Modelling voyage specific fuel type decisions under probabilistic fuel prices and ECA presence

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Supervisors:

Prof. dr. I.F.A. (Iris F.A.) Vis dr. ir. P. (Paul) Buijs

Abstract

Cost differences between Liquefied Natural Gas (LNG) Dual Fuel (DF) merchant ships active in the ECA regions and conventional vessels are not yet fully clear. Specifically, we focus on price uncertainties, variability for time spent in ECA, LNG fuel capacity constraints and the ability to change fuel types during operation to estimate differences in fuel costs between conventional and LNG DF vessels for a specific case study. This study aims to estimate fuel costs for specific price scenarios by simulating cost minimizing fuel type decisions over a large number of days and integrating stochastic price levels with stochastic ECA presence. From a case study with exhaustive experiments, it was found that LNG DF is more costly for relatively low fuel prices in which LNG prices increase and other fuel prices decrease. However, it is less costly for scenarios in which LNG is cheapest with higher HFO and MGO prices. Results also suggest that the minimal level of ECA presence ranges between 29% and 44% for the last scenarios, indicating that LNG DF is more advantageous under these conditions than previously considered in literature. LNG fuel consumption levels highly influence LNG attractiveness, in which reduced LNG fuel consumption levels render LNG DF to be most advantageous in all cases. Moreover, it is suggested that fuel type decisions should incorporate prices with LNG fuel consumption levels to further minimize fuel costs. Incorporating stochastic prices yields marginally lower ECA presence turning point estimations and slightly different fuel cost estimations than using deterministic prices.

Modelling voyage specific fuel type

decisions under probabilistic fuel

prices and ECA presence

Estimating fuel costs for LNG Dual Fuel and conventional merchant

vessels

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1

1. Preface

I would like to thank my supervisors Prof. dr. Iris Vis and dr. ir. Paul Buijs for their enthusiasm, being highly involved in this project and providing much helpful guidance. Furthermore, I would like to thank Gerard Bootsma from “Feederlines” for providing interesting knowledge and expertise on all aspects and being always available for meetings and questions. Finally, I would like to thank my friends and coworkers for helpful suggestions and helping me in the development and writing process.

2. Introduction

Liquefied Natural gas (LNG) holds much potential as an alternative fuel for the maritime transportation sector that is both environmentally sustainable and economically viable (Wang & Notteboom, 2013). As new environmental regulations in the Emission Controlled Areas (ECA) in the North and Baltic sea place strict limits on sulfur emissions, ship-owners operating in these areas are forced to either “change fuel quality by using more expensive low sulfur fuel oil” such as marine gas oil (MGO) or clean the exhaust gas with a highly expensive exhaust gas cleaning or scrubbing system (Wang & Notteboom, 2013). Moreover, ECA regulations (Tier III) limiting nitrogen oxide (NOₓ) emissions are scheduled in 2016 for newly built ships, where scrubbing technology is unable to comply without costly Selective Catalytic Reductions (SCR) systems (Brynolf, 2014; Wang and Notteboom, 2013; IMO, 2015). According to experts, the high costs of retrofitting small size dry cargo vessels sailing in the ECA zones with such abatement technology is not feasible and prone to high technological uncertainty (Wang and Notteboom, 2013).

An interesting alternative is the adoption of LNG, which is well proven technology and fully eliminates sulfur oxide (SOₓ), reduces nitrogen oxide (NOₓ) emissions with 80 to 85%, CO₂ emissions by 20 to 30% and significantly lowers particle matter (PM) emissions and is therefore fully ECA compliant (Burel, Taccani, & Zuliani, 2013; Wang & Notteboom, 2013). Modern LNG fueled engines have also highly reduced the potentially problematic accidental release of unburned methane (Brynolf, 2014; DNV, 2014). Even though LNG fueled ships typically cost 20-25% more than equivalent oil fueled ships (Wang & Notteboom, 2013), dual fuel engines capable of utilizing Heavy Fuel Oil (HFO), MGO and LNG have become a potential and well developed solution to comply with ECA regulations, because it allows changing fuel types during sailing based on fuel prices and the percentage of time in which a vessel sails through the ECA region (Burel et al., 2013; Wang & Notteboom, 2013). Furthermore, Burel et al. (2013) indicated that utilizing LNG can be economically interesting for vessels which spend more than 80% in the ECA zones with significant reductions in operational costs. Despite such economic and environmental benefits, the total cost of ownership of LNG fueled ships is not yet fully clear for ship-owners of small dry cargo vessels that sail relatively short distances. In determining important cost elements for LNG fueled vessels, the following issues in the extant literature have been under investigated.

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3 Cullinane and Bergqvist, 2014; Jiang et al., 2014). According to experts however, voyage specific fuel type decisions are imperative in influencing overall fuel costs. LNG dual fuel (LNG DF) engines allow switching fuel types during sailing and such decisions can be planned in advance and made during voyages based on the price that applies at the moment the fuel was bunkered. Based on these prices and whether or not a specific a specific fuel type is allowed in the ECA region, the cheapest fuel can be selected. This is either LNG, MGO or HFO outside the ECA area and LNG or MGO inside the ECA. Additionally, experts also indicated that route length is limited to fourteen days in utilizing LNG, due to tank capacity constraints. Ship-operators should therefore consider the extent to which LNG or MGO should be utilized both inside and outside ECA and the extent to which HFO is employed outside ECA in minimizing total fuel costs. Such decisions depend on the time spent in ECA and the total travel time. If the total travel time is less than fourteen days, operators can simply choose between MGO and LNG inside ECA and all fuel types outside ECA. Accordingly, the planning of fuel type decisions influences the total fuel costs for a specific voyage and these are different than conventional vessels employing HFO with scrubbers and/or MGO. Therefore, LNG attractiveness is dependent on such price levels and ECA presence.

Secondly, variability of ECA presence for different voyages is also an important aspect that is not yet fully considered in recent approaches. For example, Burel et al. (2013), Adachi and Kosaka (2014), Jiang et al. (2014) and Cullinane and Bergqvist (2014) have used fixed ECA presence levels in their analyses in comparing different ECA compliant technologies. The definition can be extended to include ECA percentages of route lengths. ECA presence is highly relevant for ship-owners deciding to invest in conventional or LNG fueled ships, since HFO can be employed outside these zones in case HFO price levels are lower than other fuel types. Conventional ships that only utilize HFO and MGO and pass through ECA regions less often may benefit less from dual fuel LNG engines, since they do not have to comply with ECA regulations outside ECA zones and can simply use conventional HFO technology. Experts of the Dutch shipping company “Feederlines” indicated that ECA presence is different for each voyage, since ships employ many different routes. Therefore, a stochastic level of ECA presence is proposed in this paper.

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4 Notteboom, 2013). Even though many studies suggest that LNG is able to maintain a large price advantage, the extant literature overall presents mixed price projections (Wang & Notteboom, 2013) and “supply and demand imbalances across countries are likely to cause highly volatile LNG prices” (Maxwell & Zhu, 2011). Therefore, an approach is necessary that captures the uncertain and variable nature of absolute price levels.

Potentially reduced cargo capacity due to the size of LNG tanks is another important aspect in determining total cost of ownership (Burel, 2013; Brynolf, 2014; DNV, 2014). Reduced cargo capacity entails reductions in revenue for shipments, which may result in higher freight rates and longer payback periods (Wang and Notteboom 2013). However, the effect on total cost of ownership over time in combination with probabilistic price level distributions and ECA presence levels is not yet fully considered in the extant literature.

The main subject of investigation in this paper is to examine the difference in mean fuel costs per hour between conventional ships and newly built ships that employ dual fuel engines utilizing LNG, HFO and MGO as a result of fuel type decisions under probabilistic LNG, MGO and HFO price level scenarios and probabilistic ECA presence percentages. Based on a specific fuel price that applies at the moment of bunkering and the question on whether or not a ship sails in the ECA region, the cheapest ECA compliant fuel type is selected during each voyage on a specific day. This allows fuel costs to be estimated for a large number of days by means of numerical simulation. Moreover, such fuel costs enable more insights in total costs of ownership (TCO) of newly built short sea dry cargo vessels.

One price scenario is defined as a linear price movement between 2015 and 2040 for HFO, MGO and LNG with random daily deviations from this baseline. The scenarios are based on fuel price projections of DNV (2012) and consist of a “low”, “medium” and “high” scenario (See Figure 2.3.3, 2.3.4 and 2.3.5). For purposes of sensitivity analyses, these scenarios are extended to include trend lines in which the slope coefficient is amplified (See Chapter 4).

The main research question is formulated as follows:

Under which scenarios of future probabilistic LNG, MGO and HFO prices and daily volatility do newly built LNG fueled short sea merchant vessels that operate in the ECA regions generate lower average fuel costs per hour compared to conventional ships operating in the ECA region based on voyage specific fuel type decisions and how sensitive are the outcomes to changes in price trends?

This question can be subdivided into the following sub questions.

1. What is the difference in voyage specific fuel type decisions between conventional and LNG dual fuel short sea merchant vessels as a result of fuel prices and ECA presence?

2. What is the relationship between voyage specific fuel type decisions and fuel costs?

3. What level and associated probability distribution of ECA presence is relevant for short sea dry cargo vessels operating in the North and Baltic Sea?

4. What scenarios of LNG, MGO and HFO prices and daily volatility are relevant and plausible for

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5 5. What are the estimated mean fuel costs per hour for both LNG dual fuel and conventional

ships for a given level of ECA presence and price scenario for a period of two decades?

6. What is the difference in estimated mean fuel costs per hour between dual fuel LNG and conventional ships based on future price scenarios and levels of ECA presence?

7. How sensitive are the outcomes for each LNG, MGO and HFO price scenario extension? 8. What quantifiable difference exists between the approach proposed in this paper and

approaches in existing literature that include deterministic ECA presence and deterministic prices?

The main contributions of this paper are twofold. Firstly, the extension of deterministic fuel price scenarios in current literature towards probabilistic fuel prices that include daily volatility in attempting to estimate and forecast fuel costs with greater accuracy. Secondly, to integrate probabilistic fuel prices with probabilistic levels of ECA presence in both time and route length to simulate the decision to choose certain fuel types with LNG action radius constraints during one voyage and determining fuel costs by replicating these fuel type decisions for many days over a long period for a specific price scenario. This should provide more insights in the total cost of ownership of short sea merchant vessels. Simulating the decision to select fuel types during a voyage as a result of fuel prices and ECA presence for vessels utilizing a LNG dual fuel engine has not yet been undertaken in current research, even though price uncertainties, ECA presence levels and lost cargo revenue are cited among the most important factors (Burel et al., 2013; Wang and Notteboom, 2013). The advantage of this approach is that uncertainty and risks can be incorporated into cost analyses and a more realistic picture can be obtained on the behavior of total costs of ownership for LNG fueled vessels (Wang, Chang and El-Sheikh, 2012).

This approach should result in a tool that allows ship-owners and logistic service providers to assess fuel costs based on up-to-date price level projections and ECA presence levels that are unique for different companies. Moreover, it may facilitate policy makers in evaluating the effect of implementing ECA regulations on fuel costs.

Since ECA presence is different for each voyage and future fuel prices are uncertain, an approach is necessary that captures the uncertain and variable nature of absolute price levels as well as stochastic nature of route length and ECA presence. Simulation allows modelling of a “system imitation as it progresses through time” (Robinson, 2004). Furthermore, uncertainty, complexity, interconnectedness and variability can be accounted for using simulation (Law, 2014; Robinson, 2004). In this case, it assists in obtaining more accurate results for fuel costs under probabilistic fuel prices and stochastic ECA presence.

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6 voyages. “Feederlines” is a logistic service provider in short sea shipping based in the North of Netherlands. More information on “Feederlines” is provided in Chapter 4.

This paper is structured as follows. Chapter 2 covers the conceptual model of the simulation. This answers the first three sub questions by demonstrating the difference in voyage specific fuel type decisions between LNG dual fuel- and conventional short sea vessels and the relationship between fuel type decisions and fuel costs. It also incorporates formal definitions of parameters, variables and objective functions. It also examines both model elements and important assumptions. Secondly, modelling steps are described and include data collection and input analysis. Next, parameters, variables and objective functions are formally defined, including assumptions related to model implementation. It also delivers instructions on how to determine model settings. Chapter 3 addresses the price scenarios used as input for the model and provides a generic input analysis for daily volatility. Chapter 4 engages in explaining the experiment details and settings. Finally, results, discussion, conclusions and limitations are provided.

2. Conceptual model

This chapter presents the scope of the proposed method, assumptions and answers the first two sub questions of this paper. That is, the difference in voyage specific fuel type decisions between conventional and LNG dual fuel short sea merchant vessels as a result of fuel prices and ECA presence and the relationship between voyage specific fuel type decisions and fuel costs. Moreover, it provides a stepwise explanation of the approach proposed in this paper. Finally, it defines parameters, variables, the objective function of fuel type decisions and parameter relationships in estimating average fuel costs per hour.

2.1 Scope of the model

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Figure 2.1.1. Scope of this research indicated in blue

2.2 Assumptions

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8 always attempt to minimize total fuel costs by planning fuel type decisions before starting a specific voyage. Experts from “Feederlines” confirmed such cost minimalizing behavior.

2.3 Modelling steps

Step 1.Fuel type decisions for LNG dual fuel and conventional vessels on one voyage

The first modelling step entails differentiating all possible voyage specific fuel type decisions between LNG dual fuel and conventional vessels. For LNG dual fuel vessels, such decisions consist of planning and choosing the cheapest fuel type on the day of bunkering and departure from both LNG and MGO inside ECA and LNG, MGO and HFO outside ECA.

For conventional vessels, ECA regulations require vessels to use only MGO (0,1% Sulphur) inside ECA (Cullinane and Bergqvist, 2014). For routes outside ECA, a decision can be made to employ either MGO or HFO based on spot prices that apply before departure.

One specific voyage has the following attributes. Firstly, stochastic values of ECA presence. Secondly, time spent in ECA and total travel time. These are linked to the ECA presence attribute for each voyage.

Experts from “Feederlines” indicated that LNG fueled vessels have a maximum action radius of fourteen days in using LNG. That is, such vessels can utilize LNG no longer than fourteen days without re-bunkering. All other fuel types can be used for the remaining time. This is relevant when the travel time of a voyage exceeds 14 days (336 hours) or when time in ECA exceeds 14 days, because a decision must be made whether to employ LNG or MGO either in- or outside ECA or HFO outside ECA. For example, a ship operator may choose to employ LNG for the entire time inside ECA and a portion of the time outside ECA for a total of 336 hours and HFO for the remaining time. However, one may also choose to employ LNG outside ECA and MGO inside ECA. Both decisions result in different fuel costs.

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9 is used for the remaining time in ECA. In case LNG is cheapest, it is utilized for 336 hours and MGO is for the remaining time, in which LNG can be employed either inside or outside ECA. Finally, LNG is employed inside ECA for 336 hours, MGO for the remaining time in ECA and HFO is utilized outside ECA if HFO is cheaper than MGO.

Figure 2.3.1. Fuel type decisions for one voyage for LNG dual fuel vessels

For conventional vessels, MGO is always employed inside ECA due to IMO regulations (Cullinane and Bergqvist, 2014). Outside ECA, fuel prices between HFO and MGO are simply compared and the cheapest fuel type is selected. These decisions are portrayed in Figure 2.3.2.

Figure 2.3.2. Fuel type decisions for one voyage for conventional vessels

Step 2. The relationship between fuel type decisions and fuel costs

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Step 3. Modelling a large number of voyages

A large number of voyages are constructed, which are drawn randomly from the set of historical voyages between 2012 and 2015 performed by “Feederlines”. Modelling a large number of voyages is necessary in estimating average fuel costs per hour voyage when attributes are stochastic (Robinson, 2004). Firstly, a new voyage instance is created from the set of voyages. Based on the voyage specific fuel type decisions illustrated in Figure 2.3.1 and Figure 2.3.2, fuel costs and cumulative fuel costs per hour are calculated. Since the input values are independent and randomly distributed, the mean cumulative fuel costs per hour will converge. Using the confidence interval method (Law, 2014), a new voyage from this set is created as long as the estimated error from the real mean(ε) is larger than 5% with a 95% confidence interval. The set of voyages considered represents one day in the simulation model.

Figure 2.3.2. Modelling a large number of voyages

Step 4. Modelling a large number of days

Average fuel cost per hour for a set of voyages on one specific day is calculated for a large number of days. That is, 8790 days between June 2015 and 2040. The same set of voyages that is randomly drawn from historical data is used for each specific day. That is, all voyage attributes are common random numbers. Using common random numbers is important in comparing outcomes when other model elements are not intended to interact with the random number elements (Robinson, 2004). By repeating the calculations of one set of voyages over a large number of days, the stochastic nature of ECA presence and associated route length can be integrated with probabilistic fuel prices for specific price scenarios in comparing average fuel costs per hour for conventional and LNG dual fuel vessels. A new price experiment is created that is based on a scenario. One scenario is defined as a linear price movement between 2015 and 2040 with fixed price values for each day in this period. One experiment represents a large number of iterations (𝑖𝑡) of a specific price scenario with unique fuel prices and different random deviations for 8790 days. The experiments are conducted for both LNG dual fuel and conventional vessels.

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11 confidence interval. No new iterations are performed when the number of iterations exceeds 30, because when 𝑖𝑡 is sufficiently large, it allows assuming normality for the output data regardless of the underlying distribution (Law, 2014). Normality is an important assumption in using confidence intervals (Law, 2014).

Figure 2.3.3. Modelling a large number of days with many iterations

2.4 Indices, parameters, decision variables and objective function

This section formally outlines parameters and their interrelationships, variables, objective function and the relationship with parameters to fuel costs for both LNG DF and conventional vessels.

2.4.1 Indices

The following indices are used throughout this paper. 𝑖: Index on the set of days (𝑖 = 1, . . ,8790)

𝑘: Index on the set of voyages (𝑘 = 1, . . ,1000) 𝑖𝑡: Index on the set of iterations (𝑖𝑡 = 1, . . ,41)

The index 𝑖 denotes the set of days and is set to the number of days between June 2015 and 2040 (See Chapter 2.3). The index 𝑘 represents the number of voyages that depart on a specific day. It is set to 1000 voyages in order to ensure sufficient voyages are available for the estimated error from the real mean of the output data (ε) to be larger than 5% with a 95% confidence interval. The index 𝑖𝑡 denotes the set of iterations for a specific experiment. It is set to 41 iterations to also ensure sufficient iterations are available for ε to be larger than 5%.

2.4.2 Parameters

The following parameters are defined and explained in implementing the model. 𝑈𝐻𝐹𝑂 𝑀𝑡_{: HFO consumption per hour in metric ton}

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12 𝑈𝐿𝑁𝐺 𝑀𝑡_{: LNG consumption per hour in metric ton}

𝑇_𝑀𝑎𝑥𝐿𝑁𝐺_{: Maximum travel time in using LNG (𝑇}

𝑀𝑎𝑥𝐿𝑁𝐺= 336)

𝑉_𝑖: Set of total voyages for day 𝑖

𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_{: 𝑇otal travel time in hours of voyage k on day i (𝑖 = 1, . . ,8790)∀𝑘 ∈ 𝑉} 𝑖

𝑇_𝑘,𝑖𝐸𝐶𝐴_{: Hours spent in ECA of voyage k on day 𝑖 (𝑖 = 1, . . ,8790) ∀𝑘 ∈ 𝑉} 𝑖

𝑇_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴: Hours spent outside ECA of voyage k on day 𝑖 (𝑖 = 1, . . ,8790) ∀𝑘 ∈ 𝑉_𝑖 𝐸_𝑘,𝑖: ECA presence in % of voyage k on day 𝑖 (𝑖 = 1, . . ,8790) ∀𝑘 ∈ 𝑉_𝑖

𝑃_𝑖𝐻𝐹𝑂−𝑏𝑎𝑠𝑒_{: Price HFO base in $ per metric ton on day 𝑖 (𝑖 = 1, . . ,8790)}

𝑃_𝑖𝑀𝐺𝑂−𝑏𝑎𝑠𝑒_{: Price MGO base in $ per metric tonon day 𝑖 (𝑖 = 1, . . ,8790)}

𝑃_𝑖𝐿𝑁𝐺−𝑏𝑎𝑠𝑒: Price LNG base in $ permetric ton on day 𝑖 (𝑖 = 1, . . ,8790) 𝐷_𝑖𝐻𝐹𝑂: Deviation price HFO in $ permetric tonon day 𝑖 (𝑖 = 1, . . ,8790) 𝐷_𝑖𝑀𝐺𝑂: Deviation price MGO in $ per metric ton on day 𝑖 (𝑖 = 1, . . ,8790) 𝐷_𝑖𝐿𝑁𝐺: Deviation price LNG in $ per metric ton on day 𝑖 (𝑖 = 1, . . ,8790) 𝑃_𝑖𝐻𝐹𝑂: 𝑃rice HFO in $ per metric ton on day 𝑖 (𝑖 = 1, . . ,8790)

𝑃_𝑖𝑀𝐺𝑂: Price MGO in $ permetric ton on day 𝑖 (𝑖 = 1, . . ,8790) 𝑃_𝑖𝐿𝑁𝐺: Price LNG in $ per metric tonon day 𝑖 (𝑖 = 1, . . ,8790) 𝑀: Multiplier of price baseline slope coefficient

The fuel consumption per hour is described by (𝑈𝐻𝐹𝑂, 𝑈𝑀𝐺𝑂, 𝑈𝐿𝑁𝐺) in metric ton as provided by “Feederlines”. It is corrected for British Thermal Units (mmBTU), in which mmBTU represents the caloric value or energy content in fuel. It is set to fixed values (See Table 3, Appendix).

𝑇_𝑀𝑎𝑥𝐿𝑁𝐺_{denotes the maximum time in which a vessel is able to sail on LNG and it is fixed and set to 336}

hours (14 days) as confirmed by “Feederlines”. 𝑉𝑖 is the set of total voyages generated from historical

data for day 𝑖 and represents a stream of common random numbers containing ECA presence and total travel time. Each new voyage developed in the simulation model is obtained from this set. 𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_{, 𝑇}

𝑘,𝑖𝐸𝐶𝐴 and 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴 represent the total travel time, time in ECA and time outside ECA

respectively for a specific voyage 𝑘 on day 𝑖. These are a member of the set of total voyages and contain for day 𝑖. 𝐸𝑘,𝑖 conveys the percentage of time spent in ECA. It is given by:

𝐸_𝑘,𝑖 = 𝑇_𝑘,𝑖𝐸𝐶𝐴_/𝑇

𝑘,𝑖𝑇𝑜𝑡𝑎𝑙 (1)

(𝑃_𝑖𝐻𝐹𝑂−𝑏𝑎𝑠𝑒_{, 𝑃}

𝑖𝑀𝐺𝑂−𝑏𝑎𝑠𝑒, 𝑃𝑖𝐿𝑁𝐺−𝑏𝑎𝑠𝑒) represent the price trend baselines for day 𝑖 and are based on

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13 𝑖. It is assumed that the associated values can be generated from a probability or empirical distribution. (𝑃𝑖𝐻𝐹𝑂, 𝑃𝑖𝑀𝐺𝑂, 𝑃𝑖𝐿𝑁𝐺) denote the final prices that apply on day 𝑖 and provide the input

for which fuel type decisions are made for each voyage. For each fuel type, the prevailing price of (𝑃_𝑖𝐻𝐹𝑂_,𝑃

𝑖𝑀𝐺𝑂, 𝑃𝑖𝐿𝑁𝐺) on day 𝑖 is given by:

𝑃_𝑖𝑗 = 𝑃_𝑖𝑗,𝑏𝑎𝑠𝑒+ 𝐷_𝑖𝑗Where 𝑗={𝐿𝑁𝐺, 𝑀𝐺𝑂, 𝐻𝐹𝑂} (2) Finally, 𝑀 denotes the multiplier of the price baseline slope coefficient and is used to steepen the trend lines for each price scenario. This facilitates conducting sensitivity analyses for extreme variants of the price scenarios stipulated in chapter 3.

2.4.3 Decision variables

As mentioned before, the main problem is concerned with estimating the mean fuel costs per hour for both conventional ships and newly built ships that employ dual fuel LNG engines. As such, the following decision variables are identified that provide the model output.

𝑋_𝑘,𝑖𝐿𝑁𝐺_{: Indicates whether LNG is cheapest inside or outside ECA for voyage k on day 𝑖}

𝑋_𝑘,𝑖𝐿𝑁𝐺_{= {}1, if 𝑃𝑖𝐿𝑁𝐺<𝑃𝑖𝑀𝐺𝑂 and 𝑃𝑖𝐿𝑁𝐺<𝑃𝑖𝐻𝐹𝑂

0, if 𝑃_𝑖𝐿𝑁𝐺>𝑃_𝑖𝑀𝐺𝑂or 𝑃_𝑖𝐿𝑁𝐺>𝑃_𝑖𝐻𝐹𝑂

𝑋_𝑘,𝑖𝑀𝐺𝑂_{: Indicates whether MGO is cheapest inside or outside ECA for voyage k on day𝑖}

𝑋_𝑘,𝑖𝑀𝐺𝑂_{= {}1, if 𝑃𝑖𝑀𝐺𝑂<𝑃𝑖𝐿𝑁𝐺 and 𝑃𝑖𝑀𝐺𝑂<𝑃𝑖𝐻𝐹𝑂

0, if 𝑃_𝑖𝑀𝐺𝑂>𝑃_𝑖𝐿𝑁𝐺 or 𝑃_𝑖𝑀𝐺𝑂>𝑃_𝑖𝐻𝐹𝑂

𝑋_𝑘,𝑖𝐻𝐹𝑂: Indicates whether HFO is cheapest inside or outside ECA for voyage k on day 𝑖

𝑋_𝑘,𝑖𝐻𝐹𝑂= {1, if 𝑃𝑖𝐻𝐹𝑂<𝑃𝑖𝐿𝑁𝐺 and 𝑃𝑖𝐻𝐹𝑂<𝑃𝑖𝑀𝐺𝑂 0, if 𝑃_𝑖𝐻𝐹𝑂_>𝑃

𝑖𝐿𝑁𝐺 or 𝑃𝑖𝐻𝐹𝑂>𝑃𝑖𝑀𝐺𝑂

𝐶_𝑘,𝑖𝐸𝐶𝐴_{: Fuel costs of voyage k on day 𝑖 inside ECA(𝑖 = 1, . . ,8790)}

𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴: Fuel costs of voyage k on day 𝑖 outside ECA (𝑖 = 1, . . ,8790) 𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_{: Total fuel costs of voyage k on day 𝑖 (𝑖 = 1, . . ,8790)}

𝐶_𝑘,𝑖𝐶𝑢𝑚_{: Cumulative mean fuel costs of voyage 𝑘 𝑜n day 𝑖 (𝑖 = 1, . . ,8790)}

𝐶_𝑖𝑚𝑒𝑎𝑛_{: Mean fuel costs per hour for day 𝑖 (𝑖 = 1, . . ,8790)}

𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚_{: Mean fuel costs per hour as main result for one experiment}

(𝑋_𝑘,𝑖𝐿𝑁𝐺, 𝑋_𝑘,𝑖𝑀𝐺𝑂, 𝑋_𝑘,𝑖𝐻𝐹𝑂) constitute binary variables that indicate whether or not the corresponding fuel type is cheapest for voyage 𝑘 on day 𝑖. In that case, it holds the value one, whereas it holds zero in other cases. Its value is obtained separately for voyages inside and outside ECA. Furthermore, (𝐶_𝑘,𝑖𝐸𝐶𝐴_{, 𝐶}

𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴, 𝐶𝑘,𝑖𝑇𝑜𝑡𝑎𝑙) embody ECA, non-ECA and total fuel costs respectively for voyage 𝑘 on day

𝑖. Furthermore, 𝐶𝑘,𝑖𝐶𝑢𝑚 denotes cumulative mean fuel costs and is necessary in calculating ε in using

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14 which 𝐶𝑖𝑚𝑒𝑎𝑛 = 𝐶𝑘,𝑖𝐶𝑢𝑚 when ε is larger than 5%. 𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 denotes the mean fuel costs per hour as

the main outcome of a specific experiment.

2.4.4 Objective function

In executing the decisions illustrated in Figure 2.3.1 and 2.3.2, the objective for all fuel type decisions is to minimize costs for each voyage on day 𝑖 and is defined as:

𝑚𝑖𝑛 𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙

Since following the decisions in Chapter 2.3.1 leads to the lowest fuel costs for each voyage, this objective function is relatively simply and can be solved in reasonable time for each voyage calculation.

2.4.5 Fuel costs for Dual fuel LNG

For voyages of dual fuel LNG vessels in which the total travel time is lower than the LNG tank capacity constraint, fuel costs are simply determined by the choice between LNG and MGO inside ECA, whereas LNG, MGO or HFO are used outside ECA. In any case, if MGO is cheapest, the entire voyage is always performed using MGO. In case 𝑃𝑖𝐻𝐹𝑂<𝑃𝑖𝑀𝐺𝑂< 𝑃𝑖𝐿𝑁𝐺, HFO is employed outside ECA and

MGO inside ECA (See decisions 1, 2, 3, 6, 7 and 8 in Figure 2.3.1). Total fuel costs for these instances are represented by:

𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙= 𝐶_𝑘,𝑖𝐸𝐶𝐴+ 𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴 (3) Inside ECA, both MGO and LNG can be deployed fully and the cheapest fuel type can simply be selected. Fuel costs are denoted as:

𝐶_𝑘,𝑖𝐸𝐶𝐴= (𝑃𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑘,𝑖𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ 𝑇𝑘,𝑖𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝑀𝐺𝑂) (4)

For time spent outside ECA, all three fuel types can be utilized, depending on the cheapest ECA compliant fuel. Fuel costs outside ECA are expressed as:

𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴= (𝑃𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝑀𝐺𝑂) + (𝑃𝑖𝐻𝐹𝑂∗

𝑈𝐻𝐹𝑂_{∗ 𝑇}

𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝐻𝐹𝑂) (5)

For routes in which total travel time exceeds the LNG tank capacity constraint, only a portion of a voyage can be performed utilizing LNG. In particular, voyages in which 𝑇_𝑘,𝑖𝐸𝐶𝐴<𝑇𝑀𝑎𝑥𝐿𝑁𝐺 allow LNG to be

potentially used for the entire time in ECA and a portion for the time outside ECA (See decisions 4 and 5 in Figure 2.3.1). In this case, fuel costs inside ECA depend on fuel prices, fuel consumption per hour, the time spent in ECA and whether or not MGO or LNG is cheapest. It is denoted as:

𝐶_𝑘,𝑖𝐸𝐶𝐴_{= (𝑃}

𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑘,𝑖𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ 𝑇𝑘,𝑖𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝑀𝐺𝑂) (6)

The fuel cost for the time of a voyage outside ECA is again determined by fuel type decisions between all three fuel types. For voyages outside ECA in which 𝑇_𝑘,𝑖𝐸𝐶𝐴<𝑇𝑀𝑎𝑥𝐿𝑁𝐺 and LNG is the cheapest

fuel type, LNG is employed for the time in which it is still available and the second cheapest fuel type is selected for the remaining time. In case MGO is the second cheapest fuel type (𝑃𝑖𝑀𝐺𝑂<𝑃𝑖𝐻𝐹𝑂), it is

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15 𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴_{= (𝑃}

𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ (𝑇𝑀𝑎𝑥𝐿𝑁𝐺− 𝑇𝑘,𝑖𝐸𝐶𝐴) ∗ 𝑋𝑘,𝑖𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ (𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴− (𝑇𝑀𝑎𝑥𝐿𝑁𝐺−

𝑇_𝑘,𝑖𝐸𝐶𝐴₎₎₎ ₍₇₎

In case HFO is the second cheapest fuel type (𝑃𝑖𝐻𝐹𝑂< 𝑃𝑖𝑀𝐺𝑂) for voyages outside ECA in which

𝑇_𝑘,𝑖𝐸𝐶𝐴_<𝑇

𝑀𝑎𝑥𝐿𝑁𝐺 , costs outside ECA are denoted as:

𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴_{= (𝑃}

𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ (𝑇𝑀𝑎𝑥𝐿𝑁𝐺− 𝑇𝑘,𝑖𝐸𝐶𝐴) ∗ 𝑋𝑘,𝑖𝐿𝑁𝐺) + (𝑃𝑖𝐻𝐹𝑂∗ 𝑈𝐻𝐹𝑂∗ (𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴− (𝑇𝑀𝑎𝑥𝐿𝑁𝐺−

𝑇_𝑘,𝑖𝐸𝐶𝐴₎₎₎ ₍₈₎

For passages in which 𝑇𝑘,𝑖𝐸𝐶𝐴> 𝑇𝑀𝑎𝑥𝐿𝑁𝐺 and 𝑃𝑖𝐻𝐹𝑂<𝑃𝑖𝐿𝑁𝐺< 𝑃𝑖𝑀𝐺𝑂, HFO is selected outside ECA, LNG

inside ECA for 𝑇𝑀𝑎𝑥𝐿𝑁𝐺 and MGO for 𝑇𝑘,𝑖𝐸𝐶𝐴− 𝑇𝑀𝑎𝑥𝐿𝑁𝐺 (See decision 9 in Figure 2.3.1). Accordingly, total fuel

costs are:

𝐶_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴= (𝑃𝑖𝐻𝐹𝑂∗ 𝑈𝐻𝐹𝑂∗ 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴) + (𝑃𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑀𝑎𝑥𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ (𝑇𝑘,𝑖𝐸𝐶𝐴−

𝑇_𝑀𝑎𝑥𝐿𝑁𝐺₎ ₍₉₎

For all voyages of LNG dual fuel vessels in which 𝑇_𝑘,𝑖𝐸𝐶𝐴 > 𝑇𝑀𝑎𝑥𝐿𝑁𝐺and where 𝑃𝑖𝐿𝑁𝐺<𝑃𝑖𝑀𝐺𝑂<𝑃𝑖𝐻𝐹𝑂, both

LNG and MGO can be utilized at any point during the voyage since both fuel types are allowed inside and outside ECA (See decision 10 in Figure 2.3.1). That is, LNG is employed for 336 hours and MGO for the remaining travel time irrespective of the time spent in- and outside ECA. Under this unique condition, the total fuel costs are expressed as:

𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙= (𝑃𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑀𝑎𝑥𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ (𝑇𝑘,𝑖𝑇𝑜𝑡𝑎𝑙− 𝑇𝑀𝑎𝑥𝐿𝑁𝐺)) (10)

Finally, for passages in which 𝑇𝑘,𝑖𝐸𝐶𝐴> 𝑇𝑀𝑎𝑥𝐿𝑁𝐺 and where 𝑃𝑖𝐿𝑁𝐺<𝑃𝑖𝐻𝐹𝑂 < 𝑃𝑖𝑀𝐺𝑂, LNG is employed fully

inside ECA whereas MGO is employed for the remaining time in ECA. HFO is utilized outside ECA, because LNG is no longer available and HFO is the second cheapest fuel type.

𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙= (𝑃𝑖𝐿𝑁𝐺∗ 𝑈𝐿𝑁𝐺∗ 𝑇𝑀𝑎𝑥𝐿𝑁𝐺) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ (𝑇𝑘,𝑖𝐸𝐶𝐴− 𝑇𝑀𝑎𝑥𝐿𝑁𝐺)) + (𝑃𝑖𝐻𝐹𝑂∗ 𝑈𝐻𝐹𝑂∗ 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴)

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2.4.6 Fuel costs for conventional

Because conventional ships do not have the possibility to use LNG, they are obliged to use MGO inside ECA. Outside ECA, they can choose the cheapest fuel type between HFO and MGO.

𝐶_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_{= (𝑃} 𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ 𝑇𝑘,𝑖𝐸𝐶𝐴) + (𝑃𝑖𝑀𝐺𝑂∗ 𝑈𝑀𝐺𝑂∗ 𝑇𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴∗ 𝑋𝑘,𝑖𝑀𝐺𝑂) + (𝑃𝑖𝐻𝐹𝑂∗ 𝑈𝐻𝐹𝑂∗ 𝑇_𝑘,𝑖𝑛𝑜𝑛−𝐸𝐶𝐴_{∗ 𝑋} 𝑘,𝑖𝐻𝐹𝑂) (12)

𝟑. 𝐏𝐫𝐢𝐜𝐞 𝐬𝐜𝐞𝐧𝐚𝐫𝐢𝐨𝐬

3.1 Price forecasts

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16 2040 with fixed price values for each day in this period. These stem from forecasts of the OECD, International Energy Agency (IEA) and the U.S. Energy Information Administration (EIA) and are used as model input.

The first scenario entails that all prices remain relatively low and it is labeled as the “Low” scenario. It reflects price levels that are similar to levels in 2015. Both HFO and MGO illustrate decreasing prices, whereas LNG tends to increase over time. Furthermore, the “Medium” scenario entails modest price rises for all fuel types. In particular, increases in MGO prices are in line with expectations of other studies projecting demand rises and increases in desulfurization costs (Acciaro, 2014; Wang & Notteboom, 2013). Finally, the “High” scenario reflects strongly rising prices and represents relatively extreme price levels by 2040 compared to current price levels in 2015. The fact the LNG prices appear lower relative to other fuel types in all scenarios is confirmed by Acciaro (2014) who suggested that increased competitiveness in gas markets may keep LNG prices low. MGO prices are consistently above LNG and HFO prices due to a more expensive production process associated with desulfurization (DNV, 2012; Wang and Notteboom, 2014).

3.2 Price scenarios as model input

All scenarios by DNV (2012) are chosen, because they stem from multiple and reliable sources. Furthermore, the “Low” scenario reflects prices similar to current price levels (Bunkerworld, 2015). The “Medium” and “High” scenario reflect relative extreme price levels, which allows fuel cost comparisons between LNG and conventional configurations for highly unfavorable future price trends. Limited access to data prohibited obtaining more up-to-date price projections. The scenarios provided in the model can be used for future analyses.

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Figure 3.2.1 Scenario “Low” (DNV, 2012)

Figure 3.2.2 Scenario “Medium” (DNV, 2012)

Figure 3.2.3 Scenario “High” (DNV, 2012)

3.3 Daily volatility as model input

3.3.1 Historical daily volatility

In this paper, daily volatility represents generic input data that can be used in future analyses with different linear price scenarios. Historical daily deviations were obtained from past price trends. A simple ordinary least squares (OLS) regression model was established for observable past trends of each fuel type, because it allows fitting linear trend lines to historical data to obtain daily deviations from this trend line. According to Brailsford and Faff (1996), simple regression models can be superior to more complex volatility forecasting models in forecasting price volatility. For Intermediate Fuel Oil (IFO380 or HFO) historical prices in Rotterdam, an upward trend was observed for 1351 days between the Januari 2009 and September 2012 (Bunkerindex, 2015). For LNG US-Henry Hub spot prices, a downward trend was noticed for 3433 days between December 2005 and May 2015 (IEA, 2015). For MGO spot prices in Rotterdam, an upward trend was found between Januari 2009 and March 2012 (Bunkerindex, 2015). An OLS linear regression was established for all

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18 prices and the associated trend period. Furthermore, daily deviations from the regression line were obtained and filtered by removing time intervals larger than one day, because equally spaced intervals and removal of discontinuities facilitate time series analysis (Brockwell, 2013; Eckner, 2014). In obtaining historical daily volatility, the following expression is used:

𝑉𝑜𝑙_𝑖𝑗= 𝑂_𝑖𝑗− (𝐼𝑗_{∗ 𝑖) + 𝑃}

0𝑗 Where 𝑗={𝐿𝑁𝐺, 𝑀𝐺𝑂, 𝐻𝐹𝑂} (13)

Where 𝑉𝑜𝑙_𝑖𝑗 represents volatility on day 𝑖 for a specific fuel type 𝑗, 𝑂_𝑖𝑗the observation on day 𝑖 for fuel type 𝑗,𝐼𝑗 the regression co-efficient for fuel type 𝑗and 𝑃₀𝑗 the fuel specific price on day 0. The baseline value on day 𝑖 ((𝐼𝑗∗ 𝑖) + 𝑃₀𝑗) is subtracted from the observation 𝑂_𝑖𝑗 to obtain the volatility of day 𝑖.

3.3.2 Future daily volatility

In determining future volatility for all fuel types, it is assumed that all fuel prices will exhibit volatility patterns in the future that are similar to historical data (see Chapter 2.2). It was found that the LNG US-Henry Hub spot price exhibits highly volatile behavior, with daily deviations from the regression line that range between -3.5 and 7.8 dollars per mmBTU and a standard deviation of 1.6. Highly expected future volatility of LNG prices are in line with MGO and illustrates less volatile behavior. Volatility of MGO ranged between -2.2 and 3.1 dollars per mmBTU and a standard deviation of 1.1. HFO also showed less volatility ranging between -4.2 and 2.7 with a standard deviation of 1.1 (See Table 4, Appendix).

In generating data for the values of (𝐷𝑖𝐻𝐹𝑂, 𝐷𝑖𝑀𝐺𝑂, 𝐷𝑖𝐿𝑁𝐺) that serve as the model input, historical

values for 𝑉𝑜𝑙𝑖 were fitted to common probability distributions. Kolmogorov-Smirnov (KS)

goodness-of-fit tests with significance levels of 0.05 and 0.01 are employed in assessing whether historical daily deviations from the regression line can be fitted to common probability distributions. This test and associated significance levels are commonly used in literature in matching historical data to theoretical distributions.

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4. Experiments

This chapter outlines the input analyses of the data provided by “Feederlines”, the experiment settings and definitions for the simulation model.

4.1 The case of Feederlines

“Feederlines” is a logistic service provider situated in Groningen (the Netherlands) that manages short sea dry cargo vessels which operate in the North- and Baltic Sea. It manages 37 ships including feeder vessels ranging from 2500 to 9000 Tonnage Dead Weight (TDW) and containerships in the range of 290 to 750 Twenty-foot Equivalent Unit (TEU). The uncertainty with regard to LNG DF feasibility is highly relevant for “Feederlines”, because it is highly active in the ECA regions and manages relatively small size cargo vessels. Vessels considered in this study are newly built ships with an average fuel consumption of 0.33 Mt per hour for HFO and MGO and 0.45 Mt per hour for LNG. The same fuel consumption for HFO and MGO applies to conventional vessels.

“Feederlines” was chosen, because of their extensive expertise on parameters that have been used as model input. These include ECA presence, time spent in ECA, total travel time and fuel consumption. Furthermore, the simulation model was verified and validated by experts of “Feederlines”. This included regular meetings with experts to ensure all necessary details were incorporated in the conceptual model. Furthermore, data on routes and ECA presence as provided by “Feederlines” contained accurate logs on every single voyage.

4.1 Data on voyages

“Feederlines” has provided company specific data on total travel time, time inside ECA and time outside ECA for 132 voyages between 2012 and 2015. The data has been used in calculating ECA presence (See chapter 2.4.2) for each voyage. Total travel time ranged between 17.2 and 626.4 hours with a mean of 208.8 hours (See Table 4.1.1). Values for time spent in ECA are found between 0 and 326.2 hours with a mean of 104.9 hours. Accordingly, time in ECA is lower than the LNG fuel tank constraint for time spent in ECA and higher for total travel time. ECA presence ranges between 0 and 100% with a mean of 50.7%

Data on ECA presence was evaluated using the KS goodness-of-fit test with in order to identify a fit with common probability distributions. No fit was found between ECA presence and any of common probability distributions (𝑝=0.00). Therefore, an empirical distribution was created in which values for ECA presence, associated total travel time and time in ECA were generated by selecting randomly from a pool of historical data. Using this approach, the total number of voyages (𝑉𝑖) was extended to

contain 1000 voyages, because a very large amount ensures that enough voyages are available for the estimated error from the real mean (ε) to be smaller than 5% with a 95% confidence interval (See Chapter 2.3.3).

Total travel time (Hours)

Time in ECA (Hours) ECA presence

Mean 208.8 104.9 50.7%

Range 17.2 -626.42 0 - 326.16 0 – 100%

Standard deviation 112.1 89.9 0.424

Normal distribution No (𝑃=0.00) No (𝑃=0.00) No (𝑃=0.00)

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4.2 Experiment settings

One experiment represents one specific price scenario with unique final fuel prices of (𝑃𝑖𝐻𝐹𝑂, 𝑃𝑖𝑀𝐺𝑂, 𝑃𝑖𝐿𝑁𝐺) for each day. It constitutes 8790 days and a large number of iterations with

fixed values of (𝑃𝑖𝐻𝐹𝑂−𝑏𝑎𝑠𝑒, 𝑃𝑖𝑀𝐺𝑂−𝑏𝑎𝑠𝑒, 𝑃𝑖𝐿𝑁𝐺−𝑏𝑎𝑠𝑒) and different values of (𝐷𝑖𝐻𝐹𝑂, 𝐷𝑖𝑀𝐺𝑂, 𝐷𝑖𝐿𝑁𝐺).A

database of 400.000 common random numbers for (𝐷𝑖𝐻𝐹𝑂, 𝐷𝑖𝑀𝐺𝑂, 𝐷𝑖𝐿𝑁𝐺) was constructed from

probability distributions and empirical distributions for each fuel type to ensure the availability of sufficient random data for an appropriate run-length. The random values represent common random numbers, in which the same values of volatility are used for each fuel type in other experiments. This facilitates comparison. For each experiment, a minimum of 30 iterations are performed with different random values taken from the database, because it allows assuming normality of the output data, which is a key requirement for confidence intervals (Law, 2014).

4.3 Experiment definitions

The following experiments have been performed (See Table 4.3.1).

4.3.1 Stochastic ECA presence and stochastic price levels

The first three experiments entail the “Low”, “Medium” and “High” price scenario as specified in Chapter 3 (See Figure 3.2.1, 3.2.2 and 3.2.3; Table 4.3.1) and deliver the output value of the long term mean fuel costs per hour (𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚). Both ECA presence, associated travel times and price levels are stochastic such as described in Chapter 3 and 4.1. For purposes of sensitivity analysis, the same experiments are repeated in which the slopes of the trend lines for each price scenario are amplified. That is, the slope coefficient of the trend lines for (𝑃_𝑖𝐻𝐹𝑂−𝑏𝑎𝑠𝑒, 𝑃_𝑖𝑀𝐺𝑂−𝑏𝑎𝑠𝑒, 𝑃_𝑖𝐿𝑁𝐺−𝑏𝑎𝑠𝑒) are multiplied by both two and four (𝑀=2 and 4, See Table 4.3.1). Such amplified price trends represent an extremely low price scenario for “Low” and extreme price levels for both “Medium” and “High”, because this provides more insights in the behavior of long term mean fuel costs per hour. The data provided by “Feederlines” indicates a higher fuel consumption per metric ton for ships utilizing LNG compared to HFO and MGO. Therefore, the same set of experiments are repeated in which fuel consumption per hour of LNG (𝑈𝐻𝐹𝑂 𝑀𝑡₎_{is set to both 0.45 and 0.33 Mt per hour (See Table}

3, Appendix). This illustrates a realistic proposition and one in which LNG consumption equals both other fuel types. This provides insights on the extent to which higher LNG fuel consumption may result in higher long term mean fuel costs per hour for specific price scenarios.

4.3.2 Deterministic ECA presence and stochastic price levels

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21 A positive turning point for ECA presence denotes the minimal level of ECA presence needed for LNG DF to be cheaper than conventional, whereas a negative value either implies higher or lower costs for LNG DF compared to conventional for all levels of ECA presence.

For purposes of sensitivity analyses, every experiment is conducted in which fuel consumption per hour of LNG (𝑈𝐿𝑁𝐺 𝑀𝑡₎_{is set to both 0.45 and 0.33 Mt per hour. Moreover, both sets of experiments}

have also been repeated to include route lengths that are below 14 days (𝑇𝑘,𝑖𝑇𝑜𝑡𝑎𝑙=100>𝑇𝑀𝑎𝑥𝐿𝑁𝐺) and

which exceed 14 days (𝑇𝑘,𝑖𝑇𝑜𝑡𝑎𝑙=500>𝑇𝑀𝑎𝑥𝐿𝑁𝐺), to consider the effect of the LNG tank constraint. Finally,

it is investigated to what extent the output values change when changing the slope coefficient of the price baselines by multiplying these with two and four (𝑀=2 and 4).

4.3.3 Deterministic ECA presence and deterministic price levels

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22

Price scenarios Experimental factors Output

Slope coefficient multiplier (𝑴)

Experiments ECA presence Price levels Fuel

consumption per hour* Total Travel time Decision variables

1 Low Stochastic* Stochastic 𝑈𝐻𝐹𝑂 𝑀𝑡 = 0.33 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45} And 𝑈𝐻𝐹𝑂 𝑀𝑡_{= 0.33} 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.33} Stochastic* (Linked to ECA presence) Mean fuel costs per hour (𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚) Medium High 2 Low Medium High 4 Low Medium High 1 Low Deterministic (ranging from 1 to 100) Stochastic 𝑈𝐻𝐹𝑂 𝑀𝑡 = 0.33 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45} And 𝑈𝐻𝐹𝑂 𝑀𝑡_{= 0.33} 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.33} 𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_< 𝑇_𝑀𝑎𝑥𝐿𝑁𝐺 And 𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙> 𝑇_𝑀𝑎𝑥𝐿𝑁𝐺 Identify turning point ECA presence Mean fuel costs per hour (𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚) Medium High 2 Low Medium High 4 Low Medium High 1 Low Deterministic (ranging from 1 to 100) Deterministic (Price levels by Burel, 2013) 𝑈𝐻𝐹𝑂 𝑀𝑡_{= 0.33} 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45} And 𝑈𝐻𝐹𝑂 𝑀𝑡_{= 0.33} 𝑈𝑀𝐺𝑂 𝑀𝑡_{= 0.33} 𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.33} 𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_< 𝑇_𝑀𝑎𝑥𝐿𝑁𝐺 And 𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙> 𝑇_𝑀𝑎𝑥𝐿𝑁𝐺 Identify turning point ECA presence Mean fuel costs per hour (𝐶𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚) Medium High 2 Low Medium High 4 Low Medium High

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23

5. Results

This chapter outlines the main results of the experiments. Firstly, the main results are provided that allow investigating under which price scenarios fuel type decisions lead to lower fuel costs for LNG DF vessels compared to conventional vessels and differences between the current approaches and deterministic approaches. These include stochastic prices and ECA presence. Secondly, fuel cost results and intersection points between LNG DF and conventional are revealed for deterministic ECA presence and stochastic prices. Finally, this is repeated for deterministic ECA presence and deterministic prices.

Normality tests including the Kolmogorov-Smirnov and the Shapiro-Wilk test, revealed that all output data is normally distributed in line with the normality assumption implicit in using confidence intervals (Law, 2014) (See Table 1, Appendix).

5.1 Fuel costs for stochastic ECA presence and stochastic prices

5.1.1 Normal LNG fuel consumption

The experiments for the “Low” price scenario in which LNG fuel consumption is set to a realistic value (𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.45) and in which the price baseline slope coefficient is normal (𝑀=1) revealed significantly higher average fuel costs per hour for LNG DF vessels compared to conventional vessels ($136.24 for LNG DF and $125.51 for conventional, see Figure 5.1.1) (p=0.00, See Table 5, Appendix). For the “Medium” and “High” price scenario, LNG DF fuel costs were found to be significantly lower than conventional (p=0.00, See Table 5, Appendix). That is, $305.45 and $338.18 for LNG DF and conventional respectively in the “Medium” price scenario, whereas $492.29 and $513.67 in the “High” scenario.

Figure 5.1.1 Fuel costs per hour (normal LNG fuel consumption: 𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.45, 𝑀=1)

The same set of experiments have been repeated in which the multiplier of the slope coefficient of each price baseline is increased (𝑀=2 and 4). As can be seen in in Figure 5.1.2, fuel costs per hour decrease in price scenario “Low” as a result of more sharply decreasing HFO and MGO prices and

0 100 200 300 400 500 600

Scenario Low Scenario Medium Scenario High

Fu e l c o sts ($ p e r h o u r)

Mean fuel costs per hour

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24 increasing LNG prices (See Figure 3.2.1), even though fuel type decisions for conventional ships still prove to be cheaper than LNG DF. For price scenario “Medium”, an intersection point was found in which LNG DF becomes more expensive than conventional for 𝑀=4. Larger price coefficients in scenario “Medium” yield more sharply increasing costs for LNG DF. Finally, LNG DF proves to be cheaper than conventional vessels in scenario “High” for more extreme price levels and conventional vessels become highly unfavorable. This can be attributed to high MGO prices relative to lower LNG prices as a result of changing 𝑀.

Figure 5.1.2 Sensitivity of fuel costs per hour for multiplier of price slope coefficient (𝑀) (𝑈𝐿𝑁𝐺 𝑀𝑡 =

0.45)

5.1.2 Reduced LNG fuel consumption

For experiments in which the price baseline slope coefficient is normal (𝑀=1) and LNG fuel consumption is reduced to equal fuel consumption of all other fuel types (𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.33), LNG DF vessels illustrate significantly lower fuel costs per hour in all price scenarios (See Figure 5.1.3; p=0.00, See Table 5, Appendix). This is caused by the fact that LNG DF vessels have the option to always use LNG whenever it is cheaper. Since LNG prices are likely to fall below MGO prices and fuel consumption is similar, LNG DF becomes less costly.

0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 Fu e l c o sts ($ p e r h o u r)

Multiplier of slope coefficient for price baseline (M)

Sensitivity of fuel costs for multiplier of price baseline

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25

Figure 5.1.3 Fuel costs per hour (Reduced LNG fuel consumption: 𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.33, 𝑀=1)

Plotting fuel costs per hour for steeper price trends of all price scenarios revealed significantly lower fuel costs for LNG DF fuel type decisions compared to conventional vessels in scenario “High”, while costs intersect and become higher in scenario “Medium” (See Figure 5.1.4; p=0.00, See Table 5, Appendix). It is worth noting that in scenario “Low”, LNG DF is marginally less costly than conventional, which may be attributed to more sharply decreasing MGO prices and increasing LNG prices for 𝑀=4. Due to the high MGO price in scenario “Medium” and “High”, fuel type decisions for conventional ships result in significantly higher fuel costs per hour compared to LNG DF.

Figure 5.1.4 Sensitivity analysis of fuel costs per hour for multiplier of price slope coefficient (𝑀)

(𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.33) 0 100 200 300 400 500 600 700

Scenario Low Scenario Medium Scenario High

Fu e l c o sts ($ p e r h o u r)

Mean fuel costs per hour

LNG Dual Fuel Conventional 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 Fu e l c o sts ($ p e r h o u r)

Multiplier of slope coefficient for price baseline (M) Sensitivity of fuel costs

for price coefficient

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26 It is apparent that the normal level of fuel consumption for LNG results in significantly higher costs compared to a reduced LNG fuel consumption level. For scenario “Low”, LNG DF is more expensive than conventional with normal levels of LNG fuel consumption (𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.45), whereas it is cheaper than conventional for reduced LNG fuel consumption (𝑈𝐿𝑁𝐺 𝑀𝑡 = 0.33). Furthermore, LNG DF fuel type decisions result in lower costs for scenarios “Medium” and “High”, whereas LNG DF is more expensive than conventional in scenario “Medium” for 𝑀=4 (See Figure 5.1.2).

For normal prices (𝑀=1), fuel costs are drastically reduced for reduced LNG fuel consumption compared to normal levels in scenario “Medium” and “High”. LNG is more expensive than conventional for reduced LNG fuel consumption in scenario “Low” (See Figure 5.1.5).

Figure 5.1.5 Sensitivity of fuel costs for LNG fuel consumption (𝑀=1)

5.2 Fuel costs for deterministic ECA presence and stochastic prices

5.2.1 Fuel costs as a function of ECA presence and travel time

In treating ECA presence as deterministic, it was found that LNG DF is more expensive than conventional in scenario “Low” for all levels of ECA presence, in which route length is below the LNG fuel tank constraint and LNG fuel consumption is normal (See Figure 5.2.1). This is notably caused by higher fuel consumption levels of LNG and corresponds to the findings in Chapter 5.1.2 that indicate that LNG DF is cheaper for lower consumption levels.

For travel times exceeding the LNG tank constraint, LNG DF is still more expensive than conventional for all levels of ECA presence (See Figure 5.2.2). Furthermore, a small curve is observed for LNG DF costs where ECA presence levels exceed 67.2%. This illustrates the point at which the LNG tank constraint is exceeded and the second cheapest fuel type is selected. Since fuel prices are in close proximity for scenario “Low” (See Figure 3.2.1) and LNG fuel consumption exceeds fuel consumption of other fuel types, the second cheapest fuel type may result in slightly lower average fuel costs. This

0 100 200 300 400 500 600 0.3 0.35 0.4 0.45 0.5 Fu e l c o sts ($ p e r h o u r)

LNG Fuel consumption (Mt per hour)

Sensitivity of fuel costs for LNG fuel consumption

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27 is portrayed by a lower slope coefficient of the fuel costs for LNG DF after ECA presence exceeds 67.2%.

Figure 5.2.1 Fuel costs per hour and ECA

presence for scenario Low (𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45,}_𝑇

𝑘,𝑖𝑇𝑜𝑡𝑎𝑙=100<𝑇𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

presence Scenario Low (𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45,}

𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙=500>𝑇𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

Figure 5.2.3 Fuel costs per hour and ECA presence Scenario Medium (𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45,}

𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_=100<𝑇

𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

presence Scenario Medium (𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45,}

𝑇_𝑘,𝑖𝑇𝑜𝑡𝑎𝑙_=500<𝑇

𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

For scenario “Medium”, an intersection is observed at an ECA presence level of 28.9%, in which LNG DF vessels are cheaper than conventional after this point. This applies to vessels in which total travel time is smaller than 14 days and can be explained by the large price spread between MGO and LNG in Figure 3.2.2, in which LNG DF vessels utilize LNG most of the time. Due to highe MGO prices, costs for conventional rise rapidly.

100 110 120 130 140 150 160 170 0% 20% 40% 60% 80% 100% Fu e l c o sts ($ p e r h o u r) ECA presence Fuel costs and ECA presence

Scenario Low LNG DF Conventional 100 110 120 130 140 150 160 0% 20% 40% 60% 80% 100% Fu e l c o ss ($ p e r h o u r) ECA presence Fuel costs and ECA presence

Scenario Low LNG DF Conventional 200 250 300 350 400 450 0% 20% 40% 60% 80% 100% Fu e l c o sts ($ p e r h o u r) ECA Presence ECA presence and fuel costs

Scenario Medium LNG DF Conventional 250 270 290 310 330 350 370 390 0% 20% 40% 60% 80% 100% Fu e l c o ss ($ p e r h o u r) ECA presence ECA presence and fuel costs

Scenario Medium

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28 Routes that exceed 14 days are in favor of LNG DF vessels for ECA presence levels that exceed 18% for scenario “Medium”. At 67.2%, fuel costs for LNG DF increase parallel with costs for conventional vessels, because the LNG tank capacity constraint is exceeded and the second cheapest fuel type is chosen, in which LNG remains cheaper on average.

In the “High” scenario for routes in which LNG fuel consumption is normal and travel time is below the LNG tank constraint, the point in which LNG DF is cheaper than conventional can be found at an ECA presence of 44.1%. After this point, the difference in fuel costs is relatively high and LNG DF vessels obtain a cost advantage.

For scenario “High” with normal LNG fuel consumption and travel time exceeding the LNG tank constraint, fuel costs behave similar to scenario “Medium” (Figure 5.2.4) and LNG DF is cheaper for ECA presence levels higher than 31.2% (See Figure 5.2.6).

presence Scenario High (𝑈𝐿𝑁𝐺 𝑀𝑡_{= 0.45,}_𝑇

𝑘,𝑖𝑇𝑜𝑡𝑎𝑙 =

100<𝑇𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

Figure 5.2.6 Fuel costs per hour and ECA presence for scenario “High” (𝑈𝐿𝑁𝐺𝑀𝑡₌

0.45,𝑇𝑘,𝑖𝑇𝑜𝑡𝑎𝑙 =500>𝑇𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

5.2.2 ECA presence intersection points and LNG fuel consumption

The level of ECA presence in which fuel costs of LNG DF and conventional intersect is influenced by the level LNG fuel consumption.

Results indicate that LNG fuel consumption per hour highly influences the turning point of ECA presence in which LNG DF is cheaper than conventional. For scenario “Medium” and “High”, a large change is observed in the minimum level of ECA presence between normal LNG fuel consumption and reduced fuel consumption (See Figure 5.2.7). This implies that LNG DF is cheaper than conventional for any level of ECA presence. In scenario “Low”, LNG DF is more expensive than conventional for all levels of ECA presence (See Figure 5.2.1). The intersection point in which LNG DF becomes more expensive is negative. Even though such negative intersection provide little meaning on the minimum level of ECA presence in which LNG DF is cheaper than conventional, it does illustrate highly sensitive behavior of the intersection points for both fuel consumption levels. In this

400 450 500 550 600 650 0% 50% 100% Fu e l c o sts ($ p e r h o u r) ECA presence

ECA presence and fuel costs

Scenario High

LNG DF Conventional 400 450 500 550 600 650 0% 20% 40% 60% 80% 100% Fu e l c o sts ($ p e r h o u r) ECA presence ECA presence and fuel costs

Scenario High

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29 case, the negative intersection points are associated with higher costs for LNG DF for all ECA presence levels.

Figure 5.2.7 Sensitivity of LNG fuel consumption for the turning point ECA

presence (𝑇𝑘,𝑖𝑇𝑜𝑡𝑎𝑙= 100<𝑇𝑀𝑎𝑥𝐿𝑁𝐺, 𝑀=1)

5.2.3 Turning point ECA presence and slope of price baseline

The level of ECA presence in which fuel costs of LNG DF and conventional intersect is also altered in changing the multiplier for the slope coefficient of the price baseline (𝑀).

For the “Low” price scenario, the intersection point of fuel costs for both types of vessels is negative and LNG DF is more expensive for any level of ECA presence and price baseline multiplier.

Results indicate that LNG is cheaper than conventional only in scenario “Medium” and “High” with normal LNG fuel consumption. The negative ECA presence intersection point in scenario “Low” is associated with higher costs for LNG DF for all levels of ECA presence as illustrated in Figure 5.2.1. Table 5.2.1 indicates that changing the price baseline multiplier highly affects the minimum level of ECA presence for which LNG DF yields lower costs compared to conventional. In particular, the minimal level of ECA presence ranges between 29% and 74% for the “Medium” price scenario. It increases, because the trend line of LNG may intersect with HFO for large values of 𝑀. In contrary, the minimal level of ECA presence is reduced for larger values of 𝑀 in the high price scenario which may be explained by a larger spread between LNG and HFO prices as a result of changing 𝑀 (See Figure 3.2.3).

For reduced LNG fuel consumption, all negative ECA presence intersection points are associated with LNG DF fuel costs that are lower than conventional for all levels of ECA presence, making LNG DF highly advantageous (See Figure 5.2.1).

-110% -90% -70% -50% -30% -10% 10% 30% 50% 0.3 0.35 0.4 0.45 0.5 EC A p re se n ce

Fuel consumption (Mt per hour)

Sensitivity of LNG fuel consumption for mimimal ECA presence

Scenario Low (M=1) Scenario Medium (M=1)