Tracking a system of shared autonomous vehicles across the Austin,Texas network using agent-based simulation

This study provides a large-scale micro-simulation of transportation patterns in a metropolitan area when relying on a system of shared autonomous vehicles (SAVs). The six-county region of Austin, Texas is used for its land development patterns, demographics, networks, and trip tables. The agent-based MATSim toolkit allows modelers to track individual travelers and individual vehicles, with great temporal and spatial detail. MATSim’s algorithms help improve individual travel plans (by changing tour and trip start times, destinations, modes, and routes). Here, the SAV mode requests were simulated through a stochastic process for four possible fare levels: $0.50, $0.75, $1, and $1.25 per trip-mile. These fares resulted in mode splits of 50.9, 12.9, 10.5, and 9.2% of the region’s person-trips, respectively. Mode choice results show longer-distance travelers preferring SAVs to private, human-driven vehicles (HVs)—thanks to the reduced burden of SAV travel (since one does not have to drive the vehicle). For travelers whose households do not own an HV, SAVs (rather than transit, walking and biking) appear preferable for trips under 10 miles, which is the majority of those travelers’ trip-making. It may be difficult for traditional transit services and operators to survive once SAVs become available in regions like Austin, where dedicated rail lines and bus lanes are few. Simulation of SAV fleet operations suggest that higher fare rates allow for greater vehicle replacement (ranging from 5.6 to 7.7 HVs per SAV, assuming that the average SAV serves 17–20 person-trips per day); when fares rise, travel demands shift away from longer trip distances. Empty vehicle miles traveled by the fleet of SAVs ranged from 7.8 to 14.2%, across the scenarios in this study. Implications of mobility and sustainability benefits of SAVs are also discussed in the paper.     

The travel and environmental implications of shared autonomous vehicles,using agent-based model scenarios

Carsharing programs that operate as short-term vehicle rentals (often for one-way trips before ending the rental) like Car2Go and ZipCar have quickly expanded, with the number of US users doubling every 1–2 years over the past decade. Such programs seek to shift personal transportation choices from an owned asset to a service used on demand. The advent of autonomous or fully self-driving vehicles will address many current carsharing barriers, including users’ travel to access available vehicles.This work describes the design of an agent-based model for shared autonomous vehicle (SAV) operations, the results of many case-study applications using this model, and the estimated environmental benefits of such settings, versus conventional vehicle ownership and use. The model operates by generating trips throughout a grid-based urban area, with each trip assigned an origin, destination and departure time, to mimic realistic travel profiles. A preliminary model run estimates the SAV fleet size required to reasonably service all trips, also using a variety of vehicle relocation strategies that seek to minimize future traveler wait times. Next, the model is run over one-hundred days, with driverless vehicles ferrying travelers from one destination to the next. During each 5-min interval, some unused SAVs relocate, attempting to shorten wait times for next-period travelers.Case studies vary trip generation rates, trip distribution patterns, network congestion levels, service area size, vehicle relocation strategies, and fleet size. Preliminary results indicate that each SAV can replace around eleven conventional vehicles, but adds up to 10% more travel distance than comparable non-SAV trips, resulting in overall beneficial emissions impacts, once fleet-efficiency changes and embodied versus in-use emissions are assessed.     

Preferences for shared autonomous vehicles

Shared autonomous vehicles (SAVs) could provide inexpensive mobility on-demand services. In addition, the autonomous vehicle technology could facilitate the implementation of dynamic ride-sharing (DRS). The widespread adoption of SAVs could provide benefits to society, but also entail risks. For the design of effective policies aiming to realize the advantages of SAVs, a better understanding of how SAVs may be adopted is necessary. This article intends to advance future research about the travel behavior impacts of SAVs, by identifying the characteristics of users who are likely to adopt SAV services and by eliciting willingness to pay measures for service attributes. For this purpose, a stated choice survey was conducted and analyzed, using a mixed logit model. The results show that service attributes including travel cost, travel time and waiting time may be critical determinants of the use of SAVs and the acceptance of DRS. Differences in willingness to pay for service attributes indicate that SAVs with DRS and SAVs without DRS are perceived as two distinct mobility options. The results imply that the adoption of SAVs may differ across cohorts, whereby young individuals and individuals with multimodal travel patterns may be more likely to adopt SAVs. The methodological limitations of the study are also acknowledged. Despite a potential hypothetical bias, the results capture the directionality and relative importance of the attributes of interest.     

Marginal costs of freeway traffic congestion with on-road pollution exposure externality

The health cost of on-road air pollution exposure is a component of traffic marginal costs that has not previously been assessed. The main objective of this paper is to introduce on-road pollution exposure as an externality of traffic, particularly important during traffic congestion when on-road pollution exposure is highest. Marginal private and external cost equations are developed that include on-road pollution exposure in addition to time, fuel, and pollution emissions components. The marginal external cost of on-road exposure includes terms for the marginal vehicle’s emissions, the increased emissions from all vehicles caused by additional congestion from the marginal vehicle, and the additional exposure duration for all travelers caused by additional congestion from the marginal vehicle. A sensitivity analysis shows that on-road pollution exposure can be a large portion (18%) of marginal social costs of traffic flow near freeway capacity, ranging from 4% to 38% with different exposure parameters. In an optimal pricing scenario, excluding the on-road exposure externality can lead to 6% residual welfare loss because of sub-optimal tolls. While regional pollution generates greater costs in uncongested conditions, on-road exposure comes to dominate health costs on congested freeways because of increased duration and intensity of exposure. The estimated marginal cost and benefit curves indicate a theoretical preference for price controls to address the externality problem. The inclusion of on-road exposure costs reduces the magnitudes of projects required to cover implementation costs for intelligent transportation system (ITS) improvements; the net benefits of road-pricing ITS systems are increased more than the net benefits of ITS traffic flow improvements. When considering distinct vehicle classes, inclusion of on-road exposure costs greatly increases heavy-duty vehicle marginal costs because of their higher emissions rates and greater roadway capacity utilization. Lastly, there are large uncertainties associated with the parameters utilized in the estimation of health outcomes that are a function of travel pollution intensity and duration. More research is needed to develop on-road exposure modeling tools that link repeated short-duration exposure and health outcomes.     

Intelligent transportation system based dynamic vehicle routing and scheduling with variable travel times

This paper presents a dynamic vehicle routing and scheduling model that incorporates real time information using variable travel times. Dynamic traffic simulation was used to update travel times. The model was applied to a test road network. Results indicated that the total cost decreased by implementing the dynamic vehicle routing and scheduling model with the real time information based on variable travel times compared with that of the forecast model. As well, in many cases total running times of vehicles were also decreased. Therefore, the dynamic vehicle routing and scheduling model will be beneficial for both carriers in reducing total costs and society at large by alleviating traffic congestion.     

Shared autonomous electric vehicle (SAEV) operations across the Austin,Texas network with charging infrastructure decisions

Shared autonomous vehicles, or SAVs, have attracted significant public and private interest because of their opportunity to simplify vehicle access, avoid parking costs, reduce fleet size, and, ultimately, save many travelers time and money. One way to extend these benefits is through an electric vehicle (EV) fleet. EVs are especially suited for this heavy usage due to their lower energy costs and reduced maintenance needs. As the price of EV batteries continues to fall, charging facilities become more convenient, and renewable energy sources grow in market share, EVs will become more economically and environmentally competitive with conventionally fueled vehicles. EVs are limited by their distance range and charge times, so these are important factors when considering operations of a large, electric SAV (SAEV) fleet.This study simulated performance characteristics of SAEV fleets serving travelers across the Austin, Texas 6-county region. The simulation works in sync with the agent-based simulator MATSim, with SAEV modeling as a new mode. Charging stations are placed, as needed, to serve all trips requested (under 75 km or 47 miles in length) over 30 days of initial model runs. Simulation of distinctive fleet sizes requiring different charge times and exhibiting different ranges, suggests that the number of station locations depends almost wholly on vehicle range. Reducing charge times does lower fleet response times (to trip requests), but increasing fleet size improves response times the most. Increasing range above 175 km (109 miles) does not appear to improve response times for this region and trips originating in the urban core are served the quickest. Unoccupied travel accounted for 19.6% of SAEV mileage on average, with driving to charging stations accounting for 31.5% of this empty-vehicle mileage. This study found that there appears to be a limit on how much response time can be improved through decreasing charge times or increasing vehicle range.     

Solving the User Optimum Privately Owned Automated Vehicles Assignment Problem (UO-POAVAP): A model to explore the impacts of self-driving vehicles on urban mobility

Interest in vehicle automation has been growing in recent years, especially with the very visible Google car project. Although full automation is not yet a reality there has been significant research on the impacts of self-driving vehicles on traffic flows, mainly on interurban roads. However, little attention has been given to what could happen to urban mobility when all vehicles are automated. In this paper we propose a new method to study how replacing privately owned conventional vehicles with automated ones affects traffic delays and parking demand in a city. The model solves what we designate as the User Optimum Privately Owned Automated Vehicles Assignment Problem (UO-POAVAP), which dynamically assigns family trips in their automated vehicles in an urban road network from a user equilibrium perspective where, in equilibrium, households with similar trips should have similar transport costs. Automation allows a vehicle to travel without passengers to satisfy multiple household trips and, if needed, to park itself in any of the network nodes to benefit from lower parking charges. Nonetheless, the empty trips can also represent added congestion in the network. The model was applied to a case study based on the city of Delft, the Netherlands. Several experiments were done, comparing scenarios where parking policies and value of travel time (VTT) are changed. The model shows good equilibrium convergence with a small difference between the general costs of traveling for similar families. We were able to conclude that vehicle automation reduces generalized transport costs, satisfies more trips by car and is associated with increased traffic congestion because empty vehicles have to be relocated. It is possible for a city to charge for all street parking and create free central parking lots that will keep total transport costs the same, or reduce them. However, this will add to congestion as traffic competes to access those central nodes. In a scenario where a lower VTT is experienced by the travelers, because of the added comfort of vehicle automation, the car mode share increases. Nevertheless this may help to reduce traffic congestion because some vehicles will reroute to satisfy trips which previously were not cost efficient to be done by car. Placing the free parking in the outskirts is less attractive due to the extra kilometers but with a lower VTT the same private vehicle demand would be attended with the advantage of freeing space in the city center.     

The time-dependent pollution-routing problem

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.     

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.     

Shared autonomous electric vehicle service performance: Assessing the impact of charging infrastructure

Shared autonomous vehicles (SAVs) are the next major evolution in urban mobility. This technology has attracted much interest of car manufacturers aiming at playing a role as transportation network companies (TNCs) and carsharing agencies in order to gain benefits per kilometer and per ride. It is predicted that the majority of future SAVs would most probably be electric. It is therefore important to understand how limited vehicle range and the configuration of charging infrastructure will affect the performance of shared autonomous electric vehicle (SAEV) services. In this study, we aim to explore the impacts of charging station placement, charging types (including normal and rapid charging, and battery swapping), and vehicle battery capacities on service efficiency. We perform an agent-based simulation of SAEVs across the Rouen Normandie metropolitan area in France. The simulation process features impact assessment by considering dynamic demand responsive to the network and traffic.Research results suggest that the performance of SAEVs is strongly correlated with the charging infrastructure. Importantly, faster charging infrastructure and placement of charging locations according to minimized distances between demand hubs and charging stations result in a higher performance. Further analysis indicates the importance of dispersing charging stations across the service area and its impacts on service effectiveness. The results also underline that SAEV battery capacity has to be selected carefully such that to avoid the overlaps between demand and charging peak times. Finally, the simulation results show that the performance indicators of SAEV service are significantly improved by providing battery swapping infrastructure.     

Capturing value of reliability through road pricing in congested traffic under uncertainty

Empirical studies showed that travel time reliability, usually measured by travel time variance, is strongly correlated with travel time itself. Travel time is highly volatile when the demand approaches or exceeds the capacity. Travel time variability is associated with the level of congestion, and could represent additional costs for travelers who prefer punctual arrivals. Although many studies propose to use road pricing as a tool to capture the value of travel time (VOT) savings and to induce better road usage patterns, the role of the value of reliability (VOR) in designing road pricing schemes has rarely been studied. By using road pricing as a tool to spread out the peak demand, traffic management agencies could improve the utility of travelers who prefer punctual arrivals under traffic congestion and stochastic network conditions. Therefore, we could capture the value of travel time reliability using road pricing, which is rarely discussed in the literature. To quantify the value of travel time reliability (or reliability improvement), we need to integrate trip scheduling, endogenous traffic congestion, travel time uncertainty, and pricing strategies in one modeling framework. This paper developed such a model to capture the impact of pricing on various costs components that affect travel choices, and the role of travel time reliability in shaping departure patterns, queuing process, and the choice of optimal pricing. The model also shows the benefits of improving travel time reliability in various ways. Findings from this paper could help to expand the scope of road pricing, and to develop more comprehensive travel demand management schemes.     

Bayesian network-based formulation and analysis for toll road utilization supported by traffic information provision

Congestion pricing has been proposed and investigated as an effective means of optimizing traffic assignment, alleviating congestion, and enhancing traffic operation efficiencies. Meanwhile, advanced traffic information dissemination systems, such as Advanced Traveler Information System (ATIS), have been developed and deployed to provide real-time, accurate, and complete network-wide traffic information to facilitate travelers’ trip plans and routing selections. Recent advances in ATIS technologies, especially telecommunication technology, allow dynamic, personalized, and multimodal traffic information to be disseminated and impact travelers’ choices of departure times, alternative routes, and travel modes in the context of congestion pricing. However, few studies were conducted to determine the impact of traffic information dissemination on toll road utilizations. In this study, the effects of the provisions of traffic information on toll road usage are investigated and analyzed based on a stated preference survey conducted in Texas. A Bayesian Network (BN)-based approach is developed to discover travelers’ opinions and preferences for toll road utilization supported by network-wide traffic information provisions. The probabilistic interdependencies among various attributes, including routing choice, departure time, traffic information dissemination mode, content, coverage, commuter demographic information, and travel patterns, are identified and their impacts on toll road usage are quantified. The results indicate that the BN model performs reasonably well in travelers’ preference classifications for toll road utilization and knowledge extraction. The BN Most Probable Explanation (MPE) measurement, probability inference and variable influence analysis results illustrate travelers using highway advisory radio and internet as their primary mode of receiving traffic information are more likely to comply with routing recommendations and use toll roads. Traffic information regarding congested roads, road hazard warnings, and accident locations is of great interest to travelers, who tend to acquire such information and use toll roads more frequently. Travel time formation for home-based trips can considerably enhance travelers’ preferences for toll road usage. Female travelers tend to seek traffic information and utilize toll roads more frequently. As expected, the information provided at both pre-trip and en-route stages can positively influence travelers’ preferences for toll road usage. The proposed methodology and research findings advance our previous study and provide insight into travelers’ behavioral tendencies concerning toll road utilization in support of traffic information dissemination.     

Investigating empirical implications of hysteresis in day-to-day travel time variability

Day-to-day travel time variability plays a significant role in travel time reliability. Nowadays, travelers not only seek to minimize their travel time on average, but also value its variation. The variation in the mean and the variance of travel time (across days, for the same departure time) has not been thoroughly investigated. A temporary decrease in capacity (e.g. congestion caused by an active bottleneck) leads to a quite significant difference in the variance of travel time for congestion onset and offset periods. This phenomenon results in hysteresis loops where the departure time periods in congestion offset exhibit a higher travel time variance than the ones in congestion onset with the same mean travel time. The aim of this paper is to identify empirical implications that yield to the hysteresis phenomenon in day-to-day travel times. First, empirical hysteresis loop observations are provided from two different freeway sites. Second, we investigate the potential link with the hysteresis observed in traffic networks on macroscopic fundamental diagram (MFD). Third, we build a piecewise linear function that models the evolution of travel time within the day. This allows us to decompose the problem into its components, e.g. start time of congestion, peak travel time, etc. These components, along with their probability distribution functions, are employed in a Monte Carlo simulation model to investigate their partial effects on the existence of hysteresis. Correlation among critical variables is the most influential factor in this phenomenon, which should be further investigated regarding traffic flow and traffic equilibrium principles.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots

Dial-a-ride problems are concerned with the design of efficient vehicle routes for transporting individual persons from specific origin to specific destination locations. In real-life this operational planning problem is often complicated by several factors. Users may have special requirements (e.g. to be transported in a wheelchair) while service providers operate a heterogeneous fleet of vehicles from multiple depots in their service area. In this paper, a general dial-a-ride problem in which these three real-life aspects may simultaneously be taken into account is introduced: the Multi-Depot Heterogeneous Dial-A-Ride Problem (MD-H-DARP). Both a three- and two-index formulation are discussed. A branch-and-cut algorithm for the standard dial-a-ride problem is adapted to exactly solve small problem instances of the MD-H-DARP. To be able to solve larger problem instances, a new deterministic annealing meta-heuristic is proposed. Extensive numerical experiments are presented on different sets of benchmark instances for the homogeneous and the heterogeneous single depot dial-a-ride problem. Instances for the MD-H-DARP are introduced as well. The branch-and-cut algorithm provides considerably better results than an existing algorithm which uses a less compact formulation. All seven previously unsolved benchmark instances for the heterogeneous dial-a-ride problem could be solved to optimality within a matter of seconds. While computation times of the exact algorithm increase drastically with problem size, the proposed meta-heuristic algorithm provides near-optimal solutions within limited computation time for all instances. Several best known solutions for unsolved instances are improved and the algorithm clearly outperforms current state-of-the-art heuristics for the homogeneous and heterogeneous dial-a-ride problem, both in terms of solution quality and computation time.     

The impacts of connected vehicle technology on network-wide traffic operation and fuel consumption under various incident scenarios

ABSTRACT

Incidents are a major source of traffic congestion and can lead to long and unpredictable delays, deteriorating traffic operations and adverse environmental impacts. The emergence of connected vehicles and communication technologies has enabled travelers to use real-time traffic information. The ability to exchange traffic information among vehicles has tremendous potential impacts on network performance especially in the case of non-recurrent congestion. To this end, this paper utilizes a microscopic simulation model of traffic in El Paso, Texas to investigate the impacts of incidents on traffic operation and fuel consumption at different market penetration rates (MPR) of connected vehicles. Several scenarios are implemented and tested to determine the impacts of incidents on network performance in an urban area. The scenarios are defined by changing the duration of incidents and the number of lanes closed. This study also shows how communication technology affects network performance in response to congestion. The results of the study demonstrate the potential effectiveness of connected vehicle technology in improving network performance. For an incident with a duration of 900?s and MPR of 80%, total fuel consumption and total travel time decreased by approximately 20%; 26% was observed in network-wide travel time and fuel consumption at 100% MPR.     

Vehicle routing problem and driver behaviour: a review and framework for analysis

Vehicle routing problems (VRPs) whose typical objective is to minimise total travel costs over a tour have evolved over the years with objectives ranging from minimising travel times and distances to minimising pollution and fuel consumption. However, driver behaviour continues to be neglected while planning for vehicle routes. Factors such as traffic congestion levels, monotonous drives and fatigue have an impact on the behaviour of drivers, which in turn might affect their speed-choice and route-choice behaviours. The behaviour of drivers and their subsequent decision-making owing to these factors impact the revenue of transport companies and could lead to huge losses in extreme cases. There have been studies on the behaviour of drivers in isolation, without inclusion of the objectives and constraints of the traditional routing problem. This paper presents a review of existing models of VRP, planner behaviour models in the VRP context and driver behaviour models and provides a motivation to integrate these models in a stochastic traffic environment to produce practical, economic and driver-friendly logistics solutions. The paper provides valuable insights on the relevance of behavioural issues in logistics and highlights the modelling implications of incorporating planner and driver behaviour in the framework of routing problems.     

On the degradation of performance for traffic networks with oblivious users

We consider the problem of characterizing user equilibria and optimal solutions for routing in a given network. We extend the known models by considering users oblivious to congestion in the following sense: While in the typical user equilibrium setting the users follow a strategy that minimizes their individual cost by taking into account the (dynamic) congestion due to the current routing pattern, an oblivious user ignores congestion altogether; instead, he or she decides his routing on the basis of cheapest routes on a network without any flow whatsoever. These cheapest routes can be, for example, the shortest paths in the network without any flow. This model tries to capture the fact that a certain percentage of travelers base their route simply on the distances they observe on a map, without thinking (or knowing, or caring) about the delays experienced on this route due to their fellow travelers. In this work we study the effect of such users using as the measure of network performance its price of anarchy, i.e., the ratio of the total latency experienced by the users (oblivious or not) at equilibrium over the social optimum.     

An optimization method for sustainable traffic control in urban areas

The optimization of traffic signalization in urban areas is formulated as a problem of finding the cycle length, the green times and the offset of traffic signals that minimize an objective function of performance indices. Typical approaches to this optimization problem include the maximization of traffic throughput or the minimization of vehicles’ delays, number of stops, fuel consumption, etc. Dynamic Traffic Assignment (DTA) models are widely used for online and offline applications for efficient deployment of traffic control strategies and the evaluation of traffic management schemes and policies. We propose an optimization method for combining dynamic traffic assignment and network control by minimizing the risk of potential loss induced to travelers by exceeding their budgeted travel time as a result of deployed traffic signal settings, using the Conditional Value-at-Risk model. The proposed methodology can be easily implemented by researchers or practitioners to evaluate their alternative strategies and aid them to choose the alternative with less potential risk. The traffic signal optimization procedure is implemented in TRANSYT-7F and the dynamic propagation and route choice of vehicles is simulated with a mesoscopic dynamic traffic assignment tool (DTALite) with fixed temporal demand and network characteristics. The proposed approach is applied to a reference test network used by many researchers for verification purposes. Numerical experiments provide evidence of the advantages of this optimization method with respect to conventional optimization techniques. The overall benefit to the performance of the network is evaluated with a Conditional Value-at-Risk Analysis where the optimal solution is the one presenting the least risk for ‘guaranteed’ total travel times.     

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.