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j.enpol.2017.10.022

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Energy Policy 112 (2018) 242–257
Contents lists available at ScienceDirect
Energy Policy
journal homepage: www.elsevier.com/locate/enpol
The influence of emission thresholds and retrofit options on airline fleet
planning: An optimization approach
MARK
⁎
Christoph Müller , Karsten Kieckhäfer, Thomas S. Spengler
Institute of Automotive Management and Industrial Production, Technische Universität Braunschweig, Mühlenpfordtstr. 23, D-38106 Braunschweig, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords:
Airline fleet planning
CO2 emissions
Fleet renewal
Retrofit options
Strategic planning and management
The global framework for aviation is given by growth expectation (growth rates of 2–5% p.a.) in combination
with the challenge to reduce the environmental impact. Especially airlines are under increasing pressure due to
ambitious CO2 reduction targets. To reduce fleet emissions, airlines can purchase modern and fuel efficient
aircraft or apply retrofits to the existing fleet (e.g., blended winglets). Decisions on these alternatives are part of
airline fleet planning where the development of fleet size and composition is determined. Focusing on the
transition towards energy-efficient aviation, this paper investigates the influence of emission thresholds and
retrofit options on airline fleet planning by making use of an optimization model. Based on real-world data, the
model is applied to two major European airlines for a planning horizon between 2016 and 2025. The results
indicate that emission thresholds and retrofits can make a significant contribution to achieving short term
emission targets. However, the potential is limited due to existing investment budget constraints and the fact
that retrofits are only available for short- to medium-haul aircraft. This calls for the development and certification of further retrofit programs as well as the deployment of further measures such as bio-/electrofuels or
hybrid electric aircraft.
1. Introduction
The climate impact of aviation is mainly based on emissions of
carbon dioxides (CO2), nitrogen oxides (NOx), aerosols (soot and sulphate), and increased cloudiness in the form of linear contrails as well
as cirrus clouds in the upper troposphere (Burkhardt and Kärcher, 2011;
Lee et al., 2009; Macintosh and Wallace, 2009). On a global scale, CO2
and NOx emissions are the greatest contributors to climate change with
the former contributing thousands of times more emissions than other
products of fuel burning in aviation (Timmis et al., 2015). Since 1980,
fuel-combustion-related CO2 emissions from aviation have increased at
3.6% per year, i.e., almost twice the world’s total growth rate of CO2
emissions (IEA, 2016). Today, the aviation sector accounts for approximately 12% of transport-related emissions and 2% of all humaninduced emissions (ATAG, 2017). In order to cap and eventually lower
the sector’s emissions despite expected growth rates of 2–5% in air
traffic (Airbus, 2017a; Meleo et al., 2016), the European Commission,
two US government agencies, the International Air Transport Association (IATA), and the International Civil Aviation Organization (ICAO)
have begun to explore or implement mitigation measures and reduction
targets for CO2 emissions (Schäfer et al., 2016). For instance, IATA
seeks to improve global fleet fuel efficiency by an annual average of
⁎
1.5% until 2020, stabilize net emissions as of 2020, and reduce net
emissions by 50% until 2050 compared to 2005 levels (ATAG, 2017).
In order to meet these ambitious targets, IATA has established a
four-pillar strategy based on (1) fuel-efficient aircraft technologies, (2)
efficient flight operations, (3) improved airspace and airport infrastructure, and (4) market-based instruments. A large contribution to
emissions reduction is expected to come from the implementation of
fuel-efficient airframe and engine technologies through the introduction of modern aircraft by the continuous fleet renewal process (IATA,
2013). The latest generation of aircraft offers technological improvements (geared turbofan, use of composite materials), which allow for
significant fuel burn and therefore CO2 emission reductions of up to
15% with respect to the previous aircraft generation. However, these
technology improvements generally take a long time to percolate into
the fleet in sufficiently large numbers to generate a relevant systemlevel impact due to the long use phase of aircraft (Cansino and Román,
2017). An early replacement of a sufficient number of aircraft would
mean a substantial economic burden for airlines due to the high investments required. In addition, the adoption of new aircraft is limited
to their production rate and can therefore only take place slowly. For
the above-mentioned reasons, the existing emission reduction potential
of the new aircraft generation will not be fully exploited unless fleet
Corresponding author.
E-mail address: christ.mueller@tu-braunschweig.de (C. Müller).
http://dx.doi.org/10.1016/j.enpol.2017.10.022
Received 26 July 2017; Received in revised form 10 October 2017; Accepted 12 October 2017
0301-4215/ © 2017 Elsevier Ltd. All rights reserved.
Energy Policy 112 (2018) 242–257
C. Müller et al.
minimize the net present value of the cash flows for operating the
aircraft in the fleet by deciding on the timing of investment and disposal
of aircraft. Bazargan and Hartman (2012) present an extended model
for this problem taking into account leasing of aircraft and Hsu et al.
(2011) analyze the impact of demand fluctuations on the share of
leased aircraft in the fleet. Khoo and Teoh (2014) and Rosskopf et al.
(2014) present first models for airline fleet planning where not only
economic but also environmental objectives are considered. To this end,
Khoo and Teoh (2014) develop an indicator which measures the environmental performance of an airline including CO2 emissions, noise
emissions, and fuel efficiency. A bi-objective dynamic programming
model is developed to maximize environmental performance and operational profit of an airline. Similarly, Rosskopf et al. (2014) develop a
bi-objective linear programming model that balances the minimization
of NOx emissions with the maximization of the airline’s asset value at
the end of the planning horizon.
These studies are a valuable first step towards understanding the
costs for airlines to mitigate emissions but possess two main limitations.
First, these models do not consider retrofit options on the existing fleet
and thus neglect a significant potential to reduce CO2 emissions.
Second, while the studies demonstrate the trade-off between economic
and environmental objectives, they do not allow for an analysis of the
impact of CO2 emission constraints on airline fleet planning. This,
however, is of utmost importance when discussing and setting up
emission targets for aviation. The potential for and the costs of mitigating CO2 emissions on an individual airline-level are mainly shaped
by decisions made in airline fleet planning. Without a solid understanding of the interdependencies between emission constraints and the
potential and costs of available mitigation options for the airline fleet,
realistic and at the same time demanding emission levels for aviation
cannot be identified.
renewal is stimulated or alternative measures are applied.
Retrofits at the existing fleet can be a viable alternative to early
replacement of aircraft in order to modernize fleets and reduce emissions in a short to medium timeframe. Several technologies that have
recently been introduced can also be retrofitted into in-service aircraft.
Hereby, fuel burn reductions of 5–12% can be realized (IATA, 2013).
Blended winglets, for instance, which were introduced for the Airbus
A320 in 2012, allow for fuel burn reductions of up to 4%. Since retrofits
do only require small investments and can generally be carried out
during maintenance checks, thus eliminating the need for leasing an
aircraft during that time, they can make a significant contribution to
achieving short term emission targets at reasonable costs (Schäfer et al.,
2016).
Against this background, it is the objective of this paper to assess the
impact of CO2 emission constraints on airlines’ fleet planning decisions
with a special focus on the contribution of retrofit options. In particular,
we examine the following questions: (1) What is the impact of different
CO2 emission thresholds on airline fleet planning? (2) To what extent
can retrofit options contribute towards achieving CO2 emission reductions in airline fleet planning? From this, recommendations on the
deployment of retrofit programs and the appropriate design of CO2
emission constraints in aviation are derived.
To answer the questions, we deploy a mixed-integer linear programming model that allows to study fleet planning decisions under
different emission targets. Based on existing models for airline fleet
planning from the literature, we develop a novel approach for fleet
planning with CO2 emission constraints under consideration of retrofit
options for aircraft. We concentrate our analysis on two different airline
types, namely a Full Service Network Carrier (FSNC) and a Low Cost
Carrier (LCC). The FSNC offers flights in the short, medium, and long
range with a diverse fleet (single-aisle, twin-aisle, and very large aircraft), whereas the LCC only offers flights in the short and medium
range with a fleet composed of single-aisle aircraft. Four retrofit options, namely blended winglets, electric taxiing, cabin weight reduction, and re-engining are considered for certain aircraft types (especially Airbus A320 family). For the purpose of our analysis, we set the
planning horizon to 10 years.
Our contribution is twofold. First, the application of the developed
model allows for gaining a better understanding of the economic impact
of different CO2 emission thresholds on the evolution of airlines’ fleet
composition. This facilitates the formulation of suitable CO2 emission
constraints for decision makers from policy and supports airlines in
their strategic investment decisions. Second, we extend existing optimization models for airline fleet planning to integrate retrofit options.
This also holds true for fleet planning models from other industries
(e.g., bus fleets for public transportation (Simms et al., 1984), truck
fleets in the truck-rental industry (Wu et al., 2005), rail car fleets for
freight transportation (Kallrath et al., 2017) or container ship fleets of
liner shipping companies (Pantuso et al., 2016)).
The remainder of the paper is organized as follows: after the introduction, we briefly summarize the relevant literature in Section 2
and describe retrofit options for aircraft that are already available or
will become available soon in Section 3. In Section 4, we describe the
methodology and data used. The results of the analysis are presented
and discussed in Section 5. Finally, recommendations for decision
makers from industry and policy are derived in Section 6.
3. Retrofit options
Aircraft are operated for a long time while the operational environment is changing steadily, e.g., due to new regulations or increasing fuel prices. Thus, older aircraft can often not fully comply with
new regulations or be operated economically under changing conditions. To overcome this issue, new technologies are retrofitted into
existing aircraft in order to improve the performance (Jesse et al., 2012;
Schäfer et al., 2016). This section gives an overview of different retrofit
options that can be applied in order to reduce fuel consumption and
thereby CO2 emissions of aircraft.
3.1. Blended winglets
Blended winglets are angled extensions installed at the wingtip of
certain aircraft to reduce induced drag caused by airflow patterns over
the wingtip. This improves fuel efficiency and thereby reduces emissions (The Flying Engineer, 2013). Boeing began to make winglets
available in 2001 for business jets and the B737-800. Although blended
winglets increase structural weight, the aerodynamic improvements
result in net fuel burn reductions of 2–4% for a B737-800 depending on
the stage length (Aviation Partners Boeing, 2017; Freitag and Schulze,
2009). In 2012, Airbus also introduced blended winglets under the
name “Sharklets” with the first production unit of its A320ceo (current
engine option). Compared to the traditional A320, blended winglets
allow for fuel savings of 3.5% over stage lengths greater than 6500 km
and approximately 1% for stage lengths of around 1000 km (Cansino
and Román, 2017). Given the average single-aisle aircraft operating in
2015 without winglets, a fuel burn reduction of 3% translates into fuel
savings of 83,000 gallons per year (Schäfer et al., 2016) or annual cost
savings of about $108,000 assuming the 2016 jet fuel price of $1.31 per
gallon (U.S. Energy Information Administration, 2017). Since jet fuel
prices are expected to increase again, the cost benefits will be even
higher in the future.
2. Literature review
Decisions on fleet renewal and modernization are part of airline
fleet planning where the development of fleet size and composition
over time is determined. To gain a better understanding of fleet planning decisions of airlines, diverse optimization techniques such as
linear and dynamic programming have received increasing attention in
the literature. New (1975) and Schick and Stroup (1981) develop and
apply first linear programming models for airline fleet planning, which
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Energy Policy 112 (2018) 242–257
C. Müller et al.
quite far in the certification process and plan to enter service in 2018
starting with the installation of the equipment on Boeing’s next generation 737 models, followed by a system for the A320 family and the
B737MAX at a later stage of the project (FlightGlobal, 2017). The price
of an electric taxiing system approximately corresponds to half of the
typical landing gear investment, i.e., $500,000 (Schäfer et al., 2016).
To make these benefits available to operators of in-service aircraft,
both aircraft manufacturers offer winglets as a retrofit option. Since
2001, Boeing has certified installation of blended winglets as retrofit for
different aircraft types of the B737 and B757 family as well as the B767300ER (Freitag and Schulze, 2009). Airbus offers Sharklets as retrofit
for two aircraft of the A320 family, namely the A319 and A320 since
2015. Thus, over 4000 of the total 5700 A320 in-service aircraft are
eligible to be retrofitted with Sharklets (Airbus, 2013). The installation
of blended winglets requires investments of about $750,000 for the
retrofit kit (Aviation Partners Boeing, 2017; The Flying Engineer, 2013)
and $100,000 for the installation (Schäfer et al., 2016).
3.4. Re-engining
Aircraft weight can be reduced through use of light-weighting
components such as lightweight trolleys, seats, and paints or by replacing the traditional entertainment system and paper manuals with
tablets (Wired, 2012). A reduction of seat weight by one third would
allow for a weight reduction of approximately 1000 kg and require an
investment of $300,000 (FlightGlobal, 2014; Schäfer et al., 2016).
Thereby, block fuel burn would decline by about 1.25%, which would
reduce yearly emissions of an average single-aisle aircraft by 34,000
gallons (Schäfer et al., 2016) leading to annual cost savings of about
$45,000 assuming the 2016 average jet fuel price of $1.31 per gallon.
A further promising retrofit option could lie in the use of more efficient geared turbofan engines for in-service aircraft as introduced in
the A320neo family (Jesse et al., 2012; Schäfer et al., 2016). Compared
to engines of existing aircraft from the A320 family, the new geared
turbofan engines offer fuel savings of between 10–15% per flight (Jesse
et al., 2012; Schäfer et al., 2016). Thus, a re-engining program for the
A320 family could result in a very large fuel and emission reduction,
especially since approximately 7000 aircraft from the A320 family are
currently in service that could theoretically be retrofitted (Airbus,
2017b). Although Airbus has not indicated that it is considering such a
program, we assume that from 2018 onwards, re-engining of the A319,
A320, and the A321 is possible in order to study the potential of such a
retrofit program. According to Schäfer et al. (2016), re-engining requires investments of $16 million for new engines and $650,000 for the
installation.
3.3. Electric taxiing
4. Methodology and data
Electric taxiing systems are based on the idea of using electric
motors powered by the auxiliary power unit (APU) for moving aircraft
around airports without the need to start the main engine as it is performed nowadays (Hospodka, 2014). The average taxiing time per
flight cycle (taxi-in and taxi-out) amounts to 27 min. During that time,
7% of the available thrust of the main engines is required to move the
aircraft (ICAO, 2010). Using an electric taxiing system, fuel burn can be
reduced significantly since the APU requires considerably less fuel to
power the electric taxiing system. However, the installation of additional hardware adds weight (150–300 kg depending on the system),
which increases fuel consumption during flight. Therefore, this technology is only considered for short- and medium-range aircraft. After
accounting for the taxiing system’s extra weight, the amount of fuel
burnt can be reduced by 2.8% per flight cycle. This allows to reduce fuel
consumption by 77,000 gallons for a single-aisle aircraft per year
(Schäfer et al., 2016), which translates into cost savings of about
$117,000 per aircraft per year.
Currently, WheelTug is the only company working on such an
electric taxiing system (FlightGlobal, 2016). They have progressed
4.1. Modelling approach
3.2. Cabin weight reduction
4.1.1. Concept of the model
In order to determine an optimal fleet size and composition under
consideration of emission targets and retrofit options, a mathematical
optimization model is developed. Its concept is illustrated in Fig. 1. The
model depicts both strategic (i.e., the investment plan) as well as tactical decisions (i.e., the deployment of the fleet within flight operations)
for a multi-period planning horizon.
The investment plan delivers the number of aircraft of a certain type
that should be operated in each period. At the beginning of each period,
new aircraft can be purchased or sold to extend or reduce the fleet over
time. Additionally, existing aircraft of the fleet can be retrofitted in
order to improve fuel efficiency. The number of aircraft that can be
purchased or retrofitted in each period is restricted by the supply and
the available budget. Before aircraft can be liquidated, they have to be
operated a pre-set time in the fleet. Aircraft that reach their maximum
time of operation have to be liquidated. The flight operation plan determines the assignment of the aircraft to the flights to be operated in
Fig. 1. Concept of the optimization model for fleet
planning under consideration of retrofit options.
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Energy Policy 112 (2018) 242–257
C. Müller et al.
the planning period. For this, we adopt the approach from Rosskopf
et al. (2014) and represent the airline network by net classes. A net class
is determined by two intervals, one regarding the flight distance and
one regarding the number of seats (e.g., 751–1000 km, 101–150 seats
per flight). All flights that are within the same intervals are aggregated
to one net class. The flight operation plan ensures that demand is fulfilled for all net classes by assigning feasible aircraft types to the flights
within these classes taking into account the capacity of the fleet. CO2
emissions resulting from the flight operation have to satisfy a pre-set
emission constraint (e.g., carbon-neutral growth starting in a certain
year).
Given the long-term effect of fleet planning decisions, we use a cashflow oriented approach based on minimizing the net present value
(NPV) resulting from periodic payments related to the investment and
flight operation decisions. On the one hand, cash flows include investment expenses for new aircraft and retrofits as well as liquidation
revenues that are defined for each aircraft type. On the other hand, cash
flows comprise expenses related to flight operation, i.e., fuel, maintenance, repair and overhaul (MRO), and crew and cabin. Revenues
resulting from selling seats and providing service are not included in the
model as they are assumed to be independent of the decisions on the
composition of the airline fleet and the assignment of the aircraft. On a
strategic level, revenues are mainly influenced by decisions on the
schedule design, i.e., markets to serve, frequencies, and flight schedule
to meet these frequencies, which in our case is defined by the demand
of the different net classes the airline is aiming to fulfill. In fleet planning, the focus is then on cutting cost for operating a given flight
schedule in order to increase profitability (Barnhart et al., 2003; New,
1975). This assumption is typical for airline fleet planning problems
(see, e.g., New (1975) or Schick and Stroup (1981)) and is also in line
with empirical observations, which demonstrate that fleet development
is mainly driven by passenger growth and the distance of the segment
(Kölker et al., 2016).
Aging aircraft in the fleet are penalized by higher MRO-related cash
flows, lower utilization (i.e., available flight hours per year) due to
more frequent as well as longer maintenance checks, and fuel burn
deterioration due to wear and tear. The purchase of new aircraft can be
triggered by three events. First, if the capacity of the fleet is not sufficient to satisfy demand, new aircraft need to be purchased in order to
expand the fleet. Second, if the investment for a new aircraft is less than
the savings realized over the use phase due to lower operating costs
compared to an old aircraft in the fleet, the old aircraft is replaced.
Third, if the emission constraint cannot be met with the existing fleet,
new and more fuel efficient aircraft need to be purchased. The latter
two events can also trigger the decision to retrofit aircraft of the fleet.
∑
t∈T
[FOt + ItA + ItR − Lt ]⋅(1 + i)−t
t∈T
i∈A k∈K l∈L
(2)
Capital investments for new aircraft result from the number of aircraft purchased in period t and the list price of the purchased aircraft
types i including discounts that are usually granted by aircraft manufacturers.
ItA =
∑
pit ⋅APit t ∈ T
(3)
i ∈ AB
Similarly, capital investments for retrofits depend on the number of
aircraft retrofitted in period t and the price of retrofitting the aircraft
from type i to type j .
ItR =
∑ ∑ ∑ rijkt⋅RPijt t ∈ T
(4)
i ∈ A j ∈ AR k ∈ K
Cash flows from the liquidation of aircraft depend on the number of
aircraft sold in period t at age k and the residual value of these aircraft.
Lt =
∑ ∑ sikt⋅RVikt t ∈ T
(5)
i∈A k∈K
Constraints (6)–(9) ensure that the inventory of all base aircraft
types is consistent. To this end, constraints (6) initialize the fleet at the
beginning of the planning horizon. Constraints (7) calculate the number
of aircraft owned in period t , which is given by the number of aircraft
owned in the preceding period minus the number of sold and retrofitted
aircraft. Constraints (8) relate the number of aircraft bought in period t
to the number of new aircraft owned in this period. Finally, constraints
(9) assure that new aircraft are not sold.
∑
oik1 = EFi, k − 1 − sik1 −
rijkt i ∈ AB , k ∈ K /{1}
(6)
j ∈ AR
∑
oikt = oi, k − 1, t − 1 − sikt −
rijkt i ∈
AB ,
k ∈ K /{1}, t ∈ T /{1}
(7)
j ∈ AR
oi1t = pit i ∈ AB , t ∈ T
(8)
si1t = 0 i ∈ AB , t ∈ T
(9)
Similarly to constraints (6)–(9), constraints (10)–(12) ensure that
the inventory for all retrofit aircraft types is consistent. Constraints (10)
initialize the fleet at the beginning of the planning horizon for all retrofit types. Constraints (11) determine the number of aircraft of a certain type owned in period t , which is given by the number of aircraft
owned in the preceding period minus all aircraft sold and retrofitted to
another aircraft type plus those aircraft that are retrofitted to this aircraft type. Constraints (12) assure that retrofit aircraft types cannot be
bought. Finally, constraints (13) ensure that no new retrofitted aircraft
are owned in the fleet.
4.1.2. Mathematical model formulation
The airline fleet planning problem under consideration of emission
targets and retrofit options is formulated as a mixed-integer linear
programming model. It makes use of the sets, parameters, and decision
variables as shown in Appendix A.
The objective function minimizes the NPV as a result of discounted
cash flows for flight operation FOt plus capital investments for new
aircraft ItA and retrofits ItR minus discounted cash flows from the liquidation of aircraft Lt .
Min. NPV =
∑ ∑ ∑ fiklt ⋅(FUikl⋅FPt + CCilt + MCiklt )
FOt =
oik1 = EFi, k − 1 − sik1 −
∑
rijk1 +
j ∈ AR
oikt = oi, k − 1, t − 1 − sikt −
∑
∑ rhik1
i ∈ AR , k ∈ K /{1}
(10)
h∈A
rijkt +
j ∈ AR
∑
rhikt
h∈A
i ∈ AR , k ∈ K /{1}, t ∈ T /{1}
pit = 0
i ∈ AR , t ∈ T
oi1t = 0 i ∈
(1)
AR ,
t∈T
(11)
(12)
(13)
Constraints (14) ensure that aircraft that have reached the maximum service time are sold for all aircraft types.
Cash flows for flight operation contain fuel, cabin and crew as well
as maintenance. Fuel-related cash flows depend on the fuel use (FUikl ),
which varies with the aircraft type and age as well as the stage length of
the net class and the fuel price (FP)
t . Maintenance-related cash flows
(CMCilkt ) also depend on the aircraft type, aircraft age, and the stage
length of the net class. The cash flows for cabin and crew (CCilt ) only
depend on the stage length of the net class and the aircraft type, i.e.,
they are independent of the aircraft age.
si, k +1, t = oik, t −1 i ∈ A, k ∈ {STi }, t ∈ T / {1}
(14)
Constraints (15)–(17) ensure that technological restrictions with
regard to possible retrofits are considered for the first and all remaining
periods, respectively, and that new aircraft are not retrofitted.
rijk1 ≤ EFi, k −1⋅RMij i ∈ A, j ∈ AR , k ∈ K / {1}
245
(15)
Energy Policy 112 (2018) 242–257
C. Müller et al.
rijkt ≤ oi, k −1, t −1⋅RMij i ∈ A, j ∈ AR , k ∈ K / {1},t ∈ T / {1}
(16)
rij1t = 0 i∈ A, j ∈ AR , t ∈ T
(17)
quality. The fractional values can be interpreted as the proportion of an
aircraft’s capacity to a certain net class.
Constraints (18)–(19) ensure that demand is satisfied. In particular,
constraints (18) ensure that a certain demand for seats is satisfied in
each period while constraints (19) assure that a minimum number of
flights is offered.
∑ ∑ filkt ⋅NSi ≥ DltS
∑ ∑ filkt
≥
DltF
(18)
(19)
Constraints (20)–(23) ensure that different capacity as well as fleet
assignment restrictions are considered. Constraints (20) ensure that the
capacity of the fleet, which is determined by the number of owned
aircraft and the maximum utilization of these, is not exceeded.
∑ filkt ⋅BTil ≤ oikt ⋅MUik
i ∈ I, k ∈ K, t ∈ T
(20)
l∈L
Constraints (21) ensure that demand in each net class is satisfied
only by the assignment of feasible aircraft types with regard to seat
capacity and range.
filkt ≤ ACAil ⋅M
i ∈ I , k ∈ K , l ∈ L, t ∈ T
(21)
Constraints (22) and (23) assure that the maximum aircraft and
retrofit supply, which is given by the production rate of the aircraft
manufacturer, is not exceeded in each period.
pit ≤ ASit
i ∈ AB , t ∈ T
∑ ∑ rijkt ≤ RSjt
(22)
j ∈ AR , t ∈ T
(23)
i∈A k∈K
Constraints (24) ensure that the investment budget for newly purchased aircraft and retrofits is not exceeded in each period.
ItA + ItR ≤ Bt
t∈T
(24)
In order to analyze alternative designs of an emission threshold, we
formulate two different constraints of which only one is used at a time.
Constraints (25) enforce carbon-neutral growth, i.e., starting from
period T CNG , the level of CO2 emissions must not exceed the level of the
preceding period. Contrary, constraints (26) ensure that the airline’s
CO2 emissions do not exceed a prespecified emission cap starting from
period T EC .
et ≤ et −1 t ∈{T CNG, …, T max }
(25)
et ≤ EC t ∈{T EC , …, T max }
(26)
The emissions in each period are given by the number of flights with
a certain aircraft type and age, the stage length of the net class flown,
and the CO2 emission factor of jet fuel (3.15 kg CO2e/kg jet fuel).
et =
∑ ∑ ∑ fiklt ⋅FUikl⋅3.15
i∈A k∈K l∈L
et ≥0 t ∈ T
(32)
In this study, the analysis of optimal fleet compositions to meet CO2
emission targets is scoped on two European airlines, a FSNC and a LCC
for the period from 2016 to 2025. The FSNC operates in 40, whereas the
LCC only operates in 8 net classes. The net classes and the demand data
are taken from Rosskopf (2013) and updated using the growth rates reported there such that they approximately meet seats flown and block
hours of the two airlines for the year 2016. From 2016 on, we assume
that the demand in all net classes equally growths with 2% per year. The
initial values for the flight and seat demand are given in Appendix B.
The aircraft types considered include single-aisle aircraft for the LCC
and single-aisle, two-aisle as well as very large aircraft for the FSNC.
The main characteristics of the aircraft types are based on manufacturer
specifications (Airbus, 2017c; Boeing, 2017; Bombardier, 2017) and
supplemented by data taken from Rosskopf (2013). The fuel use is
calculated using a regression model from Rosskopf (2013) for which
fuel use in the air and on the ground has been determined with the Base
of Aircraft Data Eurocontrol and the ICAO Engine Emissions Database as
well as the Database for Turboprop Engine Emissions, respectively. We
further assume that fuel use deteriorates by 0.2% per year due to wear
and tear compounded over the respective aircraft age (Morrell and
Dray, 2009). Similarly, the block times and maximum utilization of
different aircraft types are calculated based on a regression model from
Rosskopf (2013). The aircraft types included in the analysis, their
specifications, fuel use, block times, maximum flight hours per year,
and residual values are given in Appendix C. The maximum age of
aircraft is set to 30 years.
Cash flows for cabin and crew as well as maintenance, repair, and
overhaul (MRO) are calculated using the formulas reported by Liebeck
et al. (1995). MRO-related cash flows include labor, material, and
overhead for the aircraft cell and engines. In order to account for rising
MRO-related cash flows with increasing aircraft age, we adopt the
distinction of three phases in the life cycle of an aircraft, namely,
newness (until first D-Check, < 7 years), mature (between first and
second D-check, 7–14 years), and aging (> 14 years) (Dixon, 2006).
Based on these phases an aging factor is used to adjust the calculated
MRO-related cash flows with regard to the aircraft age as shown in
Appendix D.
Regarding the fuel prices, we consider three different scenarios
(low, medium, high) as shown in Fig. 2. The inflation rate, which is
considered for the price development of aircraft, retrofits, MRO-related
cash flows as well as cash flows for cabin and crew, is assumed to be 2%
p.a. over the planning horizon. The interest rates used for discounting
the cash flows are based on average values of the EBIT (earnings before
interest and taxes) margins of the two airlines between 2009 and 2016
and are set to 3% for the FSNC and 9% for the LCC. The investment
budget that can be spend on new aircraft is based on annual reports of
the two airlines and set to $1.25 billion for the LCC and $1.75 billion for
the FSNC for the first year and grows by 2% annually.
The initial fleets of the two airlines at the beginning of the planning
horizon are based on data taken from Flightradar 241 as well as annual
and sustainability reports and shown in Appendix E. Regarding the
supply of aircraft, we assume that at most 15 units of single-aisle and 6
units of two-aisle and very large aircraft can be delivered per year.
Similarly, retrofits are limited to 30 for blended winglets, electric
l ∈ L, t ∈ T
i∈A k∈K
(31)
4.2. Data
l ∈ L, t ∈ T
i∈A k∈K
fiklt ≥0 i ∈ I , k ∈ K , l ∈ L, t ∈ T
t∈T
(27)
Integer variables represent the number of aircraft purchased, sold,
and retrofitted in each period.
pit ∈ i ∈ I , t ∈ T
(28)
sikt ∈ i ∈ I , k ∈ K , t ∈ T
(29)
rijkt ∈ i∈ I , j ∈ AR , k ∈ K , t ∈ T
(30)
The number of flights, the CO2 emissions, and all cash flows can
only take on positive values. Since all decision variables related to the
fleet development are integer, it might be contended that the variables
for the number of flights should also be integer. However, we allow
fractional values for the number of flights because this reduces the
complexity of the model significantly without impairing the solution
1
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https://www.flightradar24.com/data/aircraft.
Energy Policy 112 (2018) 242–257
C. Müller et al.
Fig. 3. Development of CO2 fleet emissions for alternative emission constraints (LCC, low
fuel price scenario).
Fig. 2. Fuel price scenarios (historic values indicated in grey are taken from EIA (2017)).
aviation.
In the following, we will first analyze the two alternative designs for
an emission constraint introduced in Section 4 and their impact on
airline fleet planning without consideration of retrofits. Afterwards, the
economic and ecological potential of retrofits to contribute towards
emission reductions is studied. Each analysis concentrates on the model
outcomes for the low fuel price scenario, which can be seen as a worst
case for the development of CO2 emissions in aviation. The results are
then briefly compared to the further fuel price scenarios.
Table 1
Techno-economic characteristics of retrofit options (Freitag and Schulze, 2009; Jesse
et al., 2012; Schäfer et al., 2016; The Flying Engineer, 2013).
Retrofit
Feasible
aircraft
types
Year of
introduction
Fuel use
reduction [%]
Price
[$M]
Blended
winglets
A319-100
A320-200
A330-300
2016
2016
2019
1.0–4.0
0.85
Cabin weight
reduction
A320-200
A321-200
A340-300
A340-600
2016
1.6
0.30
Electric taxiing
A319-100
A320-200
A321-200
2018
2.8
0.50
Re-engining
A319-100
A320-200
A321-200
2018
12.5
16.65
5.1. Impact of emission constraints on airline fleet planning
0.60
To analyze the influence of emission constraints on airline fleet
planning, we compare the model outcomes of the following runs: (1) no
threshold applies (base case), (2) carbon-neutral growth has to be
achieved from 2020 onwards, and (3) a prespecified emission cap must
not be exceeded starting from 2020. For the last case, the cap is set to
the emissions in 2020 from the run without a threshold. If the model
cannot find a solution for this setting, the value is increased until a
feasible solution can be obtained.
Fig. 3 illustrates the LCC’s development of CO2 fleet emissions for
the three alternative model runs in the low fuel price scenario. As expected, a situation without any threshold leads to the highest CO2
emissions in 2025 (about 6.5 Mt). The threshold demanding for carbonneutral growth results in an emission reduction by 0.59% in 2025 and
an increase in total emissions by 2.61% over the planning horizon
compared to the base case. With an exogenous threshold, emissions in
2025 can be decreased by 8.49% and total emissions by 4.68%. Similar
outcomes can be observed for the development of the FSNC’s CO2
emissions (Fig. 4). When no emission constraint is considered, emissions amount to approximately 15.9 Mt CO2 in 2025. Here, carbonneutral growth leads to a reduction in emission by 1.57% in 2025 and
an increase in total emissions by 1.65% compared to the base case. The
exogenous threshold allows for an emission reduction by 3.52% in 2025
taxiing systems as well as weight reduction and to 5 for re-engining,
respectively. For the retrofit options, we assume the techno-economic
characteristics as described in Section 3, which are summarized in
Table 1.
5. Results and discussion
For our case study, we make use of the dataset for the two airlines
introduced earlier. Thereby, we distinguish between situations with and
without emission threshold as well as with and without retrofit options.
For each setting, the airline fleet planning is done for the time from
2016 up to and including 2025 on a yearly basis, taking into account
the different fuel price scenarios. The resulting mixed-integer linear
programs (MIP) are implemented in AIMMS. Depending on the scenario
considered, the problem instances embrace between 24,000 and
190,000 variables and between 25,000 and 200,000 constraints. The
instances can be solved with CPLEX 12.4 on a standard computer within
approximately 30 s to 450 min, allowing for a MIP gap tolerance of
0.02% for the LCC cases and 0.5% for the FSNC cases.
Before making use of the optimization model to answer the research
questions, it was comprehensively validated to build confidence that it
is suitable for its purpose. To this end, we solved the model for a
planning period between 2010 and 2016. The model outcomes for the
development of fleet size and composition, seat capacity, block hours,
and CO2 emissions were then checked to correspond to the real-world
data from the two airlines. After carrying out this validation test, we are
confident that we can use the optimization model to gain new insights
on the impact of retrofits and emission constraints on airlines’ fleet
planning decisions and the consequences for emission reduction in
Fig. 4. Development of CO2 fleet emissions for alternative emission constraints (FSNC,
low fuel price scenario).
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Energy Policy 112 (2018) 242–257
C. Müller et al.
type B787 are deployed for long-haul flights.
For the further fuel price scenarios, the results are very similar.
Obviously, higher fuel prices have a negative effect on the airline’s
payments for fuel and thus on the NPV. When no threshold is considered, this effect stimulates higher investments in modern aircraft to
some extent. Contrary, the fuel price scenario does not have an influence on the fleet planning decisions for the case of the exogenous
threshold. Here, the limited investment budget leaves no room for
further fleet modernization.
To summarize, introducing an emission target that requires to stabilize net emissions as of 2020 can significantly stimulate investments
in modern and energy-efficient aircraft. At the same time, a threshold
can have severe economic impacts on airlines, especially if the cap is set
exogenously to challenging levels. Thereby, improving the fleet’s fuel
efficiency is more challenging for an FSNC than for an LCC. Typically,
an FSNC has less leeway in investing in fleet modernization since it
operates a more diverse fleet with a higher average age. In contrast,
defining the cap for carbon-neutral growth in a way that it can be endogenously influenced by an airline’s fleet planning decision might
result in a steep increase in emissions in order to dampen the financial
consequences. Due to this negative effect, the following analysis on the
impact of retrofits will only take into account the exogenously defined
threshold.
Table 2
Deviation of NPVs, investments, and fuel payments when applying an emission threshold
compared to solutions without threshold (low fuel price scenario).
Low cost carrier
NPVs
Investments
Fuel payments
Full service network carrier
Carbonneutral
growth
Exogenous
threshold
Carbonneutral
growth
Exogenous
threshold
+ 2.90%
+ 0.83%
+ 2.72%
+ 7.22%
+ 100.26%
− 5.00%
+ 0.80%
+ 1.26%
+ 1.70%
+ 0.61%
+ 5.23%
− 0.70%
and by 0.62% in total. In all cases, the initial decrease of emissions
between 2016 and 2017 can be explained by the model’s decision to sell
aircraft of the type A380 with high fuel consumption and use more
efficient aircraft instead.
The results reveal three important mechanisms of the emission
constraints under consideration. First, carbon-neutral growth leads to a
steep increase of fleet emissions in 2020. This is due to economic
considerations, making it easier to meet the threshold in the following
periods. Second, in order to find a feasible exogenous threshold, the
2020 emissions from the run without a threshold have to be increased
by 0.95% for the LCC and by 5.23% for the FSNC. Moreover, it can be
observed that the actual emissions between 2020 and 2024 are lower
than the threshold. This underlines the challenging character of the
threshold: In order to meet the cap in the last period despite of the
growing demand, the airlines have to significantly modernize their fleet
from the beginning on. Third, the development of the fleet emissions for
the FSNC is comparable for the runs without a threshold and with the
exogenous threshold. This can be explained by the overall high utilization of the investment budget, leaving not much room for further
investments in the fleet renewal when a threshold applies.
The most important economic consequences of applying the emission constraints are summarized in Table 2. It can be seen that in all
cases the NPV deteriorates, which is especially due to the higher investments in order to adjust the fleet composition. Contrary to the
FSNC, the LCC’s investments double over the complete planning horizon when the exogenous threshold is applied. The higher investments
are partially offset by lower payments for fuel as a consequence of an
increased deployment of modern aircraft with lower fuel consumption
(Fig. 5). In total, the limited investment budget allows to purchase 170
aircraft of the type A320neo and CS100. In the run “carbon-neutral
growth”, fuel payments slightly increase because more conventional
aircraft (i.e., A320) are purchased to enable the steep increase in
emissions in 2020. Similar effects can be observed for the FSNC, although at a lower level due to the missing additional financial leeway
for fleet modernization. Yet, the emission constraints lead to a deviating
distribution of investments. The more severe the threshold, the more
energy-efficient aircraft are purchased over the planning horizon. In
particular, up to 27 aircraft of the type A350 and up to 70 aircraft of the
5.2. Impact of retrofits on airline fleet planning
For the analysis of the retrofits’ impact on fleet planning decisions,
the results of the following runs are compared: (1) without threshold
and retrofits (base case), (2) without threshold but with retrofits, (3)
with threshold as of 2020 but without retrofits, and (4) with threshold
as of 2020 and retrofits. Again, the threshold’s value is chosen in a way
that it just allows to obtain a feasible solution.
Fig. 6 compares the development of CO2 fleet emissions of the LCC
for the four runs in the low fuel price scenario. It can be seen that the
consideration of retrofit options allows for additional fuel and thus
emission savings. Without a threshold, the application of retrofits leads
to a reduction of fleet emissions by 2.97% in 2025 and by 2.22%
compared to the base case. When the exogenous cap is set, retrofits can
additionally contribute to the emission reduction in 2025 by 3.52% and
by 1.34% in total. Overall, emissions in 2025 can thus be decreased by
11.72% if an exogenous emission cap is defined and retrofits are applied. Thereby, the 2025 emissions are 2.61% lower than the 2020
emissions from the base case. This underscores the potential of retrofits
to contribute to the stabilization of the LCC’s net fleet emissions.
Fig. 7 reveals that the results for the FSNC are quite similar in the
low fuel price scenario. By applying retrofits, fleet emissions can be
reduced by 1.28% in 2025 and by 1.27% in total for the case where an
emission threshold is not considered. With the exogenous threshold,
retrofits allow for additional emission savings of 3.58% in 2020 and
2.63% in total. This adds up to an emission reduction by 6.66% in 2025
compared to the base case. In contrast to the LCC, an emission
Fig. 6. Comparison of CO2 fleet emissions for the runs with/without threshold and with/
without retrofits (LCC, low fuel price scenario).
Fig. 5. Number of modern aircraft purchased over the planning horizon (low fuel price
scenario).
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Energy Policy 112 (2018) 242–257
C. Müller et al.
Table 5
Number of retrofits applied to the FSNC's fleet in 2025 without and with emission
threshold (low fuel price scenario).
A319
Fig. 7. Comparison of CO2 fleet emissions for the runs with/without threshold and with/
without retrofits (FSNC, low fuel price scenario).
NPVs
Investments
Fuel payments
Full service network carrier
Without
threshold
With
threshold
Without
threshold
With
threshold
− 0.3%
+ 1.51%
− 2.33%
− 3.77%
− 44.04%
− 1.83%
− 0.35%
+ 0.42%
− 1.32%
+ 0.85%
+ 8.26%
− 2.77%
reduction beyond 2020 levels from the base case is not possible. Indeed,
the cap still has to be set a little bit higher (1.46%) to obtain a feasible
solution.
Retrofits can not only contribute to achieving short term CO2
emission reductions but also bear an economic potential for airlines.
This holds especially true for the LCC (Table 3). By introducing retrofits
to modernize the fleet in the low fuel price scenario without any
emission threshold, the LCC’s NPV improves by 0.3% due to lower
payments for jet fuel (− 2.33%). The retrofit options deployed in this
situation comprise winglets (A320), cabin weight reduction (A320),
and electric taxiing (A319, A320) (Table 4), which comes along with an
increase in investment by 1.51%. Investments in the re-engining option
are too high and thus bear no additional potential as long as airlines are
not forced to cut down their fleet emissions. In this case, nearly all
available retrofits are applied to the fleet (A319: winglets, electric
taxiing, and re-engining; A320: cabin weight reduction, winglets,
electric taxiing, and re-engining), allowing for an improvement of the
NPV by 3.77%.
For the FSNC, similar results can be obtained. Without a threshold,
retrofits allow for an improvement of the NPV by 0.35% due to lower
fuel payments. Thereby, especially e-taxi systems are applied to the
complete A320 family, weight reduction to the A320 and A321, as well
as winglets to the A320. Moreover, almost all A330 in the fleet are
equipped with winglets and all A340 take part in the weight reduction
program during the planning horizon (Table 5). Again, re-engining is
only an attractive option for fleet modernization if the emission
threshold is applied. In this situation, also winglets are deployed to a
No
Yes
No
Yes
Total number of aircraft in fleet
E-Taxi
Weight reduction
Winglets
Re-engining
132
120
n/a
0
0
125
125
n/a
110
33
138
138
64
54
0
109
109
67
77
95
A340
Threshold
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Total number of
aircraft in fleet
E-Taxi
Weight reduction
Winglets
Re-engining
75
53
70
66
44
44
26
19
34
34
41
n/a
0
0
53
n/a
53
20
70
64
24
0
66
66
45
56
44
44
n/a
0
44
44
n/a
34
n/a
n/a
24
n/a
n/a
n/a
19
n/a
n/a
34
n/a
n/a
n/a
34
n/a
n/a
Despite high growth expectations, airlines are more and more
challenged to cap and eventually lower their CO2 fleet emissions. Fleet
modernization (i.e., procurement of modern and fuel-efficient aircraft,
application of retrofit options such as e-taxiing or winglets to the existing fleet) can be considered as one important measure to contribute
to this target. This paper studies the potential of fleet modernization for
capping airline’s fleet emissions by making use of an optimization
model. In particular, the influence of emission thresholds and retrofit
options on airline fleet planning is analyzed for the example of a Low
Cost Carrier and a Full Network Service Carrier, taking into account the
economic and ecological consequences.
Focusing on the aviation industry’s agreement to stabilize net
emissions of air traffic as of 2020 (carbon-neutral growth), our results
indicate that the mechanisms of such an emission cap must be chosen
carefully. If the cap were to be set based on the actual emissions in
2020, airlines would have a high incentive to increase their emissions in
the previous years in order to define less stringent requirements for the
future. A much better alternative is to define the emission cap based on
the predictions of the 2020 emissions in a business-as-usual scenario.
Compared to a situation without emission cap, such an exogenous
threshold shows the potential to contribute to an emission reduction in
2025 by 8.49% for the LCC and by 3.52% for the FSNC in our case
study. However, it has to be noticed that airlines would face severe
economic consequences in this situation, which is especially due to the
higher investments for fleet modernization. For instance, the LCC’s investments double since 170 modern aircraft of the type A320-200neo
and CS100 have to be procured over the planning horizon in order to
meet the cap. Thereby, almost the entire yearly budget for fleet
A320
Threshold
A330
6. Conclusions and implications for industry and policy
Table 4
Number of retrofits applied to the LCC's fleet in 2025 without and with emission threshold
(low fuel price scenario).
A319
A321
larger extent. In contrast to the LCC, the FSNC’s NPV slightly deteriorates when the emission threshold is considered despite of the largescale application of retrofits. This is due to the fact that the retrofits
allow for a stricter emission threshold, which requires additional investments that cannot be offset by the reduction of fuel payments.
The influence of the alternative fuel price scenarios on the application of retrofit is restricted to the case where an emission threshold is
not considered. Here, more retrofits are applied to the fleet of the LCC
and the FSNC (e.g., Winglets for A319) with an increasing price in jet
fuels, leading to a further reduction in fleet emissions in 2025. Re-engining plays no role for fleet modernization not even in the high fuel
price scenario. For the case that an emission threshold is taken into
account, the limited investment budget leaves no room for the deployment of further retrofits.
Overall, the results demonstrate the economic and ecological potential of retrofits when modernizing an airline fleet. Thereby, the potential of retrofits to contribute to emission reduction is lower for the
FSCN than for the LCC. One of the main reasons is that retrofit options
for long-distance aircraft, which are operated by FSNCs, are not available up to now. Additionally, LCCs operate fleets with a lower average
age, making retrofits more economically beneficial.
Table 3
Deviation of NPVs, investments, and fuel payments when applying retrofits compared to
solutions without retrofits (low fuel price scenario).
Low cost carrier
A320
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Energy Policy 112 (2018) 242–257
C. Müller et al.
application of thresholds might steer airlines in the right direction, they
will not allow to achieve ambitious reduction targets as long as aircraft
are purely powered by conventional jet fuels.
Our study is to some extent of hypothetical nature as an emission
threshold for airlines has not been applied so far. However, several
institutions and organizations have agreed on first reduction targets for
aviation and IATA has communicated its voluntary self-agreement to
improve global fleet fuel efficiency by an annual average of 1.5% until
2020, stabilize net emissions as of 2020, and reduce net emissions by
50% until 2050 compared to 2005 levels. This situation is comparable
to the situation of the automotive industry almost 20 years ago where,
for instance, the European Automobile Manufacturers Association
(ACEA) and the European Commission signed an agreement to limit the
amount of CO2 fleet emissions from passenger cars sold in Europe.
Moreover, aviation has already been included in the European
Emissions Trading Scheme. Thus, it has to be expected that airlines will
face severe requirements to limit CO2 fleet emissions in short to
medium term and to significantly cut down fleet emission in the long
run. The optimization model introduced in this paper and the findings
presented can help policy and industry to develop and apply appropriate levels and mechanisms for an emission cap as well as corresponding technological measures for fleet modernization.
Future work should take into account that airlines typically operate
at a global scale, calling for global agreements on emission reduction in
aviation, which is out of scope of this study. The same holds true for the
analysis of economic instruments such as a carbon tax or a global
carbon offsetting scheme as proposed by IATA (2017). Further promising ways to extend the scope of the analysis would be to include
leasing decisions into the model, take into account revenues when deciding on the size and composition of the airline fleet, and make use of a
multi-objective optimization model to determine Pareto-efficient combinations of emission reduction measures.
modernization ($1.25 billion in 2016, increasing at a rate of 2% p.a.) is
invested every year. The same holds true for the FSNC.
Retrofits can contribute to further limit CO2 fleet emissions and bear
an economic potential for airlines due to the reduction of payments for
jet fuel and a better utilization of the investment budget. By applying etaxiing, weight reduction, winglets, and re-engining to meet the exogenous threshold under investigation, an overall reduction of emissions
in 2025 of 11.72% for the LCC and of 6.66% for the FSNC can be
achieved compared to a “do-nothing” situation. Thus, airlines should
take into account existing retrofit programs, i.e., weight reduction for
the A320, A321, and A340 as well as winglets for the A320, when
modernizing their fleet to save CO2-emissions and fuel payments.
Moreover, planned measures such as e-taxiing for the A320 family and
winglets for the A320 should be pursued with high priority. If available,
all those retrofits are utilized to a large extent in our optimization
model, indicating their high potential for consideration in fleet planning decisions.
As a further retrofit option, we have also taken into account reengining of the A320 family for which no program has been announced
by Airbus so far. While under conditions without a threshold this retrofit does not seem to be an economically viable alternative, it might
become of interest with stricter regulations on capping the air traffic’s
CO2 emissions. Industry should therefore consider re-engining as a future option for fleet modernization and start working on the development and certification of corresponding programs. Such a program
would be of particular interest in combination with the D-Check as the
most comprehensive MRO-check of the complete aircraft.
Despite the identified economic and ecological potential of retrofits,
a reduction of fleet emissions below 2020-levels is difficult to achieve
with the measures and technologies considered in this study. This is
especially due to the limited budget of airlines for investing in fleet
modernization, the growth expectations for air traffic, and the fact that
retrofits are only available for short- to medium-haul aircraft. Thus,
further retrofit options should be certified in future and existing retrofit
programs, which especially apply to the Airbus A320 family currently,
should be extended to additional aircraft types. Moreover, it is of utmost importance for industry and policy to develop and certify further
measures to significantly cut down CO2 emission in aviation until 2050
such as bio-/ electrofuels or hybrid electric aircraft. While the
Acknowledgement
We would like to acknowledge the support of the Ministry for
Science and Culture of Lower Saxony (Grant No. VWZN3177) for
funding the research project “Energy System Transformation in
Aviation” in the initiative "Niedersächsisches Vorab".
Appendix A. Notation of the optimization model
Sets
A
Set
AB
Set
AR
Set
K
Set
L
Set
T
Set
Parameters
ACAil
APit
ASit
Bt
M
BTil
CCilt
DltS
DltF
EFik
EC
FOt
FPt
FUikl
of
of
of
of
of
of
all aircraft types (index h, i, j )
base aircraft types AB ⊆A (e.g., “Airbus A320”)
retrofit aircraft types AR = A/AB (e.g., “Airbus A320 + Winglets”)
aircraft ages (index k ), k = 1 indicates a new aircraft
net classes (index l )
periods (index t )
Aircraft class assignment matrix indicating if aircraft type i can serve net class l
Price for aircraft type i in period t
Aircraft supply of type i in period t
Investment budget in period t
Large number
Block time of a flight in net class l with aircraft type i (flight time plus time for taxiing)
Cash flows for cabin and crew of flights with aircraft type i in net class l in period t
Demand (in seats required) in net class l in period t
Demand (in number of flights) in net class l in period t
Existing fleet of aircraft type i at age k at the beginning of the planning horizon
Emission cap, i.e., maximum allowed emissions per period
Sum of expenses for flight operations in period t
Fuel price per gallon in period t
Fuel use (gallon per flight) of aircraft type i at age k in net class l
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Energy Policy 112 (2018) 242–257
C. Müller et al.
i
Interest rate
Sum of investments for new aircraft in period t
ItA
ItR
Sum of investments for retrofits in period t
Sum of liquidation revenues from the sale of aircraft in period t
Lt
MCilkt
Maintenance-related cash flows of flights with aircraft type i at age k in net class l in period t
MUik
Maximum flight hours per year of aircraft type i at age k
Number of seats of aircraft type i
NSi
RMij
Binary retrofit matrix indicating if aircraft type i can be retrofitted to type j
RPijt
Price of retrofitting an aircraft from type i to type j in period t
RSjt
Retrofit supply of type j in period t
RVikt
Residual value of aircraft type i at age k in period t
Maximum service time of aircraft type i
STi
T CNG
Period from which on a carbon-neutral growth has to be achieved
T EC
Period from which on a prespecified emission cap must not be exceeded
T max
Last period
Decision variables
et
fiklt
oikt
pit
rijkt
sikt
CO2 emissions in period t
Number of flights with aircraft type i at age k in net class l in period t
Number of aircraft of type i and age k owned in period t
Number of aircraft of type i purchased in period t
Number of aircraft retrofitted from type i to type j at age k in period t
Number of aircraft of type i and age k sold in period t
Appendix B. Flight and seat demand data
See Appendix Tables B1–B4.
Table B1
Flight and seat demand for the FSNC in 2016 in all net classes.
Distance [km]
Seats
Flights
Seats (in 1000)
1–250
1–250
1–250
251–500
251–500
251–500
501–750
501–750
501–750
501–750
751–1000
751–1000
751–1000
1001–1500
1001–1500
1001–1500
1001–1500
1501–2000
1501–2000
2001–3000
2001–3000
2001–3000
2001–3000
3001–4000
3001–4000
3001–4000
3001–4000
4001–5000
4001–5000
5001–6000
5001–6000
6001–8000
6001–8000
6001–8000
8001–1,0000
8001–1,0000
8001–1,0000
10,001–12,000
10,001–12,000
10,001–12,000
101–150
151–210
211–300
101–150
151–210
211–300
101–150
151–210
211–300
301–400
101–150
151–210
211–300
101–150
151–210
211–300
301–400
101–150
151–210
101–150
151–210
211–300
301–400
101–150
151–210
211–300
301–400
211–300
301–400
211–300
301–400
211–300
301–400
401–600
211–300
301–400
401–600
211–300
301–400
401–600
5982
1074
619
59,127
67,742
927
29,298
36,670
802
287
21,787
13,143
1524
18,588
31,070
549
935
6148
29,044
3505
7590
1005
874
698
647
332
662
5425
1450
1017
1303
9548
8864
1223
5108
12,910
1888
520
753
523
733
170
139
7329
11,851
206
3653
6283
177
102
2718
2290
335
2385
5353
123
304
764
5094
439
1325
224
285
92
120
73
229
1199
453
226
428
2113
2962
577
1129
4243
883
115
265
247
251
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Table B2
Average distance (in km) of each net class for the FSNC (Rosskopf, 2013).
Number of seats per flight
Distance [km]
101–150
151–210
211–300
301–400
401–600
1–250
251–500
501–750
751–1000
1001–1500
1501–2000
2001–3000
3001–4000
4001–5000
5001–6000
6001–8000
8001–10,000
10,001–12,000
180
393
624
848
1228
1681
2411
3319
–
–
–
–
–
183
417
614
914
1231
1731
2343
3063
–
–
–
–
–
146
389
669
875
1038
–
2834
3365
4461
5427
6734
8827
10,062
–
–
718
–
1200
–
2936
3779
4593
5900
6788
9041
11,329
–
–
–
–
–
–
–
–
–
–
7409
9010
10,284
Table B3
Flight and seat demand for the LCC in 2016.
Distance [km]
Seats
Flights
Seats (in 1000)
1–250
251–500
501–750
751–1000
1001–1500
1501–2000
2001–3000
3001–4000
101–150
101–150
101–150
101–150
101–150
101–150
101–150
101–150
7145
61,996
122,947
95,777
98,357
57,833
27,100
4533
906
7845
15,640
12,181
15,047
8889
4433
785
Table B4
Average distance (in km) of each net class for the LCC (Rosskopf, 2013).
Distance [km]
Number of seats per flight
101–150
1–250
251–500
501–750
751–1000
1001–1500
1501–2000
2001–3000
3001–4000
180
393
624
848
1228
1681
2411
3319
Appendix C. Aircraft data
C.1 Base data of considered aircraft
Years regarding entry into service and end of production as shown in Fig. C1 as well as aircraft characteristics as displayed in Table C1 are based
on information from aircraft manufacturers (Airbus, 2017c; Boeing, 2017; Bombardier, 2017) as well as Rosskopf (2013). End of production of the
A320-200 and the A321-200 have not yet been determined. We assume that both models are build in addition to their “neo”-versions until 2021 and
2022, respectively, before being replaced by them. All prices are valid for 2016.
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Fig. C1. Entry into service (EIS) and end of production (EOP) of
considered aircraft types.
Table C1
Price, seats, and range of considered aircraft types.
Aircraft type
Price [$M]
Seats
Range [km]
A319-100
A319-100neo
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A330-900neo
A340-300
A340-600
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
89.6
98.5
98.0
107.3
114.9
125.7
256.4
287.7
238.0
275.0
308.0
432.6
46.8
110.0
260.0
358.0
225.0
71.8
132
132
156
156
190
190
277
287
275
326
325
544
127
160
352
410
224
110
4000
5000
4100
4600
4000
4500
11,750
12,130
13,700
14,600
15,000
15,200
5970
4,200
13,450
14,300
14,200
3300
C.2 Calculation of residual values of considered aircraft types
Based on values obtained from the Aircraft value analysis company (AVAC), Rosskopf (2013) carried out a regression analysis to determine the
market value of different aircraft types. This allows for calculating the market values of an aircraft type as follows:
RVikt = mi⋅e−APi ⋅ (k −1)⋅IRt i ∈ I , k ∈ K , t ∈ T
(C.1)
Here, mi is the value for the regression analysis (see Table C2), APi is the aircraft price for the year 2016 (see Table C1) and IR is the inflation rate
(assumed to be 2% per year). We assume that the application of retrofits does not alter the residual value.
Table C2
Parameters of the regression model for the calculation of residual values (Rosskopf, 2013).
Aircraft type
mi
A319-100
A319-100neo
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A330-900neo
A340-300
−
−
−
−
−
−
−
−
−
0.082
0.082
0.084
0.084
0.081
0.081
0.092
0.085
0.092
Aircraft type
mi
A340-600
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
−
−
−
−
−
−
−
−
−
0.089
0.095
0.095
0.076
0.075
0.092
0.095
0.080
0.082
C.3 Calculation of fuel use for considered aircraft types
Based on values for the fuel use of an aircraft in the air and on the ground from the Base of Aircraft Data Eurocontrol (BADA) and the ICAO
Engine Emissions Database as well as the Database for Turboprop Engine Emissions, respectively, Rosskopf (2013) carried out a regression analysis
to determine the fuel use of different aircraft types depending on the flight distance. This allows for calculating reference values of the fuel use of an
aircraft type for one flight cycle as follows:
FUilref = ei⋅Dl2 + fi ⋅Dl + gi + hi ∀ i ∈ I , l ∈ L
(C.2)
Here, Dl is the average distance of a flight in a net class (see Tables B2 and B4), and ei , fi , gi , and hi are parameters of the regression model (see
Table C3). To determine the age-specific fuel use, we further assume that fuel use of aircraft deteriorates by 0.2% per year due to wear and tear
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Table C3
Parameters of the regression model for the calculation of fuel use (Rosskopf, 2013).
Aircraft type
ei
fi
gi
hi
A319-100
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A340-300
A340-600
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
0.00002
0.00004
0.00003
0.00006
0.00005
0.00006
0.00009
0.00012
0.00005
0.00018
0.00006
0.00003
0.00017
0.00016
0.00007
0.00005
2.44
2.53
2.15
3.16
2.68
5.85
5.44
6.94
5.21
12.56
2.49
2.28
8.89
8.31
3.98
1.97
567
525
447
652
555
1441
1624
1841
1282
2880
479
507
2328
2177
1028
376
450
488
415
432
367
944
1018
1812
840
2309
460
368
1675
1566
754
348
compounded over the respective aircraft age (Morrell and Dray, 2009).
FUikl = FUilref ⋅(1 + 0.002)k ∀ i ∈ I , k ∈ K , l ∈ L
(C.3)
Since no regression parameters are available for the A319-100neo and the A330-900neo, we calculate the fuel use with respect to the values
determined for the A319-100 and the A330-300 and assume a relative fuel use reduction of 15% and 18%, respectively (Airbus, 2017c).
In order to determine the fuel use of aircraft types for which retrofit measures are applied, the fuel use of the reference aircraft is decreased by the
respective fuel use reduction (Table C4).
Table C4
Fuel use reduction of retrofit options (Hospodka, 2014; Schäfer et al., 2016; The Flying Engineer, 2013; Yann, 2013).
Retrofit
Fuel use reduction
Blended winglets
Cabin weight reduction
Electric taxiing
Re-engining
1.0% (Dl≤1000 ), 1.8% (1000 <Dl≤4000 ), 4.0% (Dl >4000 )
1.2% per flight cycle
2.8% per flight cycle
12.5% per flight cycle
C.4 Calculation of block times for considered aircraft types
Based on values obtained from the Sabre Airport Data Intelligence Database, Rosskopf (2013) carried out a regression analysis to determine the
block times of different aircraft types depending on the flight distance. This allows calculating the block times as follows:
BTil = ci⋅Dl + di ∀ i ∈ I , l ∈ L
(C.4)
Since no regression parameters are available for the A319-100neo and the A330-900neo, we use the value of the A319-100 and A330-900,
respectively (see Table C5). This assumption is reasonable as cruise speed does not differ between the versions. This can also be seen from a
comparison of the parameters of the A320-200 and the A320-200neo, which are identical.
Table C5
Parameters of the regression model for the calculation of block times (Rosskopf, 2013).
Aircraft Type
ci
di
A319-100
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A340-300
A340-600
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
0.076
0.077
0.077
0.075
0.075
0.072
0.072
0.070
0.071
0.066
0.078
0.076
0.068
0.068
0.071
0.076
36.6
35.0
35.0
39.3
39.3
44.9
44.4
50.9
43.2
64.8
31.7
36.5
51.0
51.0
43.2
36.6
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C.5 Calculation of maximum flight hours per year for the considered aircraft types
Based on reference values of the maximum number of flight hours per year of the world fleet, Rosskopf (2013) found that the maximum number
of flight hours decreases by approximately 1% yearly since the number of planned und unplanned maintenance checks increases as the aircraft ages.
Taking this and a reference value for the maximum number of flight hours per year into account, this maximum number of flight hours per year for
any aircraft can be determined as follows:
MUik = MUikref ⋅(1 − 0.01)k − kref ∀ i ∈ I , k ∈ K
(C.5)
Here, MUikref is the maximum number of flight hours of an aircraft type for a reference age (see Table C6 for the FSNC and Table C7 for the LCC).
Since no reference values are available for the A319-100neo and the A330-900neo, we use the value of the A319-100 and A330-900, respectively.
This assumption seems reasonable as the values do not differ for the A320-200 and the A320-200neo, too.
Table C6
Parameters of the regression model for the calculation of block times for the FSNC (Rosskopf, 2013).
Aircraft type
MUikref
kref
Aircraft type
MUikref
kref
A319-100
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A340-300
A340-600
3430
3306
3306
3077
3077
5561
5139
4952
9
17
17
10
10
4
11
4
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
4704
4577
2862
3430
5427
5427
4299
3430
9
2
19
9
15
15
7
9
Table C7
Parameters of the regression model for the calculation of block times for the LCC (Rosskopf, 2013).
Aircraft type
MUikref
kref
Aircraft type
MUikref
kref
A319-100
A320-200
A320-200neo
A321-200
3430
3306
3306
3077
9
17
17
10
A321-200neo
B737-300
B737-8MAX
CS 100
3077
2862
3430
3430
10
19
9
9
Appendix D. Calculation of MRO-related cash flows
Reference values for the MRO-related cash flows (MCilref ) are calculated with the formulas developed by Liebeck et al. (1995) using the data
displayed in Table D1. In order to account for rising MRO-related cash flows with increasing aircraft age, we adopt the distinction of three phases in
the life cycle of an aircraft, namely, newness (until first D-Check, < 7 years), mature (between first and second D-check 7–14 years), and aging (> 14
years) (Dixon, 2006). Based on these three phases, the factor
Table D1
Technical characteristics of the considered aircraft types.
Aircraft type
Engines
SLST [kN]
MTGW [t]
Airframe weight [t]
A319-100
A319-100neo
A320-200
A320-200neo
A321-200
A321-200neo
A330-300
A330-900neo
A340-300
A340-600
A350-900
A380-800
B737-300
B737-8MAX
B747-400
B747-8
B787-8
CS 100
2
2
2
2
2
2
2
2
4
4
2
4
2
2
4
4
2
2
105
120
118
120
120
147
319
320
151
260
375
311
98
108
252
298
285
104
70
76
77
78
83
83
212
242
275
365
268
560
63
78
397
448
220
54
35
36
34
35
43
44
115
116
121
155
121
270
29
36
163
191
97
29
SLST: Sea level static thrust, MTGW: Maximum takeoff gross weight.
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⎧ 0.12⋅k + 0.18 k < 7
AFMk = 1
7 ≤ k ≤ 14
⎨
⎩ 0.037⋅k + 0.49 k > 14
(D.1)
is used to calculate the MRO-related cash flows as
MCiklt = MCilref ⋅AFMk⋅IRt −1993 i ∈ I , k ∈ K , l ∈ L, t ∈ T ,
(D.2)
where IR is the inflation rate (assumed to be 2% per year), which is required since the formulas by Liebeck et al. (1995) are based on 1993 labor rates
($25/maintenance man hour) and valid for an aircraft that is approximately 10 years old (Rosskopf, 2013).
Appendix E. Initial fleet of the FSNC and the LCC
See Appendix Tables E1 and E2.
Table E1
Initial fleet of the LCC.
Aircraft type
A319-100
A320-200
Aircraft age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
9
13
12
1
9
9
26
3
10
17
10
13
28
20
12
7
25
17
Table E2
Initial fleet of the FSNC.
Aircraft type
Aircraft age
1
A319-100
A320-200
A320-200neo
A320-200 (Winglets)
A321-200
A330-300
A340-300
A340-600
A350-900
A380-800
B737-300
B747-400
B747-8
3
7
2
7
2
3
4
5
6
7
2
5
2
3
3
1
3
9
1
8
3
10
5
8
9
10
11
12
13
14
15
16
17
18
19
20
21
7
10
3
22
23
24
25
3
26
27
28
1
9
4
10
1
5
1
7
4
4
3
1
6
5
1
6
2
3
5
1
8
1
4
2
2
9
1
2
1
1
2
2
1
2
1
4
1
7
1
2
2
2
3
5
2
4
6
6
5
3
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