Fuel Distribution Networks

Table of Contents

List of Figures

List of Tables

List of Abbreviations

1 Introduction

2 Technical Background
2.1 Alternative Fuels
2.2 Characteristics of the Fuels Focused on
2.2.1 LNG
2.2.2 CNG
2.2.3 LPG
2.2.4 DME
2.2.5 Hydrogen
2.3 Driving Ranges of Vehicles Powered with Alternative Fuels.

3 Methodological Background
3.1 Infrastructure Buildup Approaches of Fuel and Haulage Companies
3.2 Theoretical Approach of Mathematical Optimization
3.2.1 Location-Allocation Models for Infrastructure Networks
3.2.2 The Set Covering Fuel Station Location Model (SCFLM)

4 Estimating the Optimum Distribution Network with the SCFLM
4.1 Defining and Modelling the Sample Network
4.2 Implementing the SCFLM
4.3 Applying the SCFLM to Various Transportation Networks
4.4 Validity of Results

5 Implications for Alternative Fuel Introduction
5.1 Fuel Suitability for Long Haul Applications
5.2 Possible First Expansion along Transportation Routes
5.3 Possible First Expansion along Logistic Centres
5.4 Outlook on Transition towards a Public Fuel Distribution

6 Conclusions

References

Appendix

List of Figures

Figure 1: Schematic Work Structure.

Figure 2: LNG Fueling Station.

Figure 3: CNG high-Pressure Refueling System.

Figure 4: LPG Fueling System.

Figure 5: DME and Propane Fueling System

Figure 6: Hydrogen Fuel Station.

Figure 7: Example of a Round-Trip between Two Nodes.

Figure 8: Optimum Number of Fuel Stations Estimation Process.

Figure 9: Sample Transportation Network of Eurotank.

Figure 10: Defining Nodes of the Transportation Network.

Figure 11: Defining Paths of the Transportation Network.

Figure 12: Feasibility Results of the Sub model for Eurotank.

Figure 13: Screenshot of the LINGO Model for Eurotank.

Figure 14: LINGO Solution Report for Eurotank in the Case of Using LNG.

Figure 15: Transportation Network of Eurotank with Additional Location Possibilities.

Figure 16: Main European Transportation Routes

Figure 17:European Logistic Centers.

Figure 18: Empirically Deduced Alternative Fuel Adoption Process.

Figure 19: Adoption of Alternative Fuel and Fleet.

List of Tables

Table 1: Comparison of Several Alternative Fuels´ Properties.

Table 2: Vehicle Ranges for Different Alternative Fuels

Table 3: Stakeholders of Fuel Station Buildup and their Approaches.

Table 4: Possible Fuel Distribution Infrastructure for Eurotank.

Table 5: Possible Fuel Distribution Structure for Eurotank with Additional Locations.

Table 6: Minimum Number of Fuel Stations for the Basic Networks of Several Companies.

Table 7: Minimum Number of Fuel Stations for Extended Networks of Several Companies.

Table 8: Biggest European Logistic Firms by Revenue.

List of Abbreviations

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1 Introduction

Transport is a key factor in modern economies. There are an estimated 31.5 million road goods vehicles running on Europe’s motorways each year, which are coping with a steadily increasing amount of goods transported [European Communities 2007: p. 45]. Although these vehicles are crucial to guarantee the ubiquitous goods availability we are used to, and to assure the flexibility of European industry, they are also part of mankind’s most pressing current problems.

For instance, the emission of greenhouse gases, i.e. carbon dioxide (CO2), methane (CH4), nitrous oxide (NO2), hydrofluorocarbons (HFC), perfluorocarbons (PFC) and sulphur hexafluoride (SF6), due to fuel combustion in goods transport constitutes about 20 per cent of overall greenhouse gas emission and is only outnumbered by emissions of the energy industry [European Communities 2005: p. 140]. Overall decrease of these contaminants shall be, of course, one of the main objectives in the long-term, but in particular within urban agglomerations it is also of great interest to decrease local emission levels as a first sep. Changing over to less carbon-intensive fuels can reduce local carbon dioxide and other emissions, even if the well-to-wheel emission level does not improve notably.

Apart from the emission problem, nearly 99% of the overall fuel consumption in transport is provided by fossil fuels [Gilbert/Perl 2008: p. 120; Eurostat 2008] and therefore competing for the finite crude oil resources with other industries, in particular the energy industry. There are many different forecasts of how long world’s oil reserves will last [Deffeyes 2006: p. 48; CERA 2006], but independently of these estimations it is undeniable that they will end sometime. Hence, it is the second vital transport-related challenge to make it independent from fossil energy resources by developing and introducing renewable fuels, complying technologies to run them and a reliable infrastructure to distribute them. Although there are still many problems to solve regarding technical issues, many viable solutions for running vehicles by other means than diesel and gasoline are already available. However, the biggest problem seems to be the distribution [Farrell et al. 2003: p. 148; Zhao/Melaina 2006: p. 1302-1303]. Since vehicles and fueling infrastructure are complementarities, most customers do not use these vehicles because they can not refill them properly, and fuel companies do not introduce new fuel stations due to a lack of customers, that would use them. Consequently the main challenge currently is to break through this „chicken-egg“ problem and build up a fuel distribution network, which allows the use of alternative fuels-driven vehicles in the same safe, cheap and convenient way it works with fossil fuels. Pursuing this idea the focus of this paper will lie on long distance transportation, although many of the findings can be transferred both, to other road transport sectors as well as to passenger traffic.

There are basically two different possibilities to approach the “chicken-egg” problem, mentioned above. One of them considers a comprehensive public refueling network. The first step of this approach is to establish a fairly big initial number of fuel stations, ideally in order to maximize the number of clients, which can be served [Kuby/Lim 2005; Lin et al. 2005]. Next this small network is being expanded stepwise according to the evolutionary dynamics discovered by research on the dynamic characteristics of the vehicle-infrastructure system [Struben 2006a; Janssen et al. 2006]. The main problem of this approach is that private clients are not willing to plan their trips to depend upon the fuel station network, so that a quite big number of fuel stations is required both at the beginning and during the later development [Struben 2006a; Yeh 2007].

The other approach is to introduce alternative fuels for limited transport applications first and then develop this first set of facilities towards a broad public infrastructure with respect to the same system’s dynamic characteristics. Those applications can be city buses, single interurban bus fleets, taxi fleets, single truck fleets or other. The infrastructure should then aim to cover 100% of the fuel demand, however, it could incorporate the behavior of rational drivers, so that fewer fuel stations are needed. It will be shown that the latter approach is more likely to be successful and can lead the way for the setup of a comprehensive fueling station network, wherefore it will be explored in this work.

Following this idea the present work aims to answer three questions. First, it shall be shown for different types of alternative fuels, what their distribution infrastructure within representative long haul transportation networks should look like, i.e. how many refilling facilities are needed and where they should be located, in order to provide competitive coverage of a certain area for minimal costs. Second, these results will be interpreted together with the fuels’ specific characteristics, resulting in an assessment of the suitability of the fuels for long haul applications. Third, an outlook will be given on fundamental coherences of the long-term development of a sustainable introduction of an alternative fuel.

In a first step technical and methodological background for the work will be given. Characteristics of the several fuels considered and their implications for handling the fuels will be discussed. Then, with the intention to consider industrial experience, it will be shown, what different kinds of industrial approaches for fuel station buildup respectively new fuel introduction exist and it will be discussed why first fuel introduction in limited applications is both the most promising alternative and the one allowing to point out the fuels’ infrastructure relevant differences in the best way. It will be shown that concentrating on this demand focused approach mentioned above the problem’s complexity can be reduced to such an extent that adequate research means in terms of mathematical optimization models can be applied, what leads to optimum solutions and therefore outperforms intuitive or simulation-based foundings of decision making. Therefore the vital backdrop section will be finally completed with the presentation of an adequate mathematical optimization model to support this approach with a profound methodology.

In the next step, the implementation and functionality of the optimization model will be discussed on the basis of a sample transportation network. Following, the optimum solution for locating fuel stations subject to minimize their total number as well as the result’s validity will be discussed for a representative set of haulage companies, leading to the answer of the first question. Combining these results with other qualitative characteristics of the fuels considered their overall suitability for long-haul applications will be discussed.

Finally an outlook will be given on the further development of the ideal distribution network for the most suitable alternative fuel. Thereby primarily possible first expansion steps will be discussed, before findings of both empirical research and research on infrastructure-vehicle adoption system’s dynamics with respect to a sustainable long-term development of the alternative fuel’s introduction will be examined. Figure 1 summarizes this work’s main steps, the background information used and the main findings.

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Figure 1: Schematic Work Structure.

2 Technical Background

In this section the variety of alternative fuels as well as their general characteristics will be discussed. Then, the work will focus on those fuels which can not be dispensed by the same means that are used for distributing petrol but require dedicated fueling facilities or at least remarkable changes in the dispensing system. These fuels will be examined subsequently in more detail with respect to their general characteristics, and finally driving ranges of vehicles using each of these fuels will be derived, as one of the central constraints for fuel station allocation.

2.1 Alternative Fuels

The term alternative fuels has a very general character and covers all types of fuels that are neither gasoline nor petroleum diesel, not necessarily implying a production from renewable sources. One of the most popular alternative fuels in Central Europe, in particular in Germany, where it exceeds 40% of worldwide production, is biodiesel [Worldwatch Institute 2007]. It is commonly produced by the etherification of vegetable oils, but the hydrogenation of these oils is also being considered. Rapeseed oil and sunflower oil are the most widespread feedstocks in Europe. In spite of the great advantage of being renewable resources, biodiesel has a set of considerable shortcomings, including very low land use efficiency, a higher emission of nitrogen oxide, relative high production costs and a controversial well-to-wheel environment impact [Volvo 2007, UNEP 2007]. An alternative which is considered to have slightly better overall characteristics is synthetic diesel. It is produced by gasification of biomass and tends to be more favorable, especially regarding land use efficiency, and therefore also regarding well-to-wheel CO2 emissions.

Another two similarly popular and disputed fuels are methanol and ethanol. These alcoholic fuels, in particular methanol, outcompete diesel fuels in terms of energy efficiency and land use efficiency, however, require more adaptations at the vehicle, and have also to face the competitive situation of food and fuel production concerning cultivation areas [Worldwatch Institute 2007: pp. 161, 224].

Liquefied petroleum gas (LPG) is a mixture of mainly propane and butane. It is manufactured during the refining of crude oil, or extracted from oil or gas streams as they emerge from the ground. LPG offers some distinct advantages over gasoline and diesel, including being non-toxic, emitting very few particulate matter and greatly reducing hydrocarbons and carbon monoxide emissions. Since it is gaseous, LPG mixes well with air before entering the engine, resulting in low carbon monoxide emissions. Due to its lower energy density and inferior lubricity characteristics as well as some other shortcomings, mentioned later in the text, the availability of heavy-duty engines is currently limited [Elvers 2008: pp. 140 – 152].

Dimethylether (DME) is a gas handled in liquid form, which is produced by gasification of biomass and has attractive properties as a fuel, like a high cetane number, its relative good well-to-wheel energy efficiency or the reduction of engine noise levels and, most important, considerably low emissions of all greenhouse gases as well as particulate matter. Despite this set of advantages it has the unfavorable ability to dissolve most sealing materials used in automotive applications and therefore requires dedicated sealings [Volvo 2007, Hansen/Mikkelsen 2001, Refuel 2008].

Other promising alternatives to gasoline and petroleum diesel are compressed natural gas (CNG) and liquefied natural gas (LNG), which both mainly consist of methane. Both are favorable in terms of overall energy efficiency and overall emission level. Although currently both of them are produced by processing natural gas, a resemblant fuel, the so called biogas, which also consists primarily of methane, and therefore has a very similar behavior after being processed properly, can be extracted from renewable resources by biomass gasification. Albeit natural gas has the advantage of noticeably lower emissions of air toxins and carbon dioxide it has a lower efficiency and therefore higher fuel consumption compared to diesel [Worldwatch Institute 2007: pp. 260-61, Volvo 2007].

The last usually mentioned propellant, while talking about alternative fuels is, of course, Hydrogen. As water is the only product to be obtained while burning Hydrogen, it has an enormous favorable prerequisite to be used as a transportation fuel. Unfortunately the fact that Hydrogen can not be found in its pure form in nature and has to be extracted from other sources as well as other properties, like the very low volumetric density, and its wide range of inflammability concentrations in air, make it very difficult to handle and unlike to replace common fuels in the near future [Klein/Ranke 2008: pp. 197 – 232, Hordeski 2007: pp. 11-30].

Since this work is not exploring the dedicated technical solutions in detail, but pursues a more generic approach, it is thoroughly realistic to focus all of these fuels. Nevertheless, it seems evident, that while focusing at supply infrastructure in general and number and location of fuel station in particular it is useful to delimit the scope to only those fuels that can not be distributed by the existing petrol infrastructure. Due to this fact the further work is focusing on Methane, i.e. LNG and CNG, DME, LPG and Hydrogen.

2.2 Characteristics of the Fuels Focused on

After having defined the terminology of alternative fuels with respect to this work and discussed their general properties in the previous section, in the following, the physical and chemical characteristics of the fuels focused on in this paper, their implications on handling the fuels and finally the resulting driving range for each fuel will be discussed in more detail.

2.2.1 LNG

LNG is processed natural gas. As to obtain an acceptable energy density it has to be liquefied. During this liquefaction process in a first step, several contaminants like CO2 are removed and the resulting gas is cooled to -163°C, where it becomes a liquid. Due to this processing LNG is a clear and odorless cryogenic liquid, which is non-corrosive, non-toxic, lighter then air and quickly vaporizes when spilled, but also is flammable at concentrations of 5-15% in air [Horne 2006]. The transport and storage are performed at a pressure of about 3.5 bar, but require a very good insulation of the vessel. Within the pump-dispenser system and in the vehicle’s tank temperature and pressure rise, so that it is about 5.5 – 6.9 bar and -129°C in tank [Horne 2006]. LNG has an energy density by weight of about 46 MJ/kg and a volumetric one of 18 – 24 MJ/L [Eberhardt 2002, Berger 2007].

LNG has several characteristics which make it particularly suitable for vehicle use. Although it is produced from a mixture of raw components and therewith contributes to global pollution and climate change, it burns inherently cleaner and causes notably lower greenhouse gas emissions than diesel and petrol. It is suitable for both spark ignition and compression ignition engines, however, performs better in compression ignition engines. Compared to CNG, which is a natural gas derivate too, it can store about 2.5 times more energy, making it much more favorable in particular for the use in vehicles [Gilbert/Perl 2008: pp. 136-37]. As remarkable shortcomings the notably higher ignition temperature in comparison with diesel, as well as the required insulation should be mentioned [Nexgen 2008]. This insulation effects the tank to be relatively big what causes, together with the better performance in diesel engines, LNG’s use as a fuel to be in trucks mainly.

Once the insulation of all storage vessels is realized the distribution of LNG entails no major problems. LNG is delivered to fuel stations by tankers as a cryogenic liquid and is thus independent of a pipeline network. In a next step it is stored in an appropriately insulated vessel at saturation point and dispensed to vehicles in vapor condition [Horne 2006: pp. 37-38]. This process is shown in

Figure 2. Being a liquid, LNG has a higher density than CNG and thus considerably higher fueling rates. With a few changes to be carried out at the fueling system, LNG fuel stations can also economically provide CNG, what is then usually referred to as liquefied compressed natural gas (LCNG) [Nexgen 2008].

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Figure 2 : LNG Fueling Station [Nexgen 2008].

2.2.2 CNG

CNG is the short form for compressed natural gas. Due to its low energy density the natural gas is compressed to its CNG form at a pressure of 200-250 bar. CNG is in its natural form odorless, but it is mixed with an odorant to facilitate the detection of leakage. It is non-toxic and lighter than air, so that it will disperse in case of leakage, however, it is flammable at the same concentration in air as LNG is [De 2004]. In great quantities it is stored and transported at its production pressure of 200 – 250, although the on-board storage takes place at a pressure of 6.8 – 8.6 bar [Berger 2007]. With about 46 MJ/kg CNG has a similar energy density by mass as LNG, but its volumetric energy density of 7-9MJ/L is considerably lower, therefore CNG vehicle applications have disadvantages in terms of payload, load volume and driving range [Berger 2007, Haudek 1998].

Owing to its high physical-chemical stability natural gas has a high octane number and thus a remarkably higher antiknock performance compared to gasoline. CNG does not have to be vaporized prior to ignition and therefore offers a more stable combustion, accompanied by lower hydrocarbon emissions [Elvers 2008: pp. 164 – 165]. Furthermore burning CNG expels less air toxins and particulates than diesel engines. Similar to LNG, the lower emissions of CNG are balanced by a lower efficiency of the engine, a slightly lower well-to-wheel efficiency and a more sophisticated fueling system [Elvers 2008: pp. 165 – 166]. As stated above the biggest disadvantage of CNG is its low volumetric energy density, resulting either in very big tanks with high requirements on pressure or in a very low driving range.

Although CNG stations do not have to be necessarily connected to a pipeline, if they are not, they have a very limited capacity and face the problem of pressure dropping with each filling. Once the pressure drops, the refueling time increases noticeably while the quantity of CNG dispensed to a vehicle decreases [De 2004]. Another alternative is to use LNG as a feedstock to create CNG at the fueling station, but the most effective method to run CNG stations is to connect them directly to a local fuel distribution system as depicted in Figure 3. In this case the gas is delivered at a low pressure of about 18 – 25 mbar by the pipeline and in a next stage compressed and conveyed to a high pressure storage cascade. This storage cascade usually consists of several banks with different pressure levels. Each of the banks is connected with a separate line to the dispenser where the choice of the actual bank for the CNG stream is done depending on the pressure difference between vehicle and dispenser, and the gas flow speed [Elvers 2008: p. 163]. There are also so called on-line fueling systems where the vehicles are refilled by a compressor directly from the pipeline, but due to fueling times of about 8 to 10 hours they are only applicable at home depots of fleets [Elvers 2008: pp. 162–163, De 2004: pp. 3-6].

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Figure 3 : CNG high-Pressure Refueling System [GreenField 2008].

2.2.3 LPG

LPG, or liquefied petroleum gas, is a mixture of hydrocarbon gases which mostly contains about 60% propane and 40% butane. It is mostly manufactured during the refinement of crude oil and compressed up to its moderate vapour pressure at normal temperature, where it becomes a liquid [LPG Australia 2007]. In its natural form it is colorless, odorless and heavier than air, what holds some danger since it can collect in pits when spilled. However, it has a very narrow range of flammability, which is arrived at concentrations of 2-10% in air [Elvers 2008: p. 151]. Usually it is mixed with an odorant to facilitate the detection of leakages. While the storage and transport pressure of LPG is about 8.9 bar, the pressure in vehicle tank is slightly higher at 9.6 bar [Shell 2006]. With 25-29 MJ/L and about 50MJ/kg LPG has both relatively high energy density by mass and by volume and thus is comparable with its energy characteristics to petrol [LPG Australia 2007].

The main advantages in the use of LPG lie in its local environmental impact. While burning LPG no evaporative emissions and no contaminations of soil and aquifiers occur, and the level of emitted particulate matter as well as hydrocarbons and carbon monoxide is very low [Elvers 2008: p. 150]. Nevertheless LPG is a fossil fuel and does not solve neither the dependency on finite resources nor the environmental impact of burning fossil resources. Throughout the whole process of handling LPG high safety standards are required in spite of its limited flammability, because in the event of leakage it can migrate considerable distances and tends to accumulate at low points. However, safety aspects are not the biggest problem with respect to a use of LPG in heavy duty trucks. Rather the fact that a conversion of diesel engines as to be run with LPG is expensive and otto engines have some disadvantages regarding a use in trucks. The most important of these shortcomings are a 20-30% lower efficiency, a remarkably more critical temperature handling under high charge as well as shorter service intervals and consequently higher service costs [conf. interviews 5, 13, 17].

LPG is stored and transported to the vehicle as liquid under modest pressure. This of course requires special vessels and tanks as well as a dedicated fueling station. Nevertheless the resulting problems are manageable, the tank insulation is smaller than in the case of LNG and CNG and the fuel station design is rather simple with modest costs of installation. A typical LPG fuel station basically consists of an exchangeable storage tank, a dispenser as well as pipes and valves connecting both as can be seen in Figure 4.

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Figure 4 : LPG Fueling System [FAS 2008].

Despite the simplicity of the dispensing system there is a problem with respect to the LPG distribution resulting from the availability of LPG. As a side-product of crude oil refinement LPG is available everywhere across Europe, however, the total amount of LPG is limited and can not be raised any desired, what makes a widespread use of LPG as a fuel difficult [conf. interviews 4, 5, 17]. Most of the past LPG applications have been set up due to a local oversupply of LPG, like the Netherlands, encouraged by the closeness to huge refineries and huge turnover of natural, or France by a relative overproduction of petrol compared to diesel and therewith an oversupply with LPG.

2.2.4 DME

DME is the acronym for Dimethylether, a colorless gaseous combination of carbon monoxide and Hydrogen with a typical ethereal odor. DME is conventionally produced using methanol or natural gas as a feedstock, by methanol synthesis or hydration. However, also production methods from renewable sources, like the black liquor gasification are considered, what would make DME independent from fossil resources. [Paas 1997: p. 1, Ekbom et al. 2003]. Since it is heavier than air and therefore tends to settle to low lying areas, it is common to add an odorant for leak detection. It is flammable at concentrations of 3.4-20% in air, what is a fair wide range compared to the other fuels considered in this work [Paas 1997]. DME is transported and stored at a relatively low pressure of about 5 bar, which rises then in the vehicle tank to 17.5-21.5 bar and in the injection system even reaches 220 bar [Paas 1997, LPG Australia 2007]. It has an energy density by mass of 28 MJ/kg and a volumetric energy density of 19 MJ/L [Paas 1997]. Due to its poor lubricity the design of several vehicle components like fuel injectors and pumps has to be adapted [Paas 1997]. Nevertheless DME can be used in diesel engines without any bigger complications and definitely easier than it is the case for the fuels discussed above.

DME is considered a promising substitute for diesel with test results showing similar driving behavior as a diesel vehicle, but with considerably lower emissions [Hayashi 2002]. It contains no sulphur and causes no carbon bond, and therefore no particulate matter nor soot, when combusted. These environmental characteristics are probably its main advantage over diesel, followed by the ability to be produced from renewable energy sources [Worldwatch Institute 2007]. Against the backdrop of other alternative fuels it is distinguished by its relative high energy density and high cetane number, which allows an application more suitable for current industry demands [Volvo 2007, Hansen/Mikkelsen 2001]. Nevertheless the energy content of DME is about half the one of diesel, so that special fuel supply systems are required in order to obtain the same output power as diesel engines.

Due to the low pressure and the liquid state of matter the transport of DME can be carried out easily with simple vessels and other standard equipment. For the distribution of DME basically the same dispensing system that is used for propane can be applied, with a few changes only. First DME tends to serve another market than propane. While propane is mostly applied in light-duty vehicles, DME tends to be used within the heavy-duty segment. Therefore larger storage tanks and higher flow rates are required at DME dispensing. Moreover most of the elastomers used on propane components would have to be displaced for the use of DME, due to the fact that DME dissolves most of these materials. Despite these few adaptations the dispensing system is structurally identical to the installation for propane [Ahlvik/Eriksson 2006: pp. 43 – 45]. It basically consists of a storage tank, pump, dispenser and common parts like valves, fittings and meters. Figure 5 shows an exemplary fuel dispensing installation, which can be used for both, DME and propane. In general it can be stated that the distribution of DME is less complicated than in case of natural gas and LPG.

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Figure 5 : DME and Propane Fueling System [Paas 1997].

2.2.5 Hydrogen

Despite Hydrogen being the most abundant chemical element in our universe it is relatively rare on earth in its elemental form. Therefore it usually has to be produced by steam reforming, the Kvaerner Process or extracted from hydrocarbons or from water, but also other methods like the biological production by algae are considered [Marek 2007]. Hydrogen is in its natural form a colorless and odorless gas. Due to the fact that it is the lightest of all elements it disperses very quickly, when released in air, so that leakages are quickly diluted. Nevertheless it has a very wide range of flammability with 4-75% by volume in air, what holds a notable danger [Plugpower 2007]. There are basically two different ways to drive vehicles with Hydrogen. The first one is the use of Hydrogen in fuel cells, where the Hydrogen is used to produce electrical energy, which then drives an electrical motor. Although this is a very promising alternative for the long-term, current technology does not allow reaching acceptable driving ranges with Hydrogen [Rand/Dell 2008]. Therefore the second alternative is more probable to be feasible in the mid-term, which is to burn Hydrogen directly in an internal combustion engine (ICE). Although Hydrogen can be run in both spark-ignition and diesel engines, most of the efforts with respect to hydrogen-powered engines are concentrated on spark-ignition engines.

The storage possibilities of Hydrogen are manifold, and can be roughly divided into storage as a pressurized gas, storage as a cryogenic liquid and metal hydride storage. In pressurized form a pressure of at least 300 bar is needed, while storing in liquid form requires the Hydrogen to be cooled to -253°C. The storage systems in hydrides are supposed to be the most promising ones, but are scarcely at the beginning of their development [Thomas/Keller 2003; Ogden 1999: pp. 244-245], therefore this work will discuss only the storage in tanks for use in ICE.

Whereas Hydrogen’s energy density by mass of 118 – 140 MJ/kg is by far the highest of all the fuels considered, it has the lowest energy density by volume with 2.9 – 7.7 MJ/L [Berger 2007, Bossel 2003]. Hydrogen’s potential for fueling vehicles is controversial, but characteristics like its high energy density and burning without local emissions are at least excellent theoretical prerequisites for that [Romm 2005]. Burning Hydrogen in an ICE is connected to a number of problems. Hydrogen has a very low volumetric energy density, what limits the driving range for ICEs, too. It is inflammable at low temperatures, what causes pre-ignition problems and makes ignition control difficult, and has a high stoichiometric air/fuel ratio, what results in a diminished power output. Despite these problems, appropriately modified, the driving behavior of a hydrogen-powered car with an ICE does not differ remarkably from a conventional gasoline or diesel engine, however these modifications are significant [Ogden 1999: p. 229].

Regarding the fuel stations there exist a huge variety of possible designs. The most applicable solution for transportation demands is a fuel station with big storage tanks and smaller high pressure tanks for Hydrogen distribution, as can bee seen in Figure 6. The Hydrogen is delivered to the fuel station in liquid form by a Hydrogen container vehicle, where it is stored in an underground tank. In the next step it is compressed by a cryo compression unit and transported to the site high-pressure Hydrogen storage tanks. From there it is dispensed as a compressed gas to vehicles in the same way as mentioned above for the case of high-pressure CNG refueling systems [Linde 2008]. Merely the refueling time is longer in case of Hydrogen and with about 30 minutes for a heavy duty vehicle still too long for being accepted by clients from the haulage industry [HyFLEET 2008].

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Figure 6 : Hydrogen Fuel Station [Rachlin 2004, Linde 2008].

Table 1 displays an overview of the discussed fuel characteristics. The energy densities depicted in this figure naturally differ depending on the conditions at which the fuel is handled. Nevertheless, with the exception of Hydrogen for all fuels a standardized state of usage can be assumed, so that the spreads of energy densities are caused by quality differences mainly. Only for Hydrogen the spread stated in Table 1 is due to different storage states and not fuel quality differences. The higher value is achieved by storage at 700 bar and a temperature of -253° C. The following section will discuss how these properties affect the driving ranges of vehicles used for long haul transportation.

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Table 1 : Comparison of Several Alternative Fuels´ Properties.

2.3 Driving Ranges of Vehicles Powered with Alternative Fuels.

When considering driving ranges for the different fuels, one has to pay attention predominantly to two characteristics: energy density by volume and engine energy efficiency.

The energy density by volume for the several fuels is depicted in Table 1. Assuming a typical tank size for heavy duty trucks of 1000 L this number implies the amount of energy that can be stored in an exemplary tank of this capacity for the several fuels considered, which can be seen in Table 2. Of course, for some fuels like CNG and Hydrogen the storage of this amount is not without problems, and can affect other disadvantages like a grave loss of payload. However, for the purposes of this work it shall be assumed that the on-board storage of 1000 L is possible for each of the fuels considered.

The meaning of engine’s energy efficiency used in this work signifies how efficient an ICE powered with one of these fuels converts the chemical energy stored in the tank into mechanical energy in the engine’s pinion shaft in comparison to a sample diesel engine. The detailed figures for these efficiencies have been estimated on the base of an engine efficiency study for passenger cars, published by the European Commission [EUCAR/CONCAWE 2007].

This report lists different energy consumptions of a 1.6 L ICE powered by various types of fuels [EUCAR/CONCAWE: pp. 15, 19]. These figures have been converted linearly into the energy efficiency factors listed in Table 2 in the manner shown in the following example for CNG.

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Transferring this to the engine’s fuel consumption an engine size should be assumed, that is representative for the considered application. Interviews with haulage companies and engine producers showed that an approximately 12 L heavy-duty diesel engine can be assumed as such a representative for long haul applications. The average fuel consumption of such an engine is strongly depending on the characteristics of the transport process, but has an overall average of 34 – 36 L/100 km [Tschakert 2007: p. 12; Schwarz 2007a: p. 13; Schwarz 2007b: p. 18]. Assuming a slightly higher fuel consumption of 40 L/100 km the estimation of total vehicle range is made as shown in the following example of CNG.

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The amount of chemical energy stored in the sample tank corresponds to the lower energy density by volume given in Table 1. The only exception is Hydrogen because the energy density range listed in Table 1 does not represent a spread of possible fuel qualities, but two different way of storing Hydrogen. While storing the Hydrogen under low pressure conditions leads to a volumetric energy density of 2,9 MJ/L the high pressure storage considered in this work provides the higher figure of 7,7 MJ/L.

The vehicle ranges estimated in this manner are listed in Table 2 and will be used later as a constraint within the optimization model presented in chapter 3. However, in the first instance, methodological approaches taken of both Industry and mathematical optimization for designing a fuel station network shall be discussed.

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Table 2 : Vehicle Ranges for Different Alternative Fuels

3 Methodological Background

After having examined the fuels’ characteristics and therewith restrictions in their use, this section deals with the different approaches of industry and research, i.e. mathematical optimization, while designing a new fuel distribution infrastructure. This chapter will be concluded with the introduction of the optimization model used within this work.

3.1 Infrastructure Buildup Approaches of Fuel and Haulage Companies

Whenever thinking about the methodology of introducing something new, a first step should be to review what experience already exists in similar fields of work. Regarding the build-up of new fuel dispensing points this experience is likely to be found within the stakeholders involved in the build-up of those facilities, therefore those companies have been interviewed in the scope of this work.

When discussing the resulting approaches of these companies for building up fuel stations for both alternative and common fuel, one has to distinguish two different groups of stakeholders, as shown in Table 3.

The first group are companies operating public or semi-public fuel stations independently, or within a franchise system with others. Interviews conducted with those companies show basically two different approaches of deciding the development of new fuel stations. Firms that build up and run fuel stations themselves usually serve a small group of niche clients with any kind of dedicated product or service. This can be an alternative fuel not available at the majority of public fuel stations, or customized technical as well as service solutions with connection to fueling vehicles. One example is the well developed and, in particular in Germany, very competitive market for biodiesel and related technical solutions. There exists a wide variety of companies in this market segment, like the Need Fuel Supply GmbH, the PROKON Oil GmbH both situated in Germany, Rix Biodiesel from Great Britain and an enormous number of small retailers with few facilities all over the world. These companies with their fairly small fuel station network usually take a stepwise approach of expanding their service. At the beginning they look for haulage or other companies, which they can supply exclusively with fuel products. In this manner they build up a first fuel station somewhere close to these customers, which is later serving other clients, too. The exact location of these fuel stations is usually restricted to a few possible places and then finally grounded on general statistical data like the number of trucks at the road sections considered. The expansion of the initial fueling infrastructure occurs in the same stepwise way until the company has reached a certain size at which location decisions become also subject to competitors’ behavior. Summarizing the findings, small fuel companies, which try to establish a new fuel dispensing infrastructure, do not choose a holistic approach of infrastructure network optimization, but first focus on supplying few customers and then try to extend their clientele by serving a stepwise increasing number of customers [conf. interviews 2, 4, 6, 9, 19].

Major petroleum companies, operating big international networks, have a more holistic approach when setting up a fuel station network. First of all such a concern already has at its disposal a huge fuel station infrastructure. This infrastructure then, is naturally the starting point when introducing a new fuel. For instance, when the Austrian petroleum company OMV introduced urea into the diesel market, it simply chose a subjective number of their existing fuel stations with the highest sales of diesel. Shell went a similar way while introducing urea, by concentrating on high diesel sales, closeness to truck repair shops and competitors locations. When considering an extension of the common fuel station network instead of an introduction of a new network, real fuel demand is even less important, since the revenues of a fuel stations in some countries are already strongly depending of the included shop area and therefore of the consumer flows [Hess 2008, Collins 2000]. Therefore petrol companies operating common petrol stations of course focus on consumer flows, but more in the way that fast food restaurants and retail stores do [Minale 2000: p. 11, Lakshmanan/Hannsen 1965]. It is not crucial where the consumers have to refill their vehicles, but at which location most of them are passing by and could make a break, eat something and incidentally refuel their vehicle. The location decision at these companies is supported with statistical data in a more regular way than for the small fuel companies, but still is limited to the extent of publicly available transport amounts or traffic densities at road sections. All of the interviewed companies denied special effort to estimate where the customers of a certain fuel station come from [conf. interviews 1, 6, 14, 15, 18].

Despite these proceedings constitute a fairly holistic approach, it can not be stated that it has the main objective to cover fuel demand. The key decision variables within these methods are rather consumer flows, marketing aspects and overall company growth subject to competitors’ behavior rather than a flow bounded demand of fuel.

The second group of companies with interest to this work are all kinds of haulage companies. Regarding their fueling policy one can distinguish three different types of haulage companies – those operating an in-house fuel station by themselves at their own area, those which are supplied by a dedicated fuel station close to their home site or close to their customers’ site and those using public fuel dispensing facilities mostly at special conditions [conf. interviews 3, 4, 7, 12, 20, 21]. Companies of the latter type do not have any influence on fuel station buildup, but are one of the clients of big fuel companies whose approach has been already discussed above. In case of firms that have to be supplied by dedicated fuel stations at few locations, we are considering the clients of small fuel companies, so that the approach usually chosen is the same as discussed in case of these small fuel companies. The last type of haulage companies, i.e. those covering their demand themselves, face the problem to locate one ore more fueling facilities in order to cover all their demand of fuel. According to the conducted interviews the solution of this problem is fairly easy. The companies operate their diesel trucks with tanks having a tank volume of about 1000 L, what allows them to supply all their trucks with one single fuel station at their home ground in most of the cases.

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Table 3 : Stakeholders of Fuel Station Buildup and their Approaches.

The empirical analysis’ results can be summarized as followed. Depending on the scale of the considered application and the operator’s interests there are three ways to introduce fuel innovations in practice which are illustrated in Table 3. A holistic but more business-focused one, usually taken by big petrol companies, a demand-oriented one, with a stepwise extension subject to acquiring new single customer and expanding then towards public service and finally a completely demand-focused one, taken by haulage companies for their mostly relative small transportation network, which they have to supply with fuel.

As it is the aim of this work to show differences in fuel supply needs basing on differences of the fuels’ characteristics, the holistic, business focused approach will be omitted in the following. Focusing on the last two approaches, i.e. the approaches 1 and 2 in Table 3 also has the advantage that the transportation networks considered are clear and manageable with quantitative tools and methods with reasonable effort. By this means the resulting numbers and locations are not only good in a subjective way, but exact, optimal subject to predefined criteria and reproducible. Furthermore the stepwise introduction of an alternative fuel within rather limited applications has some other advantages in form of lower investments required and favorable fleet characteristics, such as: high fuel usage per vehicle, mostly urban locations, fixed or limited routes and typically a desire to promote goodwill [Zhao/Melaina 2006: p. 1305].

In the next section various mathematical optimization approaches of network allocation will be discussed in general and the concrete model will be developed which allows an optimal fuel station location as to cover the entire demand of every company considered and make a stepwise network extension possible.

3.2 Theoretical Approach of Mathematical Optimization

Mathematical optimization as a branch of Operations Research provides many methods which can be used to arrive at the best possible solution of a complex real problem, subject to any given constraints. Although there are various several kinds of optimization models, linear programing approaches are the only one to be regarded within this work. This is due to the fact, that linear programs are much easier to deal with than nonlinear ones (Ehrgott 1999, Lindo 2008) and still can depict the real problem of fuel station location in a very good way, as will be shown later on. Nevertheless fuel stations can be built up as a whole only, so that all approaches discussed are integer linear programs (ILP). It should be kept in mind that due to the integer character common methods of linear programing can not be applied, although the constraints and objective functions used in the models describe linear correlations (Chineck 2003, Vanderbei 2008: p.385-405). Dedicated integer programing methods like branch and bound are to be used instead. In the following various approaches for different network allocation problems shall be discussed and finally this work’s ILP will be introduced.

3.2.1 Location-Allocation Models for Infrastructure Networks

When mathematical optimization regarding civil issues became a considerable field of research, fuel stations were a ubiquitous good in all industrialized countries. Their number is even rather decreasing than going up during the last decades [Scottish Parliament 2000]. Due to this fact, optimization of fuel station locations has attracted no attention during the whole 20th century. Only when climate issues became increasingly important to the public at the end of 90s and alternative fuels where investigated to a great extent the question arose how vehicles driven by those fuels could be supplied with the fuel needed.

The small body of work dedicated to answer this question builds upon results from related problems of facility location. Most of these attempts were made to provide solutions either for questions regarding the location of plants or warehouses, or selling points of consumer goods and are usually subsumed as Location Allocation Models (LAMs). Although there are several different classifications of LAMs [Dileep 2001: p. 16, Gosh et al. 1995] for the purpose of this work four different types of LAMs shall be distinguished.

P-median models have the objective to find locations for a given number (p) of facilities, which minimize the average distance that separates customers from their nearest facility [Dileep 2001: p. 17, ReVell/Swain 1970]. The solution is p-weighted medians of the demand points represented on a graph. Usual applications of a p-median model are locations of food distribution facilities, and public institutions like libraries and health-care centers. A special form of p-median models is the p-choice problem. It is in its structure very similar to the p-median problem, however, incorporates the fact that customers sometimes do not use the facility next to them but one that is optimal regarding a multipurpose trip. By applying probability choice rules, those models predict the customer’s behavior and estimate a set of facility locations that maximizes the number of customers served [Lakshmanan 1965].

The p-center problem deals with placement of p facilities to minimize the maximum distance from a facility to the demand point it is assigned. Typical applications are emergency facilities like fire stations, police stations and ambulance services [Dileep 2001: p. 17].

Covering models identify locations that provide users access to service facilities within a specified distance or travel time. A special case of the covering model which is important within the approach of this work is the set covering model. It assumes that consumers beyond a certain maximum distance do not use the service and thus finds the minimum number and locations of facilities needed to serve all potential customers within a specified distance [Church 1974, Toregas/ReVelle 1973].

The last type of location allocation problems are flow interception models. Instead of locating facilities to serve fixed points in space, these models aim to cover demand that consists of origin-destination flows along the network’s paths. The first models of this type where introduced at the beginning of the 90s [Hodgson 1992, Berman et al. 1992] and aim to locate p facilities so as to maximize the total flow of potential customers who pass by at least one of the facilities on their pre-planned trips. Although there are many extensions of these Flow Capturing Location Models (FCLM), all of them consider a flow as captured, if it passes once by a facility and therefore do not incorporate a possible necessity to capture a flow more than once nor the distance of a flow’s starting point to the location [Kuby/Lim 2005: p. 130]. In their Flow Refueling Location Model (FRLM) Kuby and Lim addressed this lack, and presented a model that aims to locate fuel stations so as to maximize the flow along paths of the network considered, subject to a maximum vehicle range [Kuby/Lim 2005]. The FRLM is the basis for the theoretical approach of this work and therefore shall be presented in the following.

The FRLM aims to locate a given number p of refueling stations on a network so as to maximize the total flow volume refueled. Flows are defined as to occur along shortest paths between origin-destination (O-D) pairs q.

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The objective function (3) maximizes the total flow that can be refueled with p facilities. Constraint (4) requires a combination of facilities h to be open and able to refuel a flow q for considering the flow q as captured. Constraint (5) assures that a combination of facilities h is only considered as open if a possible facility location k is included in a combination h and a facility is assigned to this location. Equation (6) limits the number of facilities located to a given number p, and constraints (7) finally are integrality requirements for the binary variables [Kuby/Lim 2005:pp. 134 – 35].

Since this is a flow maximizing model, it is applicable for problems of allocating a limited amount of resources so that the demand is covered in the best possible way, but not necessary entirely. Therefore it has to be changed for the aims of this work towards a set covering model, as it has been discussed above. As a result one obtains the model discussed in the following chapter.

3.2.2 The Set Covering Fuel Station Location Model (SCFLM)

As discussed in chapter 3.1 the introduction of an alternative fuel shall occur first in a limited application, which can be quantified by available data and shows a manageable overall complexity. Such an application can be the transportation network of one or several haulage companies operating within an area that can be regarded as an own transportation network. Then an optimization model is needed that helps to answer the question of how many fuel stations are needed and where they shall be located to cover the overall fuel demand within this network, i.e. to replace the fuel currently used by an alternative.

So the main changes towards the FRLM discussed above are that the number of fuel stations is not given, but has to be estimated in the way to be a minimum solution and the amount of flows is not to be maximized, but captured entirely. As a result of these changes we obtain the set Covering Fuel Station Location Model (SCFLM) shown below.

MIN Z =Abbildung in dieser Leseprobe nicht enthalten (8)

Subject to:

Abbildung in dieser Leseprobe nicht enthalten (9)

Abbildung in dieser Leseprobe nicht enthalten (10)

Abbildung in dieser Leseprobe nicht enthalten (11)

With the notation as followed:

q = Index of O-D pairs

Q = Set of O-D pairs

h = Index of combinations of facilities

H = Set of combinations of facilities

k = potential facility location

K = Set of potential facility locations

xk = 1 if facility located at k, otherwise 0

bqh = 1 if combination h able to refuel O-D pairs q, otherwise 0

ahk = 1 if facility location k in combination h, otherwise 0

vh = 1 if all facilities in combination h are open, 0 otherwise

The objective function (8) minimizes the number of facilities x located at possible locations k. The constraint (9) assures that each flow in the considered network is captured, i.e. that no vehicle running within this network runs out of fuel. Constraint (10) holds combinations of facilities h closed until facilities are installed at all possible locations included in this combination; in the same way as the constraint (5) did it for the FRLM. Finally, again all variables are restricted to be binary by the constraint (11).

The most important Input for the SCFLM is the matrix b, i.e. the information which combinations of fuel stations are able to refill which flows within the network. Following [Kuby/Lim 2005] the Figure 7 illustrates, why it is necessary to consider combinations of facilities rather than single locations to answer this question.

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Figure 7 : Example of a Round-Trip between Two Nodes.

Assuming five cases with different vehicle ranges there are five different solutions for locating fuel stations as to be able to refill a round-trip, which is repeated on a regular basis. In all cases it is assumed that the vehicle starts full, if there is a fuel station located at the starting point of the vehicle and it starts with a half-filled tank, if there is no fuel station located at the starting point. This assumption is valid because if one can start at O with a half-filled tank and reach a fuel station without running out of fuel, it is also possible to make the reverse trip from the fuel station to O.

In Case 1 the range of the vehicle is over 500 km. This means that one single fuel station anywhere on the path is able to refill the vehicle. In Case 2 the driving range is assumed to be 700 km. In this case one can see that one single fuel station at O is not able to refuel the vehicle, because it would run out of fuel on the way back from D. The same results for a single fuel station at A, the vehicle can not be filled at A and then driven to D and back. However, if there were a facility at B the trip could be covered, one can drive with the full vehicle 600 km from B to D and back, refill the vehicle, go 400 km from B to O and back, refill the vehicle and so on. In Case 3, where the vehicle range is assumed to be 400 km, no single fuel station is able to refill the round-trip from O to D. One can see that only the combination of locating a fuel station at each B and D can refuel the round-trip. In Case 4, where the vehicle range is any number between 300 and 399 km, one can see that the two facilities installed in Case 3 are not able anymore to refuel the round-trip. Instead at least three stations are needed, one at each B and D and one at either A or O. Once the range drops beneath the maximum link length on the path, i.e. in Case 5, it becomes impossible to refill the round-trip along the path with fuel stations at nodal locations only. This more complex problem with possible fuel stations locations anywhere along the path will not be dealed with in this work. One idea of how this problem could be approached can be found at [Kuby/Lim 2007].

Once one have realized that one have to consider combinations of localities rather than single locations, the question arises how those combinations of fuel stations can be estimated among all combinations, that are able to refuel a certain flow. To answer this question a sub model, proposed by [Kuby/Lim 2005], has been implemented in Java. Assuming a given list of possible fuel station locations h, which is the power set of all locations, and a given list of flows along paths from origins to destinations in the network q, which do not have necessarily to represent shortest path from origin to destination, the following algorithm determines all viable combinations h that can refuel each path q.

Step 1: Initializations.

- Establish an empty master list of all combinations h.

Step 2: Beginning with the next path q on the list, generate a list of all possible combinations h of the nodes on the path, i.e. the power set of the network’s nodes. For example, for the path in Figure 7, the possible combinations are {O}, {A}, {B}, {D}, {O,A}, {O,B}, {O,D}, {A,B}, {A,D}, {B,D}, {O,A,B}, {O,A,D}, {O,B,D}, {A,B,D}, {O,A,B,D}.

Step 3: Remove facility combinations that can not refuel a vehicle of the given range on the given path. For each combination:

- Begin at the origin node of path q. If there is a facility at the origin, set the remaining fuel range equal to the vehicle range. Else, set the remaining fuel range equal to half of the vehicle range.
- Move to the next node at the round-trip path and subtract the distance travelled from the remaining fuel range, and check the following four conditions in the order as given:
- If the remaining fuel range is less then zero, fuel would have run out before the node was reached. Remove this combination of facilities from the list of possible combinations for path q and go back to the start of step 3 for the next combination.
- If the node is the destination, then:
- If the destination node has a refueling station, this combination of facilities can refuel this path. Keep it in the list of combinations for path q, and go back to the start of step 3 for the next combination.
- Else, return to the top of step 3.2.
- If the node is the origin, the vehicle has made it back without running out of fuel. Keep the combination in the list of combinations for path q, and go back to the start of step 3 for the next combination.
- If the node has a refueling station, set the remaining fuel range equal to the vehicle range, and go to the top of the step 3.2.
- Else, return to the top of step 3.2.
- When all possible combinations have been evaluated for path q, go to step 4.

Step 4: Repeat steps 2-5 for all paths q.

This sub model delivers all input needed for the SCFLM, i.e. a list of feasible fuel station combinations h for each flow q, and therefore the matrix bqh, and finally all fuel stations k included in each combination h, and therefore the matrix ahk. The implementation of this model will be discussed in the following.

4 Estimating the Optimum Distribution Network with the SCFLM

The implementation of the SCFLM with its required sub model has been realized in three parts, as can be seen in Figure 8. The first one is a small database, which serves as an input device for the structure of the considered network and is accompanied by a simple configuration file to input the driving ranges. The second part is a Java Application, which realizes the algorithm showed in section 3.2.2 and delivers, basing on the network structure depicted in the database, the main input for the actual optimization model, the SCFLM. The latter has been implemented in the optimization software LINGO and finally estimates the minimum number of fuel stations for the considered case.

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Figure 8: Optimum Number of Fuel Stations Estimation Process.

In the following two sections, basing on the transportation net of a real haulage company, it will be first shown exemplary how the transportation network structure has been depicted in the database and then, in the second step, how the SCFLM has been implemented in this special case.

4.1 Defining and Modelling the Sample Network

As an example serves the transportation network of Eurotank, a Swedish tank operator, transporting various kinds of chemical products, primarily between Sweden, the Netherlands and Germany. As will be proofed later in the text, the transportation structure of Eurotank represents the distances driven within the European long haul sector fairly well. This company basically runs the following four routes on a regular basis:

- Helsingborg – Amsterdam – Rotterdam
- Helsingborg – Köln – München
- Helsingborg – München
- Helsingborg – Stockholm

All routes are round-trips and for all of them the way back occurs along the same paths as the first way. In order to reduce complexity, distances between the cities have been rounded up to the next decimal power and sections taken by ferry have been assumed as normal road sections, since they are rather short in this case. Expressing the routes as a transportation network, one obtains the schematic illustration in Figure 9.

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Figure 9: Sample Transportation Network of Eurotank.

To depict this network structure in a way that can be used for the further calculation, a small database has been developed with the freeware program SQLiteadmin. In this program one can input the several nodes of the network by adding them as new locations, then connect them with paths and finally define the trips within this so defined network. Whereas this procedure is explained more detailed in Appendix A.1, Figure 10 and Figure 11 give an impression of how the network’s nodes respectively paths depicted in the database look like.

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Figure 10: Defining Nodes of the Transportation Network.

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