Network-based real option models

Building on earlier work to incorporate real option methodologies into network modeling, two models are proposed. The first is the network option design problem, which maximizes the expanded net present value of a network investment as a function of network design variables with the option to defer the committed design investment. The problem is shown to be a generalized version of the network design problem and the multi-period network design problem. A heuristic based on radial basis functions is used to solve the problem for continuous link expansion with congestion effects. The second model is a link investment deferral option set, which decomposes the network investment deferral option into individual, interacting link or project investments. This model is a project selection problem under uncertainty, where each link or project can be deferred such that the expanded net present value is maximized. The option is defined in such a way that a lower bound can be solved using an exact method based on multi-option least squares Monte Carlo simulation. Numerical tests are conducted with the classical Sioux Falls network and compared to earlier published results.     

Ferry service network design: optimal fleet size,routing, and scheduling

The study formulated a ferry network design problem by considering the optimal fleet size, routing, and scheduling for both direct and multi-stop services. The objective function combines both the operator and passengers’ performance measures. Mathematically, the model is formulated as a mixed integer multiple origin–destination network flow problem with ferry capacity constraints. To solve this problem of practical size, this study developed a heuristic algorithm that exploits the polynomial-time performance of shortest path algorithms. Two scenarios of ferry services in Hong Kong were solved to demonstrate the performance of the heuristic algorithm. The results showed that the heuristic produced solutions that were within 1.3% from the CPLEX optimal solutions. The computational time is within tens of seconds even for problem size that is beyond the capability of CPLEX.     

Controlling road congestion via a low-complexity route reservation approach

This work introduces a novel route reservation architecture to manage road traffic within an urban area. The developed routing architecture decomposes the road infrastructure into slots in the spatial and temporal domains and for every vehicle, it makes the appropriate route reservations to avoid traffic congestion while minimizing the traveling time. Under this architecture, any road segment is admissible to be traversed only during time-slots when the accumulated reservations do not exceed its critical density. A road-side unit keeps track of all reservations which are subsequently used to solve the routing problem for each vehicle. Through this routing mechanism, vehicles can either be delayed at their origin or are routed through longer but non-congested routes such that their traveling time is minimized. In this work, the proposed architecture is presented and the resulting route reservation problem is mathematically formulated. Through a complexity analysis of the routing problem, it is shown that for certain cases, the problem reduces to an NP-complete problem. A heuristic solution to the problem is also proposed and is used to conduct realistic simulations across a particular region of the San Francisco area, demonstrating the promising gains of the proposed solution to alleviate traffic congestion.     

Intermodal hub-and-spoke network design: Incorporating multiple stakeholders and multi-type containers

This paper develops a mathematical program with equilibrium constraints (MPEC) model for the intermodal hub-and-spoke network design (IHSND) problem with multiple stakeholders and multi-type containers. The model incorporates a parametric variational inequality (VI) that formulates the user equilibrium (UE) behavior of intermodal operators in route choice for any given network design decision of the network planner. The model also uses a cost function that is capable of reflecting the transition from scale economies to scale diseconomies in distinct flow regimes for carriers or hub operators, and a disutility function integrating actual transportation charges and congestion impacts for intermodal operators. To solve the MPEC model, a hybrid genetic algorithm (HGA) embedded with a diagonalization method for solving the parametric VI is proposed. Finally, the comparative analysis of the HGA and an exhaustive enumeration algorithm indicates a good performance of the HGA in terms of computational time and solution quality. The HGA is also applied to solve a large-scale problem to show the applicability of the proposed model and algorithm.     

Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

This paper investigates the nonlinear distance-based congestion pricing in a network considering stochastic day-to-day dynamics. After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.     

Application of Ant System to network design problem

Network design problem (NDP) is the problem of choosing from among a set of alternative projects which optimizes an objective (e.g., minimizes total travel time), while keeping consumption of resources (e.g., budget) within their limits. This problem is difficult to solve, because of its combinatorial nature and nonconvexity of the objective function. Many algorithms are presented to solve the problem more efficiently, while trading-off accuracy with computational speed. This increase in speed stems from certain approximations in the formulation of the problem, decomposition, or heuristics. This study adapts a meta – heuristic approach to solve NDP, namely Ant System (AS). The algorithm is first designed, and then calibrated to solve NDP for the Sioux Falls test network. The behavior of the algorithm is then investigated. The result seems encouraging.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Application of multiple criteria decision making for network improvement

In this paper we propose application of multiple criteria decision making to problems of a metropolitan network improvement plan. Initially, a bilevel multiple objective network design model is considered in two objectives which are minimal government budget and minimal total travel time of road users. We seek feasible improvement alternatives among those bottleneck links in an existing road network structure and travel demand. We present an effective heuristic algorithm to obtain noninferior solutions; then ELECTRE III multiple criteria decision making and group decision making are used to evaluate and to select a compromise solution among those noninferior solutions. From the design phase in multiple criteria decision making, multiple objective mathematical programming is used to formulate a continuous network design model. However, from the phase of evaluation, multiple criteria decision making to solve the discrete network design problem. The network of metropolitan Taipei is taken as an example to illustrate the operation of this model.     

New technology and the modeling of risk-taking behavior in congested road networks

Intelligent transport systems provide various means to improve traffic congestion in road networks. Evaluation of the benefits of these improvements requires consideration of commuters’ response to reliability and/or uncertainty of travel time under various circumstances. Various disruptions cause recurrent or non-recurrent congestion on road networks, which make road travel times intrinsically fluctuating and unpredictable. Confronted with such uncertain traffic conditions, commuters are known to develop some simple decision-making process to adjust their travel choices. This paper represents the decision-making process involved in departure-time and route choices as risk-taking behavior under uncertainty. An expected travel disutility function associated with commuters’ departure-time and route choices is formulated with taking into account the travel delay (due the recurrent congestion), the uncertainty of travel times (due to incident-induced congestion) and the consequent early or late arrival penalty. Commuters are assumed to make decision on the departure-time and route choices on the basis of the minimal expected travel disutility. Thus the network will achieve a simultaneous route and departure-time user equilibrium, in which no commuter can decrease his or her expected disutility by unilaterally changing the route or departure-time. The equilibrium is further formulated as an equivalent nonlinear complementarity problem and is then converted into an unconstrained minimization problem with the use of a gap function suggested recently. Two algorithms based on the Nelder–Mead multidimensional simplex method and the heuristic route/time-swapping approach, are adapted to solve the problem. Finally, numerical example is given to illustrate the application of the proposed model and algorithms.     

Biofuel refinery location and supply chain planning under traffic congestion

This research focuses on planning biofuel refinery locations where the total system cost for refinery investment, feedstock and product transportation and public travel is minimized. Shipment routing of both feedstock and product in the biofuel supply chain and the resulting traffic congestion impact are incorporated into the model to decide optimal locations of biofuel refineries. A Lagrangian relaxation based heuristic algorithm is introduced to obtain near-optimum feasible solutions efficiently. To further improve optimality, a branch-and-bound framework (with linear programming relaxation and Lagrangian relaxation bounding procedures) is developed. Numerical experiments with several testing examples demonstrate that the proposed algorithms solve the problem effectively. An empirical Illinois case study and a series of sensitivity analyses are conducted to show the effects of highway congestion on refinery location design and total system costs.     

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.     

Transit network design for small-medium size cities

This paper proposes a novel heuristic to solve the network design problem for public transport in small-medium size cities. Such cities can be defined as those with a diameter of a few kilometers with up to a few hundred thousand residents. These urban centers present a specific spatial configuration affecting the land use and mobility system. Transportation demand is widespread in origin and concentrated in a small number of attraction points close to each other. This particular structure of demand (‘many-to-few’) suggests the need for specific methodologies for the design of a transit system at a network level. In this paper, such design methodologies are defined in terms of models and solution procedures and tested on a selected case study. The solution methods show promising results. The key variables of the model are the routes and their frequencies. The constraints of the problem affect the overall demand to be served, the quality of the proposed service (transfer, load factors) and the definition of routes.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

Feedback control speed harmonization algorithm: Methodology and preliminary testing

The capacity drop phenomenon, which reduces the maximum bottleneck discharge rate following the onset of congestion, is a critical restriction in transportation networks that produces additional traffic congestion. Consequently, preventing or reducing the occurrence of the capacity drop not only mitigates traffic congestion, but can also produce environmental and traffic safety benefits. In addressing this problem, the paper develops a novel bang-bang feedback control speed harmonization (SH) or Variable Speed Limit (VSL) algorithm, that attempts to prevent or delay the breakdown of a bottleneck and thus reduce traffic congestion. The novelty of the system lies in the fact that it is both proactive and reactive in responding to the dynamic stochastic nature of traffic. The system is proactive because it uses a calibrated fundamental diagram to initially identify the optimum throughput to maintain within the SH zone. Furthermore, the system is reactive (dynamic) because it monitors the traffic stream directly upstream of the bottleneck to adjustment the metering rate to capture the dynamic and stochastic nature of traffic. The steady-state traffic states in the vicinity of a lane-drop bottleneck before and after applying the SH algorithm is analyzed to demonstrate the effectiveness of the algorithm in alleviating the capacity drop. We demonstrate theoretically that the SH algorithm is effective in enhancing the bottleneck discharge rate. A microscopic simulation of the network using the INTEGRATION software further demonstrates the benefits of the algorithm in increasing the bottleneck discharge rate, decreasing vehicle delay, and reducing vehicle fuel consumption and CO₂ emission levels. Specifically, compared with the base case without the SH algorithm, the advisory speed limit increases the bottleneck discharge rate by approximately 7%, reduces the overall system delay by approximately 20%, and reduces the system-wide fuel consumption and CO₂ emission levels by 5%.     

A network model for gate assignment

In this research we developed a network model that will help the airport authorities assign flights to gates both efficiently and effectively. The model was formulated as a multi-commodity network flow problem. An algorithm based on the Lagrangian relaxation, with subgradient methods, accompanied by a shortest path algorithm and a Lagrangian heuristic was developed to solve the problem. The model was tested using data from Chiang Chiek-Shek Airport.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.