel time reliability, in this article defined as the probability that the actual travel time deviates from the anticipated value. We extend the linear programming cell transmission model-based dynamic traffic assignment (LP CTM-DTA) model to account for travelers’ consideration of uncertainty regarding saturation flow rates (in this article referred to as capacities). It is shown that these reliability considerations can be accounted for by simply reducing the road capacities appearing in the constraint set of the classical LP CTM-DTA model. More importantly, we provide results on the amount of capacity reduction necessary to ensure a certain reliability level. Although in the proposed model any probability distribution can be used to model the uncertainty, the selection of a specific probability distribution can potentially be burdensome for the modeler. To this end, we also present results on the class of symmetric probability distributions that has been particularly popular in the robust optimization literature. Properties for this broad class of distributions will be derived within the context of the introduced model. In numerical case studies, the model predicts that travel patterns can be significantly different when accounting for travelers’ reliability considerations.

The Evacuation Optimal Network Design Problem: Model Formulation and Comparisons

Abstract The goal of this paper is twofold. First, we present a stochastic programming-based model that provides optimal design solutions for transportation networks in light of possible emergency evacuations. Second, as traffic congestion is a growing problem in metropolitan areas around the world, decision makers might not be willing to design transportation networks solely for evacuation purposes since daily traffic patterns differ tremendously from traffic observed during evacuations. This is especially true when potential disaster locations are limited in number and confined to specific regions (e.g. coastal regions might be more prone to flooding). However, as extreme events such as excessive rainfall become more prevalent everywhere, it is less obvious that the design of transportation networks for evacuation planning and congestion reduction is mutually exclusive. That is, capacity expansion decisions to reduce congestion might also be reasonable from an evacuation planning point of view. Conversely, expansion decisions for evacuation planning might turn out to be effective for congestion relief. To date, no numerical evidence has been presented in the literature to support or disprove these conjectures. Preliminary numerical evidence is provided in this paper.

Relaxing the Multivariate Normality Assumption in the Simulation of Transportation System Dependencies: an Old Technique in a New Domain

Abstract By far the most popular method to account for dependencies in the transportation network analysis literature is the use of the multivariate normal (MVN) distribution. While in certain cases there is some theoretical underpinning for the MVN assumption, in others there is none. This can lead to misleading results: results do not only depend on whether dependence is modeled, but also how dependence is modeled. When assuming the MVN distribution, one is limiting oneself to a specific set of dependency structures, which can substantially limit validity of results. In this paper an existing, more flexible, correlation-based approach (where just marginal distributions and their correlations are specified) is proposed, and it is demonstrated that, in simulation studies, such an approach is a generalization of the MVN assumption. The need for such generalization is particularly critical in the transportation network modeling literature, where oftentimes there exists no or insufficient data to estimate probability distributions, so that sensitivity analyses assuming different dependence structures could be extremely valuable. However, the proposed method has its own drawbacks. For example, it is again not able to exhaust all possible dependence forms and it relies on some not-so-known properties of the correlation coefficient.

Revisiting a class of liner fleet deployment models

A class of liner fleet deployment models in the literature is revisited. We point to an implicit (and unnecessary) assumption in this class of models that can lead to fleet deployment plans that employ more vessels than strictly necessary. New analytical results are derived to relax this assumption, leading to a new and more realistic liner fleet deployment model. In a case study, it is found that the new model can lead to a substantial reduction in the fleet deployment cost, up to 15 percent. Moreover, it is observed that the new model is particularly timely in the current era where vessel sharing agreements and mega vessels are the norm, as the cost savings grow with the vessel size.

The coopetition game in international liner shipping

ABSTRACT In maritime freight transportation, carriers build collaborative relationships with other carriers while competing with each other to optimize their own profits. In such a scenario, a game of coopetition is formed. We formulate a nonlinear mixed-integer problem to determine the optimal levels of coopetition for a single company and embed the resulting problem into a general game theoretic framework. A diagonalization algorithm that incorporates an ascent direction search technique is developed to effectively evaluate the game. The numerical results show that carriers choose similar coopetition levels to maximize their profits, and the coopetition game can reach equilibrium under general conditions.

Modeling Traffic Incident Duration Using Quantile Regression

Traffic incidents occur frequently on urban roadways and cause incident-induced congestion. Predicting incident duration is a key step in managing these events. Ordinary least squares (OLS) regression models can be estimated to relate the mean of incident duration data with its correlates. Because of the presence of larger incidents, duration distributions are often right-skewed; that is, the OLS model underpredicts the durations of larger incidents. Therefore, this study applies a modeling technique known as quantile regression to predict more accurately the skewed distribution of incident durations. Quantile regression estimates the relationships between correlates and a chosen percentile—for example, the 75th or 95th percentile—while the OLS regression is based on the mean of incident duration. With the use of incident data related to more than 85,000 (2013 to 2015) incidents for highways in the Hampton Roads area of Virginia, quantile regression results indicate that the magnitudes of parameters and predictions can be quite different compared with OLS regression. In addition to predicting durations of larger incidents more accurately, quantile regressions can estimate the probability of an incident lasting for a specific duration; for example, incidents involving congestion and delay have an approximately 25% chance of lasting more than 100.8 min, while incidents excluding congestion and delay are estimated to have a 25% chance of lasting more than 43.3 min. Such information is helpful in accurately predicting durations and developing potential applications for using quantile regressions for better traffic incident management.

Traffic Flow Theory-Based Stochastic Optimization Model for Work Zones on Two-Lane Highways

AbstractRoad maintenance is essential to ensure a safe and efficient transportation system. Unfortunately, work zones can give rise to significant delays to road users. In this paper, two major limitations in the current work zone optimization models are addressed. First, we relax the assumption of determinism, and model vehicle arrivals as being stochastic. While previous work has shown that this relaxation is important in the quantification of user delay at work zones, no model exists that explicitly accounts for stochasticity in the optimization of work zones. Second, unlike in previous work in which idealized traffic flow modeling techniques have been used, the proposed model employs the traffic flow theory–based cell transmission model, yielding a more accurate and realistic representation of traffic flow dynamics. The focus in this paper is on two-lane two-way highways. A case study is presented to illustrate the proposed model.