Equilibrium models in multimodal container transport systems

Optimizing the performance of multimodal freight transport networks involves adequately balancing the interplay between costs, volumes, times of departure and arrival, and times of travel. In order to study this interplay, we propose an assignment model that is able to efficiently determine flows and costs in a multimodal network. The model is based on a so-called user equilibrium principle, which is at the basis of Dynamic Traffic Assignment problems. This principle takes into account transport demands to be shipped using vehicles that transport single freight units (such as trucks) or multiple freight units (such as trains and barges, where demand should be bundled to reach efficient operations). Given a particular demand, the proposed model provides an assignment of the demand over the available modes of transport. The outcome of the model, i.e., the equilibrium point, minimizes users’ generalized costs, expressed as a function of mode, travel time and related congestion, and waiting time for bundling sufficient demand in order to fill a vehicle. The model deals with these issues across a doubly-dynamic time scale and in an integrated manner. One dynamic involves a learning dynamic converging towards an equilibrium (day-to-day) situation, reflecting the reaction of the players towards the action of the others. Another dynamic considers the possible departure time that results in minimum expected costs, also due to the fact that players mutually influence each other on the choice of departure times, due to congestion effects and costs for early/late arrival of freight units. This is a choice within a given time horizon such as a day or a week. We present a study on the influence and sensitivity of different model parameters, in order to analyse the implications on strategic decisions, fostering a target modal share for freight transportation. We also study under which conditions the different modes can be substitutes for each other.     

Environmental Assessment of Freight Transportation in the U.S. (11 pp)

Goal, Scope and Background This study provides a life cycle inventory of air emissions (CO2, NOx, PM10, and CO) associated with the transportation of goods by road, rail, and air in the U.S. It includes the manufacturing, use, maintenance, and end-of-life of vehicles, the construction, operation, maintenance, and end-of-life of transportation infrastructure, as well as oil exploration, fuel refining, and fuel distribution. Methods The comparison is performed using hybrid life cycle assessment (LCA), a combination of process-based LCA and economic input-output analysis-based LCA (EIO-LCA). All these components are added by means of a common functional unit of grams of air pollutant per ton-mile of freight activity. Results and Discussion Results show that the vehicle use phase is responsible for approximately 70% of total emissions of CO2 for all three modes. This confirms that tailpipe emissions underestimate total emissions of freight transportation as infrastructure, pre-combustion, as well as vehicle manufacturing and end-of-life account for a sizeable share of total emissions. Differences between tailpipe emissions and total system wide emissions can range from only 4% for road transportation's CO emissions to an almost ten-fold difference for air transportation's PM10 emissions. Conclusion Rail freight has the lowest associated air emissions, followed by road and air transportation. Depending on the pollutant, rail is 50-94% less polluting than road. Air transportation is rated the least efficient in terms of air emissions, partly due to the fact that it carries low weight cargo. It emits 35 times more CO2 than rail and 18 times more than road transportation on a ton-mile basis. It is important to consider infrastructure, vehicle manufacturing, and pre-combustion processes, whose life-cycle share is likely to increase as new tailpipe emission standards are enforced. Recommendation and Outlook Emission factors, fuel efficiency, and equipment utilization contribute the most to uncertainty in the results. Further studies are necessary to address all variables that influence these parameters, such as road grade, vehicle speed, and vehicle weight. A focus on regional variation, end-of-life processes, fuel refining processes, terminals, as well as more accurate infrastructure allocation between freight and passenger transportation would strengthen the model.     

Estimating the Material Stock of Roads: The Vietnamese Case Study

This study is a pioneering effort to quantify the materials stocked in the road network of a developing country, Vietnam, and analyze its relationships to the country's recent economic development. National road networks function as capital and infrastructure investments that are necessary catalysts for countries’ development, while requiring the extraction of vast amounts of construction materials for expansion and maintenance causing environmental impacts. However, there has so far been little research on the subject, especially in developing countries. We compile material stock and flow accounts for Vietnam's roads from 2003 to 2013 on the national and provincial levels, finding that approximately 40% of the domestic consumption of construction materials is for expanding and maintaining the road network, and the materials stocked in the road network doubled from 1,321 million metric tons in 2003 to 2,660 million metric tons in 2012. Material stock growth rates closely resembled those of gross domestic product (GDP) in this period, suggesting a codependency of physical infrastructure development and economic development. On the provincial level, our results show local disparities in the stock and its capacity to support the transportation of passengers and freight, especially considering the surging growth of vehicles in urban centers. By showcasing the challenges of conducting a material flow and stock analysis in a developing country, this study not only sheds light on Vietnam's transportation material stock and its policy implications, but also serves as a case study for further work in similar countries.     

Ecology profile of the german high-speed rail passenger transport system,ICE

Intention, Goal, Scope, Background, Objectives  Environmental effects caused by the railway transport services have rarely been investigated in depth from a systemic point of view. A screening LCA, called ecology profile, of the German high-speed passenger train system, the ICE, is presented here, based on a study conducted by the University of Halle and the Deutsche Bahn AG, the major German rail operator. In this study, the resource consumption caused by traction, manufacturing and maintenance of ICE trains, as well as construction and operation of the supporting rail infrastructure and buildings, have been evaluated using cumulative energy demand (CED), cumulative material input per service unit (MIPS) and CO₂ emissions as indicators. Methods  Approximately 200 items of inventory data were collected from DB AG experts, manufacturers, site balances and the associated literature. They were allocated in order to derive 100-person-kilometre-related mass and energy consumption figures. The appropriate CED, MIPS and CO₂ factors were applied in order to quantify the indirect efforts associated with the inventory data. Conclusions  For the reference high-speed route investigated, Hanover-Wuerzburg, the railroad infrastructure does not contribute the high share of resource consumption to the life cycle of the transport service which was expected from other studies. For the reference route, the CED of the infrastructure contributes 13% to the total CED per 100 person kilometres, whilst the energy demand of the traction process dominates the life cycle. Within the railway infrastructure, the construction of tunnels and the heating of rail points during winter time are significant primary-energy active components, whereas the energy requirement for maintaining the railway stations is a minor factor in comparison. The environmental impact of new technologies for designing rail tracks have also been analysed. The new ballastless slab track technology investigated needs higher absolute resource inputs in the construction phase compared with the traditional gravel bed, but due to higher life expectancy, it competes favourably at the 100-person-kilometre level, at least in terms of material requirements. Efforts to reduce the traction energy consumption of the ICE train will have the greatest impact on the CED of the transport system. In summary, a total of 48 kg of solid primary resources are needed for a passenger to travel 100 km by ICE. Recommendations/Outlook  The results presented can be used for modelling other high-speed railway transport systems. A comparison of the ecology profiles of the German, French and Japanese high-speed train systems would be of interest in order to identify potential areas for improvement. Additional studies are needed to evaluate the short-hop, commuter train service. Further efforts should be directed to comparing the infrastructure of the high speed train and that of highway road traffic.     

On the Influence of Freight Trains on Humans: A Laboratory Investigation of the Impact of Nocturnal Low Frequency Vibration and Noise on Sleep and Heart Rate

Background

A substantial increase in transportation of goods on railway may be hindered by public fear of increased vibration and noise leading to annoyance and sleep disturbance. As the majority of freight trains run during night time, the impact upon sleep is expected to be the most serious adverse effect. The impact of nocturnal vibration on sleep is an area currently lacking in knowledge. We experimentally investigated sleep disturbance with the aim to ascertain the impact of increasing vibration amplitude.

Methodology/Principal Findings

The impacts of various amplitudes of horizontal vibrations on sleep disturbance and heart rate were investigated in a laboratory study. Cardiac accelerations were assessed using a combination of polysomnography and ECG recordings. Sleep was assessed subjectively using questionnaires. Twelve young, healthy subjects slept for six nights in the sleep laboratory, with one habituation night, one control night and four nights with a variation of vibration exposures whilst maintaining the same noise exposure. With increasing vibration amplitude, we found a decrease in latency and increase in amplitude of heart rate as well as a reduction in sleep quality and increase in sleep disturbance.

Conclusions/Significance

We concluded that nocturnal vibration has a negative impact on sleep and that the impact increases with greater vibration amplitude. Sleep disturbance has short- and long-term health consequences. Therefore, it is necessary to define levels that protect residents against sleep disruptive vibrations that may arise from night time railway freight traffic.     

Modeling copper demand in China up to 2050: A business‐as‐usual scenario based on dynamic stock and flow analysis

In this paper, we develop a dynamic stock model and scenario analysis involving a bottom‐up approach to analyze copper demand in China from 2005 to 2050 based on government and related sectoral policies. The results show that in the short‐term, China's copper industry cannot achieve a completely circular economy without additional measures. Aggregate and per capita copper demand are both set to increase substantially, especially in infrastructure, transportation, and buildings. Between 2016 and 2050, total copper demand will increase almost threefold. Copper use in buildings will stabilize before 2050, but the copper stock in infrastructure and transportation will not yet have reached saturation in 2050. The continuous growth of copper stock implies that secondary copper will be able to cover just over 50% of demand in 2050, at best, even with an assumed recycling rate of 90%. Finally, future copper demand depends largely on the lifetime of applications. There is therefore an urgent need to prolong the service life of end‐use products to reduce the amount of materials used, especially in large‐scale applications in buildings and infrastructure.     

Operative transportation planning in consumer goods supply chains

Transportation management in today’s consumer goods industry can be characterized by a high proportion of outsourced transportation services. Due to rising freight costs consumer goods manufacturers are looking for opportunities to increase the efficiency of their transportation network. This study presents an operational transportation planning problem typical of the consumer goods industry focusing on a network of suppliers, production facilities and warehousing locations. It comprises an analysis of freight costs in a consumer goods transportation network based on the freight rate structures. In this analysis a number of opportunities for efficiency gains are identified and consolidated in an operative transportation planning problem which is then numerically investigated. Furthermore, an overview of processes and organizational structures in transportation management is given with special focus on the integration of existing commercial Transportation Management Systems (TMS).     

Combining a Spatial Model and Demand Forecasts to Map Future Surface Coal Mining in Appalachia

Predicting the locations of future surface coal mining in Appalachia is challenging for a number of reasons. Economic and regulatory factors impact the coal mining industry and forecasts of future coal production do not specifically predict changes in location of future coal production. With the potential environmental impacts from surface coal mining, prediction of the location of future activity would be valuable to decision makers. The goal of this study was to provide a method for predicting future surface coal mining extents under changing economic and regulatory forecasts through the year 2035. This was accomplished by integrating a spatial model with production demand forecasts to predict (1 km²) gridded cell size land cover change. Combining these two inputs was possible with a ratio which linked coal extraction quantities to a unit area extent. The result was a spatial distribution of probabilities allocated over forecasted demand for the Appalachian region including northern, central, southern, and eastern Illinois coal regions. The results can be used to better plan for land use alterations and potential cumulative impacts.     

Life Cycle Inventories of Transport Services: Background Data for Freight Transport (10 pp)

Background, Goal and Scope The ecoinvent database is a reference work for life cycle inventory data covering the areas of energy, building materials, metals, chemicals, paper and cardboard, forestry, agriculture, detergents, transport services and waste treatment. Generic inventories are available for freight and passenger transport including air, rail, road, and water transport. The goal of freight transport modelling is to provide background data for transport services, which occur between nearly any two process steps of a product system. This paper presents and discusses the model structure, basic assumptions and results for selected freight transport services.Main Features Transport services are divided into several datasets referred to as transport components. In addition to vehicle operation (comprising vehicle travel and pre-combustion), infrastructure processes such as vehicle maintenance, manufacturing and disposal, as well as transport infrastructure construction, operation and disposal, are also modelled. In order to link the various transport components to the functional unit of one tonne kilometre (tkm), so-called demand factors are determined. In the case of transport infrastructure that is not exclusively used by freight transport, allocation is essential. The respective allocation parameters employed for line infrastructure construction/disposal and operation datasets (including land use) are yearly Gross-tonne kilometre performance (Gtkm) and kilometric vehicle/train performance. Results are presented for selected environmental exchanges related to gaseous emissions (climate change gases, nitrogen oxides, and hydrocarbons), heavy metal (zinc and cadmium) emissions to soil and air, as well as BOD (Biological Oxygen Demand), and land use. Particle emissions are further distinguished into fine (PM2.5) and coarse (diameter between 2.5 and 10 µm) particles. The results presented comprise both an intra- and inter-modal comparison.Results and Discussions A comparison of Swiss and European rail transport reveals considerably lower emissions from Swiss rail transport due to the almost exclusive use of hydropower as traction energy. For gaseous emissions, freight transport by water or rail exhibits considerably better performance than road transport (65-92% less gaseous emissions). As far as zinc and cadmium emissions to soil are concerned, water and rail transport produce less than 1% of the emissions resulting from road transport for either pollutant. For zinc and cadmium emissions to air, road transport has the highest emissions; however, the emissions due to water and rail transport range from 2 to 18% of the emission levels arising from road transport. Particle emissions show a more diverse pattern. Whilst fine particle emissions due to water and rail transport are considerably lower than road transport, rail transport with respect to coarse particles performs worse than road transport. Dominance analysis reveals the importance of infrastructure processes. For instance, the NMHC-emissions of infrastructure processes account for 40%, 30% and 50% of emissions for road, rail and barge transport, respectively. For the demand factor of infrastructure operation, a sensitivity analysis of the employed allocation factor was performed, revealing no sensitivity for gaseous emissions and particles. On the other hand, considerable changes in both emission levels and in the ranking of transport modes is observed for land occupation. Finally, we varied selected operation parameters for road transport, resulting in considerable reductions of CO2 and NOX emissions of up to 60%. In one extreme case (load factor: 100%), NOx emissions for vehicle operation of a lorry are lower than for inland water transport. Only as a result of the considerably higher NOx emissions occurring in infrastructure processes does road transport score worse than water transport, with the ranking remaining the same as for the generic data presented in ecoinvent 2000.Conclusions and Perspectives The provided datasets allow for a preliminary screening of the importance of transport processes within a product life cycle. In the cases for which transport processes are identified as sensitive for the overall outcome of certain product life cycle or for transport specific comparisons, the modular structure and transparent documentation of demand factors allows for an easy and transparent integration of more case-specific data for selected transport components.     

Technoecological analysis of energy carriers for long‐haul transportation

Long‐haul transportation demand is predicted to increase in the future, resulting in higher carbon dioxide emissions. Different drivetrain technologies, such as hybrid or battery electric vehicles, electrified roads, liquefied natural gas and hydrogen, might offer solutions to this problem. To assess their ecological and economic impact, these concepts were simulated including a weight and cost model to estimate the total cost of ownership. An evolutionary algorithm optimizes each vehicle to find a concept specific optimal solution. A model calculates the minimum investment in infrastructure required to meet the energy demand for each concept. A well‐to‐wheel analysis takes into account upstream and on‐road carbon dioxide emissions, to compare fully electric vehicles with conventional combustion engines. Investment in new infrastructure is the biggest drawback of electrified road concepts, although they offer low CO₂ emissions. The diesel hybrid is the best compromise between carbon reduction and costs.     

Eyjafjallaj?kull and 9/11: The Impact of Large-Scale Disasters on Worldwide Mobility

Large-scale disasters that interfere with globalized socio-technical infrastructure, such as mobility and transportation networks, trigger high socio-economic costs. Although the origin of such events is often geographically confined, their impact reverberates through entire networks in ways that are poorly understood, difficult to assess, and even more difficult to predict. We investigate how the eruption of volcano Eyjafjallajökull, the September 11th terrorist attacks, and geographical disruptions in general interfere with worldwide mobility. To do this we track changes in effective distance in the worldwide air transportation network from the perspective of individual airports. We find that universal features exist across these events: airport susceptibilities to regional disruptions follow similar, strongly heterogeneous distributions that lack a scale. On the other hand, airports are more uniformly susceptible to attacks that target the most important hubs in the network, exhibiting a well-defined scale. The statistical behavior of susceptibility can be characterized by a single scaling exponent. Using scaling arguments that capture the interplay between individual airport characteristics and the structural properties of routes we can recover the exponent for all types of disruption. We find that the same mechanisms responsible for efficient passenger flow may also keep the system in a vulnerable state. Our approach can be applied to understand the impact of large, correlated disruptions in financial systems, ecosystems and other systems with a complex interaction structure between heterogeneous components.     

交通网络空间互动视角下生态足迹驱动机制

长江中游城市群是中部崛起战略的重要区域,同时依托长江黄金水道面临发展和保护的困境。交通网络空间互动视角下的生态足迹驱动机制研究对统筹长江中游城市群经济社会高质量发展和生态文明高水平建设以实现可持续发展具有重要意义。基于生态足迹模型测度了长江中游城市群县域尺度的可持续发展状况,并在STIRPAT模型框架下基于交通网络空间互动关系挖掘生态足迹的驱动机制和空间效应,为交通网络扩张背景下的跨区域生态治理与可持续发展提供参考。研究结果显示：(1)2010—2017年,长江中游城市群县域生态足迹均值有所下降;(2)道路交通网络和铁路交通网络规模均有所扩大,但连通性略有下降;(3)在基于交通网络构建的空间互动媒介下,城镇化率和人均GDP对生态足迹具有显著的促进作用,而第三产业增加值占比对生态足迹产生抑制影响,且生态足迹表现出积极的空间外溢效应。基于以上研究结果,建议在基于交通网络加强区域生态协同发展的同时,建设产业互促、资源互通、技术互享的区域联动可持续发展新格局。     

Pollution and Cost in the Coke-Making Supply Chain in Shanxi Province, China

An integrated system trade-off model has been developed to assess costs and pollution associated with transportation in the coke-making supply chain in Shanxi Province, China. A transportation-flow, cost-minimization solver is combined with models for calculating coke-making plant costs, estimating transportation costs from a geographic information system road and rail database, and aggregating coke-making capacity among plants. Model outputs of economic cost, nitrogen oxides (NO_x) emissions, and transport distributions are visualized using an Internet-based graphic user interface. Data for the model were collected on survey trips to Shanxi Province as well as from secondary references and proxies. The modularity and extensibility of the system trade-off model facilitate introduction of new data sets in order to examine various planning scenarios.
Scenarios of coke-making plant aggregation, rail infrastructure improvement, and technology transfer were evaluated using the model. Costs and pollution emissions can be reduced by enlarging coke-making plants near the rail stations and closing down other plants. Preferential minimization of transportation costs gives a lower total cost than simply minimizing plant costs. Therefore, policy makers should consider transportation costs when planning the reallocation of coke-making capacity in Shanxi Province. Increasing rail-transport capacity is less effective than aggregating plant capacity. On the other hand, transfer of low-pollution truck technology results in a large emission reduction, however, reflecting the importance of truck transportation in the Shanxi Province coke-making industry.     

The impact of epizootics on livelihoods

Epizootics (nonhuman animal disease epidemics) can have detrimental impacts on livelihoods through a complex interaction of demographic trends, food production, and animal disease. Differences in the rate of demographic shifts, including rates of population growth, economic growth, urbanization, environmental sustainability, and role of women in society, are strong driving forces that will determine to what extent food demand will be matched by food production capacity. Epizootics can negatively affect commerce and trade in all countries, and in low-income countries limited infrastructure and resources as well as competing priorities provide additional disincentive to controlling or eradicating animal diseases. Economic growth is critical to overcoming disparities among countries and is best supported by integrated animal health, public health, labor, and foreign policies. The adverse impacts of epizootics can be largely overcome through programs that support job growth along the value-added chain of food production and will require significant investments in science- (risk-) based education.     

Climatic similarity and biological exchange in the worldwide airline transportation network

Recent increases in the rates of biological invasion and spread of infectious diseases have been linked to the continued expansion of the worldwide airline transportation network (WAN). Here, the global structure of the WAN is analysed in terms of climatic similarity to illuminate the risk of deliberate or accidental movements of climatically sensitive organisms around the world. From over 44,000 flight routes, we show, for each month of an average year, (i) those scheduled routes that link the most spatially distant but climatically similar airports, (ii) the climatically best-connected airports, and (iii) clusters of airports with similar climatic features. The way in which traffic volumes alter these findings is also examined. Climatic similarity across the WAN is skewed (most geographically close airports are climatically similar) but heavy-tailed (there are considerable numbers of geographically distant but climatically similar airports), with climate similarity highest in the June-August period, matching the annual peak in air traffic. Climatically matched, geographically distant airports form subnetworks within the WAN that change throughout the year. Further, the incorporation of passenger and freight traffic data highlight at greater risk of invasion those airports that are climatically well connected by numerous high capacity routes.     

绿色基础设施的洪水调节服务供需测度研究进展

绿色基础设施(green infrastructure, GI)可提供高效且可获取的洪水调节服务,其供需测度是提升服务水平的基础与前提,可为城市土地利用与绿色基础设施规划提供决策依据。以GI洪水调节服务供需为研究对象,梳理GI洪水调节服务供需的概念内涵、主体构成和尺度关系。回顾了GI洪水调节服务供需测度方法,包括土地利用测度法、生态系统测度法和洪水调蓄模型法等供应水平测度方法,以及风险评估法、洪水淹没模型法和经济损失法等需求水平测度方法。基于生态系统服务的供需关系,构建了GI洪水调节服务供需分析框架,通过供需数量均衡和空间匹配将供需关系分为四种情景,对应服务动态平衡、调整服务供需水平和服务流动机制3种调控手段。从服务测度重点、动态变化分析、供需阈值效能、服务流动机制等四个方面提出了未来研究方向,以期对绿色基础设施规划研究和生态系统服务管理与决策研究有所启示。     

Multi-hop driver-parcel matching problem with time windows

Crowdsourced shipping can result in significant economic and social benefits. For a shipping company, it has a potential cost advantage and creates opportunities for faster deliveries. For the society, it can provide desirable results by reducing congestion and air pollution. Despite the great potential, crowdsourced shipping is not well studied. With the aim of using the spare capacities along the existing transportation flows of the crowd to deliver small-to-medium freight volumes, this paper defines the multi-driver multi-parcel matching problem and proposes a general ILP formulation, which incorporates drivers’ maximum detour, capacity limits, and the option of transferring parcels between drivers. Due to the high computational complexity, we develop two heuristics to solve the problem. The numerical study shows that crowdsourced shipping can be an economic viable and sustainable option, depending on the spatial characteristics of the network and drivers’ schedules. Furthermore, the added benefits increase with an increasing number of participating drivers and parcels.     

Bi-level optimization programming for the shipper-carrier network problem

The paper presents a bi-level modeling approach that captures hierarchical relationships between shippers and carriers in maritime freight transportation networks. Ocean carriers, land carriers and port terminal operators provide transportation services at different parts of the multimodal network. Port terminal operators are regarded as a special type of carrier due to their behavior. The carriers determine service charges and delivery routes (port services) through competition and interactions among themselves. Shippers are users of the transportation services. Shippers choose a sequence of carriers, based on the carriers’ pricing and routing decisions. These relationships are captured in a bi-level model where carriers are the leaders and shippers are the followers. The paper focuses on the behavior of shippers having the transportation service information with spatial price equilibrium. A numerical example is used to demonstrate the validity of the developed model.     

Mass vaccination for the 2009 H1N1 pandemic: approaches, challenges, and recommendations

The 2009 H1N1 pandemic stimulated a nationwide response that included a mass vaccination effort coordinated at the federal, state, and local levels. This article examines a sampling of state and local efforts during the pandemic in order to better prepare for future public health emergencies involving mass distribution, dispensing, and administration of medical countermeasures. In this analysis, the authors interviewed national, state, and local leaders to gain a better understanding of the accomplishments and challenges of H1N1 vaccination programs during the 2009-10 influenza season. State and local health departments distributed and administered H1N1 vaccine using a combination of public and private efforts. Challenges encountered during the vaccination campaign included the supply of and demand for vaccine, prioritization strategies, and local logistics. To improve the response capabilities to deal with infectious disease emergencies, the authors recommend investing in technologies that will assure a more timely availability of the needed quantities of vaccine, developing local public health capacity and relationships with healthcare providers, and enhancing federal support of state and local activities. The authors support in principle the CDC recommendation to vaccinate annually all Americans over 6 months of age against seasonal influenza to establish a standard of practice on which to expand the ability to vaccinate during a pandemic. However, expanding seasonal influenza vaccination efforts will be an expensive and long-term investment that will need to be weighed against anticipated benefits and other public health needs. Such investments in public health infrastructure could be important for building capacity and practice for distributing, dispensing, and administering countermeasures in response to a future pandemic or biological weapons attack.     

Efficient scheduling of team truck drivers in the European Union

This paper studies the problem of scheduling working hours of team drivers in European road freight transport where a sequence of ?? locations must be visited within given time windows. Since April 2007 working hours of truck drivers in the European Union must comply with regulation (EC) No 561/2006. These regulations impose standard limits on the daily driving times of truck drivers and extended daily limits that may only be used twice a week for each driver. We present a depth-first-breadth-second search method which can find a feasible schedule complying with standard daily driving time limits in O(??²) time, if such a schedule exists. Furthermore, we show that this method can also be used to find schedules complying with regulation (EC) No 561/2006 if daily driving times may exceed the standard limit.