Trial-and-error method for congestion pricing scheme under side-constrained probit-based stochastic user equilibrium conditions

A toll pattern that can restrict link flows on the tolled links to some predetermined thresholds is named as effective toll solution, which can be theoretically obtained by solving a side-constraint traffic assignment problem. Considering the practical implementation, this paper investigates availability of an engineering-oriented trial-and-error method for the effective toll pattern of cordon-based congestion pricing scheme, under side-constrained probit-based stochastic user equilibrium (SUE) conditions. The trial-and-error method merely requires the observed traffic counts on each entry of the cordon. A minimization model for the side-constrained probit-based SUE problem with elastic demand is first proposed and it is shown that the effective toll solution equals to the product of value of time and optimal Lagrangian multipliers with respect to the side constraints. Then, employing the Lagrangian dual formulation of the minimization method, this paper has built a convergent trial-and-error method. The trial-and-error method is finally tested by a numerical example developed from the cordon-based congestion pricing scheme in Singapore.     

Reliable sensor deployment for network traffic surveillance

New sensor technologies enable synthesis of disaggregated vehicle information from multiple locations. This paper proposes a reliable facility location model to optimize traffic surveillance benefit from synthesized sensor pairs (e.g., for travel time estimation) in addition to individual sensor flow coverage (e.g., for traffic volume statistics), while considering probabilistic sensor failures. Customized greedy and Lagrangian relaxation algorithms are proposed to solve this problem, and their performance is discussed. Numerical results show that the proposed algorithms solve the problem efficiently. We also discuss managerial insights on how optimal sensor deployment and surveillance benefits vary with surveillance objective and system parameters (such as sensor failure probabilities).     

Optimal biofuel supply chain design under consumption mandates with renewable identification numbers

The Renewable Identification Number (RIN) system is a tracking mechanism that enforces the U.S. Renewable Fuel Standard by monitoring obligated parties’ compliance with the biofuel consumption mandates. This paper incorporates the RIN system into the design of a biofuel supply chain that addresses independent decisions of non-cooperative farmers, biofuel manufacturers, and blenders. Game-theoretic models are developed to examine the impacts of the RIN system on individual stakeholders’ decisions (e.g., on farmland use, bio-refinery investment, biofuel production) and the competition between food and biofuel industries, in both a perfectly competitive scenario and a monopoly scenario. For the perfectly competitive scenario, Nash equilibrium can be obtained by solving a convex optimization problem. For the monopoly scenario, a bi-level Stackelberg leader–follower model is developed, from which we found that a rigid mandate on blenders may suppress the total biofuel production. To avoid such unintended consequences, a relaxed unit-RIN based penalty scheme is proposed and shown to improve the overall biofuel supply chain performance. Managerial insights are drawn from a numerical case study for the state of Illinois.     

Economic and emissions impacts of renewable fuel goals for aviation in the US

The US Federal Aviation Administration (FAA) has a goal that one billion gallons of renewable jet fuel is consumed by the US aviation industry each year from 2018. We examine the economic and emissions impacts of this goal using renewable fuel produced from a Hydroprocessed Esters and Fatty Acids (HEFA) process from renewable oils. Our approach employs an economy-wide model of economic activity and energy systems and a detailed partial equilibrium model of the aviation industry. If soybean oil is used as a feedstock, we find that meeting the aviation biofuel goal in 2020 will require an implicit subsidy from airlines to biofuel producers of $2.69 per gallon of renewable jet fuel. If the aviation goal can be met by fuel from oilseed rotation crops grown on otherwise fallow land, the implicit subsidy is $0.35 per gallon of renewable jet fuel. As commercial aviation biofuel consumption represents less than 2% of total fuel used by this industry, the goal has a small impact on the average price of jet fuel and carbon dioxide emissions. We also find that, under the pathways we examine, the cost per tonne of CO₂ abated due to aviation biofuels is between $50 and $400.     

Simultaneous passenger train routing and timetabling using an efficient train-based Lagrangian relaxation decomposition

This paper focuses on the simultaneous passenger train routing and timetabling problem on the rail network consisting of both unidirectional and bidirectional tracks using an efficient train-based Lagrangian relaxation decomposition. We first build an integer linear programming model with many 0–1 binary and non-negative integer decision variables, after then reformulate it as a train path-choice model for providing an easier train-based Lagrangian relaxation decomposition mechanism based on the construction of space-time discretized network extending from node-cell-based rail network. Moreover, through reformulating safety usage interval restrictions with a smaller number of constraints in this reformulated model, the train-based decomposition needs fewer Lagrangian multipliers to relax these constraints. On the basis of this decomposition, a solving framework including a heuristic algorithm is proposed to simultaneously optimize both the dual and feasible solutions. A set of numerical experiments demonstrate the proposed Lagrangian relaxation decomposition approach has better performances in terms of minimizing both train travel time and computational times.     

Optimal toll locations and toll levels in congestion pricing schemes: a case study of Stockholm

As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.     

Joint inventory-location problem under the risk of probabilistic facility disruptions

This paper studies a reliable joint inventory-location problem that optimizes facility locations, customer allocations, and inventory management decisions when facilities are subject to disruption risks (e.g., due to natural or man-made hazards). When a facility fails, its customers may be reassigned to other operational facilities in order to avoid the high penalty costs associated with losing service. We propose an integer programming model that minimizes the sum of facility construction costs, expected inventory holding costs and expected customer costs under normal and failure scenarios. We develop a Lagrangian relaxation solution framework for this problem, including a polynomial-time exact algorithm for the relaxed nonlinear subproblems. Numerical experiment results show that this proposed model is capable of providing a near-optimum solution within a short computation time. Managerial insights on the optimal facility deployment, inventory control strategies, and the corresponding cost constitutions are drawn.     

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.     

Equilibrium analysis of the scheduling of tours in congested networks

In this paper, we develop a model of travel in tours that joins several locations by travel through a congested network. We develop a microscopic analysis in continuous time of individual benefits obtained by spending time at each of the locations and costs incurred through travel between them. This is combined with a continuous time macroscopic equilibrium model of travel during congested peak periods to show how individuals' travel choices are influenced by the congestion that result from corresponding choices made by others. We show how different travellers can achieve identical net utilities by making different combinations of choices within the equilibrium. The resulting model can be used to investigate the effect on travel behaviour and individual utility of various transport interventions, and we illustrate this by considering the effect of a peak‐period charge that eliminates congestion.     

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.     

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.     

Airport taxi planning: Lagrangian decomposition

The airport taxi planning (TP) module is a decision tool intended to guide airport surface management operations. TP is defined by a flow network optimization model that represents flight ground movements and improves aircraft taxiing routes and schedules during periods of aircraft congestion. TP is not intended to operate as a stand‐alone tool for airport operations management: on the contrary, it must be used in conjunction with existing departing and arriving traffic tools and overseen by the taxi planner of the airport, also known as the aircraft ground controller. TP must be flexible in order to accommodate changing inputs while maintaining consistent routes and schedules already delivered from past executions. Within this dynamic environment, the execution time of TP may not exceed a few minutes. Classic methods for solving binary multi‐commodity flow networks with side constraints are not efficient enough; therefore, a Lagrangian decomposition methodology has been adapted to solve it. We demonstrate TP Lagrangian decomposition using actual data from the Madrid‐Barajas Airport. Copyright © 2011 John Wiley & Sons, Ltd.     

Measuring marginal congestion costs of urban transportation: Do networks matter?

In determining the marginal cost of congestion, economists have traditionally relied upon directly measuring traffic congestion on network links, disregarding any “network effects,” since the latter are difficult to estimate. While for simple networks the comparison of the network-based congestion costs with the link-based ones can be done within a theoretical framework, it is important to know whether such network effects in real large-scale networks are quantitatively significant.In this paper we use a strategic transportation planning model (START) to compare marginal congestion costs computed link-by-link with measures taking into account network effects. We find that while in aggregate network effects are not significant, congestion measured on a single link is a poor predictor of total congestion costs imposed by travel on that link. Also, we analyze the congestion proliferation effect on the network to see how congestion is distributed within an urban area.     

Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach.     

Green supply chain network design to reduce carbon emissions

We consider a supply chain network design problem that takes CO₂ emissions into account. Emission costs are considered alongside fixed and variable location and production costs. The relationship between CO₂ emissions and vehicle weight is modeled using a concave function leading to a concave minimization problem. As the direct solution of the resulting model is not possible, Lagrangian relaxation is used to decompose the problem into a capacitated facility location problem with single sourcing and a concave knapsack problem that can be solved easily. A Lagrangian heuristic based on the solution of the subproblem is proposed. When evaluated on a number of problems with varying capacity and cost characteristics, the proposed algorithm achieves solutions within 1% of the optimal. The test results indicate that considering emission costs can change the optimal configuration of the supply chain, confirming that emission costs should be considered when designing supply chains in jurisdictions with carbon costs.     

A heterogeneous reliable location model with risk pooling under supply disruptions

This paper investigates a facility location model that considers the disruptions of facilities and the cost savings from the inventory risk-pooling effect and economies of scale. Facilities may have heterogeneous disruption probabilities. When a facility fails, its customers may be reassigned to other surviving ones to hedge against lost-sales costs. We first develop both an exact and an approximate expression for the nonlinear inventory cost, and then formulate the problem as a nonlinear integer programming model. The objective is to minimize the expected total cost across all possible facility failure scenarios. To solve this problem, we design two methods, an exact approach using special ordered sets of type two (SOS2) and a heuristic based on Lagrangian relaxation. We test the model and algorithms on data sets with up to 150 nodes. Computational results show that the proposed algorithms can solve the problem efficiently in reasonable time. Managerial insights on the optimal facility deployment, customer assignments and inventory control strategies are also drawn.     

Real-time congestion pricing strategies for toll facilities

This paper analyzes the dynamic traffic assignment problem on a two-alternative network with one alternative subject to a dynamic pricing that responds to real-time arrivals in a system optimal way. Analytical expressions for the assignment, revenue and total delay in each alternative are derived as a function of the pricing strategy. It is found that minimum total system delay can be achieved with many different pricing strategies. This gives flexibility to operators to allocate congestion to either alternative according to their specific objective while maintaining the same minimum total system delay. Given a specific objective, the optimal pricing strategy can be determined by finding a single parameter value in the case of HOT lanes. Maximum revenue is achieved by keeping the toll facility at capacity with no queues for as long as possible. Guidelines for implementation are discussed.     

A framework for evaluating the dynamic impacts of a congestion pricing policy for a transportation socioeconomic system

This paper provides a modeling framework based on the system dynamics approach by which policy makers can understand the dynamic and complex nature of traffic congestion within a transportation socioeconomic system representation of a metropolitan area. This framework offers policy makers an assessment platform that focuses on the short- and long-term system behaviors arising from an area-wide congestion pricing policy along with other congestion mitigation policies. Since only a few cities in the world have implemented congestion pricing and several are about to do so, a framework that helps policy makers to understand the impacts of congestion pricing is currently quite relevant. Within this framework, improved bus and metro capacities contribute to the supply dynamics which in turn affect the travel demand of individuals and their choice of different transportation modes. Work travel and social networking activities are assumed to generate additional travel demand dynamics that are affected by travelers’ perception of the level of service of the different transportation modes, their perception of the congestion level, and the associated traveling costs. It is assumed that the, population, tourism and employment growth are exogenous factors that affect demand. Furthermore, this paper builds on a previously formulated approach where fuzzy logic concepts are used to represent linguistic variables assumed to describe consumer perceptions about transportation conditions.     

Comparison of “Advanced” biofuel cost estimates: Trends during rollout of low carbon fuel policies

Costs of producing “advanced” biofuels (those with the lowest GHG and land use impacts) have not decreased in recent years as envisioned by analysts. Despite aggressive policy incentives, no transition to a lower cost mature industry has occurred. Information about the cost dynamics and slow industry emergence is of major interest to policymakers and others seeking to understand the likely success – and cost – of incentive programs. This paper reviews literature on production cost at the plantgate – without considering taxes or delivery costs – for selected biofuel technology pathways using a levelized cost of fuel approach, applying common financing assumptions for capital amortization and converting all values to year 2016 dollars, and examines results in the current low carbon fuel policy context. The average production cost estimate for cellulosic ethanol was $4 per gallon-gasoline equivalent (gge). For drop-in fuels, the pyrolysis-biocrude-hydro treatment pathway had the lowest average production cost estimate at about $3.25/gge. Biomass to liquid (BTL) production cost estimates averaged $3.80/gge, while hydrotreated esters and fatty acids (HEFA) – the sole fuel studied gaining commercial traction – averaged about $3.70/gge. Estimate ranges did not allow any definitive rank ordering of the fuels by production cost. Production cost estimates are higher in later than in earlier publications for non-HEFA fuels due primarily to higher costs for feedstock and capital expenditure components. This may reflect learning from early but largely unsuccessful commercialization efforts that yielded more realistic (and higher cost) information and detail on feedstock provision and conversion processes.