Qiang Meng

AN EQUIVALENT CONTINUOUSLY DIFFERENTIABLE MODEL AND A LOCALLY CONVERGENT ALGORITHM FOR THE CONTINUOUS NETWORK DESIGN PROBLEM

The continuous network design problem (CNDP) is characterized by a bilevel programming model and recognized to be one of the most difficult and challenging problems in transportation. The main difficulty stems from the fact that the bilevel formulation for the CNDP is nonconvex and nondifferentiable, and indeed only some heuristic methods have been so far proposed. In this paper, the bilevel programming model for CNDPs is transferred into a single level optimization problem by virtue of a marginal function tool. By exploring the inherent nature of the CNDP, the marginal function for the lower-level user equilibrium problem is proved to be continuously differentiable and its functional value and derivative in link capacity enhancement can be obtained efficiently by implementing a user equilibrium assignment subroutine. Thus a continuously differentiable but still nonconvex optimization formulation of the CNDP is created and a locally convergent augmented Lagrangian method is applied to solve this equivalent problem. The descent direction in each step of the inner loop of the solution method can be found by doing an all or nothing assignment. These favorable characteristics indicate the potential of the algorithm to solve large CNDPs. Numerical examples are presented to compare the proposed method with some existing algorithms.

Containership Routing and Scheduling in Liner Shipping: Overview and Future Research Directions

This paper reviews studies from the past 30 years that use operations research methods to tackle containership routing and scheduling problems at the strategic, tactical, and operational planning levels. These problems are first classified and summarized, with a focus on model formulations, assumptions, and algorithm design. The paper then gives an overview of studies on containership fleet size and mix, alliance strategy, and network design at the strategic level; frequency determination, fleet deployment, speed optimization, and schedule design at the tactical level; and container booking and routing and ship rescheduling at the operational level. The paper further elaborates on the needs of the liner container shipping industry and notes the gap between existing academic studies and industrial practices. Research on containership routing and scheduling lags behind practice, especially in the face of the fast growth of the container shipping industry and the advancement of operations research and computer technology. The purpose of this paper is to stimulate more practically relevant research in this emerging area.

HIGHWAY PRICING AND CAPACITY CHOICE IN A ROAD NETWORK UNDER A BUILD-OPERATE-TRANSFER SCHEME

It is often argued lately that the private sector should be allowed to build and operate roads in a transportation network at its own expense, in return it should receive the revenue from road toll charge within some years, and then these roads will be transferred to the government. This type of build-operate-transfer (B-O-T) projects is currently fashionable worldwide, especially for developing countries short of funds for road construction. One of the important issues concerning a highway B-O-T project is the selection of the capacity and toll charge of the new road and the evaluation of the relevant benefits to the private investor, the road users and the whole society under various market conditions. This paper deals with the selection and evaluation of a highway project under such a B-O-T scheme. For a given road network with elastic demand, mathematical models are proposed to investigate the feasibility of a candidate project and ascertain the optimal capacity and level of toll charge of the new highway. The response of road users to the new B-O-T project is explicitly considered. The characteristic of the problem is illustrated graphically with a numerical example.

Benefit distribution and equity in road network design

Abstract In the classical continuous network design problem, the optimal capacity enhancements are determined by minimizing the total system cost under a budget constraint, while taking into account the route choice behavior of network users. Generally the equilibrium origin–destination travel costs for some origin–destination (O–D) pairs may be increased after implementing these optimal capacity enhancements, leading to positive or negative results for network users. Therefore, the equity issue about the benefit gained from the network design problem is raised. In this paper, we examine the benefit distribution among the network users and the resulting equity associated with the continuous network design problem in terms of the change of equilibrium O–D travel costs. Bilevel programming models that incorporate the equity constraint are proposed for the continuous network design problem. A penalty function approach by embodying a simulated annealing method is used to test the models for a network example.

Departure time, route choice and congestion toll in a queuing network with elastic demand

This paper deals with the modeling of peak-period congestion and optimal pricing in a queuing network with elastic demand. The approach employed in our study is a combined application of the space-time expanded network (STEN) representation of time-varying traffic flow and the conventional network equilibrium modeling techniques. Given the elastic demand function for trips between each origin-destination pair and the schedule delay cost associated with each destination, the departure time and route choice of commuters and the optimal variable tolls of bottlenecks will be determined jointly by solving a system optimization problem over the STEN. Our STEN approach can deal with general queuing network with elastic demand, and allow for treatment of commuter heterogeneity in their work start time and schedule delay cost, and hence make a significant advance over the previous simple bottleneck models of peak-period congestion.

Ship collision risk assessment for the Singapore Strait

The Singapore Strait is considered as the bottleneck and chokepoint of the shipping routes connecting the Indian and the Pacific Ocean. Therefore, the ship collision risk assessment is of significant importance for ships passing through the narrow, shallow, and busy waterway. In this paper, three ship collision risk indices are initially proposed to quantitatively assess the ship collision risks in the Strait: index of speed dispersion, degree of acceleration and deceleration, and number of fuzzy ship domain overlaps. These three risk indices for the Singapore Strait are estimated by using the real-time ship locations and sailing speeds provide by Lloyds MIU automatic identification system (AIS). Based on estimation of these three risk indices, it can be concluded that Legs 4W, 5W, 11E, and 12E are the most risky legs in the Strait. Therefore, the ship collision risk reduction solutions should be prioritized being implemented in these four legs. This study also finds that around 25% of the vessels sail with a speed in excess of the speed limit, which results in higher potentials of ship collision. Analysis indicates that the safety level would be significantly improved if all the vessels follow the passage guidelines.

Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions

Conventional analysis of optimal congestion pricing relies on three primary elements, namely, the speed-flow relationship, the demand function, and the generalized cost. Analytical demand functions tailed for congestion pricing are, however, difficult to establish in practice even with advanced transport modeling techniques. Inspired and motivated by the recent commentary and analytical works in the literature, this study proposes a trial-and-error implementation scheme of marginal-cost pricing on a general road network when the demand functions are unknown. Given a trial of a set of link tolls, the revealed aggregate link flows can be observed at ease; based on the observed link flows, a new set of link tolls can be determined and used for the next trial. We propose such an iterative toll adjustment procedure based on the method of successive averages, and present a rigorous theoretical proof of its convergence. The iterative procedure presented here allows for a traffic planner to estimate easily the socially optimal congestion tolls in a network without resorting to demand functions.

Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium

This article proposes an optimization model for simultaneous estimation of an origin-destination (O-D) matrix and a travel-cost coefficient for congested networks in a logit-based stochastic user equilibrium (SUE). The model is formulated in the form of a standard differentiable, nonlinear optimization problem with analytical stochastic user equilibrium constraints. Explicit expressions of the derivatives of the stochastic user equilibrium constraints with respect to origin-destination demand, link flow, and travel-cost coefficient are derived and computed efficiently through a stochastic network-loading approach. A successive quadratic-programming algorithm using the derivative information is applied to solve the simultaneous estimation model. This algorithm converges to a Karusch-Kuhn-Tucker point of the problem under certain conditions. The proposed model and algorithm are illustrated with a numerical example.

An Overview of Maritime Waterway Quantitative Risk Assessment Models

The safe navigation of ships, especially in narrow shipping waterways, is of the utmost concern to researchers as well as maritime authorities. Many researchers and practitioners have conducted studies on risk assessment for maritime transportation and have proposed risk reduction/control measures accordingly. This article provides a detailed review and assessment of various quantitative risk assessment models for maritime waterways. Eighty-seven academic papers and/or project reports are summarized and discussed. The review then proceeds to analyze the frequency and consequence estimation models separately. It should be pointed out that we further summarize the advantages and disadvantages of frequency estimation models and provide recommendations for their application. From the overview, we find that the quantification of the impact of human error is of great importance and should be considered in future studies. Possible solutions are also proposed in the discussions.

A chance constrained programming model for short-term liner ship fleet planning problems

This article deals with a short-term Liner Ship Fleet Planning (LSFP) problem with cargo shipment demand uncertainty for a single liner container shipping company. The cargo shipment demand uncertainty enables us to propose a chance constraint for each liner service route, which guarantees that the liner service route can satisfy the customers’ demand at least with a predetermined probability. Assuming that cargo shipment demand between any two ports on each liner service route is normally distributed, this article develops an integer linear programming model with chance constraints for the short-term LSFP problem. The proposed integer linear programming model can be efficiently solved by any optimization solver such as CPLEX. Finally, a numerical example is carried out to assess the model and analyze impact of the chance constraints and cargo shipment demand.