a fuel tankering model applied to a domestic airline network

A fuel tankering model applied to a domestic airline network

Jose Alexandre Tavares Guerreiro Fregnani,Carlos Muller and Anderson Ribeiro Correia*

Department of Civil Engineering, Instituto Tecnologico de Aeronautica (ITA), Sao Jose dos Campos, Brazil

SUMMARY

This paper presents a linear programming model designed to determine the optimum fuel loading quantitiesalong a route network for a Brazilian domestic airline. Assuming that there are no volume purchase orstorage capacity restrictions on each station, the analysis is carried out for one aircraft on one day of itsschedule. Results are extrapolated for a monthly and yearly basis. Through the proposedmodel, it is seen thatsuch a fuel tankering technique leads to a 5% economical saving, but produces a 1% additional fuel burn. Adiscussion on the environmental impact for this procedure is also proposed. Copyright# 2011 JohnWiley&Sons, Ltd.

KEY WORDS: air transport; operations research; airlines operational costs; fuel tankering; flightoperations; linear programming

1. INTRODUCTION

According to recent studies carried out by the [1], fuel consumption is the second highest direct

operating cost component for airlines, behind only labor costs. It is estimated that fuel consumption

represents 20% or more of the total direct operating costs for any kind of airline. A remarkable

characteristic of commercial aviation is being in extremely competitive markets with lower profit

margins when compared with other transportation modes. Hence, the airlines that can manage

fuel consumption efficiently will undoubtedly reap competitive advantages that may well ensure their

survival. IATA [1] also estimates that currently for every dollar spent on fuel, airlines have to generate

15–20 dollars in revenue to obtain the same profit margin.

Moreover, the price of oil has risen dramatically since 2000. Despite the technological strides taken

by the oil industry that have led to the discovery of new reserves, the influences – above al the

geopolitical nature of the Middle East – or even unconventional influences, such as natural disasters

and global financial crisis in 2008, have contributed to instability and an increase in prices in recent

years. Figure 1 reflects the worldwide fuel price for US passenger and cargo airlines, using data made

available by the Department of Transportation (DOT) and Air Transport Association (ATA). It is very

clear that market prices for jet fuel are highly correlated with the prices of crude oil (home heating oil).

The average price for a barrel of oil was US$26.01 at the beginning of 2002, US$56.08 at the end

of 2005 and reached the outstanding peak of US$161.13 on August 2008, when the price was

artificially raised through a severe market speculation. In the beginning of 2009 the prices decreased

deeply affected by the world economical recession started by the end of 2008. However fuel price

is recovered reaching approximately US$ 70.00 in mid 2010. Average prices paid for jet fuel are

a function of long-term contracts, spot market prices, and point of sale, deeply affected by country’s

economic health. Therefore added attention has been paid to fuel consumption by airlines in recent

years. It is an increasingly common survival practice for airlines to establish fuel conservation

JOURNAL OF ADVANCED TRANSPORTATION

*Correspondence to: Anderson Ribeiro Correia, Department of Civil Engineering, Instituto Tecnologico de Aeronautica(ITA), Sao Jose dos Campos, Brazil. E-mail: [email protected]

Copyright # 2011 John Wiley & Sons, Ltd.

J. Adv. Transp. 2013; 47:386–398Published online 9 February 2011 in Wiley Online Library (wileyonlinelibrary com).DOI: 10.1002/atr.6666666666666 6 6 6 6 6 6 6 6 6 6 6 6 6 6 61 2

programs, where a set of measures involving the areas of operations and maintenance is created to

minimize consumption. Multidisciplinary teams at the airlines analyze all the aspects that may generate

additional consumption, such as: the drag degradation (matching of surfaces, seals, and closures, the state

of paintwork, polishing, flight controls rigging, and so on), engine wear, cleanliness of the airplanes, extra

basic operating weight (BOP) through the absorption of dust and moisture, as well as the establishment of

operating procedures linked to flying techniques and procedures decision making, amongst others. The

operational area has a great impact on the reduction of consumption, as it is the only sector capable of

influencing and directly determining the total volume of fuel consumed and supplied on the routes,

through appropriate policies and procedures applied to the pilots and dispatchers (Figure 2).

According to studies carried out by EMBRAER [2], a 1% fuel saving can easily be achieved through

coherent operational practices such as operational procedures focused on easily executed fuel savings

(which do not involve large investments), mostly concentrated just on pilot’s training and flight

dispatch. One of the most commonly adopted procedures by the airlines is what is known as

‘‘Economic Fueling’’ or ‘‘Fuel Tankering,’’ as presented below.

2. THE FUEL TANKERING PROCEDURE

Fuel price variations in each locale, an absence of fuel (e.g., at remote airports), or contractual

restrictions with suppliers along the routes may result in transporting more fuel than the minimum

required by regulations from certain locations, so as to minimize supply costs. The practice of carrying

an extra quantity of fuel is called ‘‘Fuel tankering’’ or ‘‘Economic Supply.’’ As carrying extra fuel

results in extra weight and therefore produces additional fuel consumption in the sector referred to, it is

important to analyze the transport cost of this additional fuel. Generally, airlines analyze the economic

feasibility of transporting fuel sector-by-sector, for each aircraft. In each sector, if tankering is feasible,

it is planned to supply the aircraft at the origin with such a quantity of extra fuel that the remainder at

Figure 1. Evolution of crude oil and jet fuel prices.

Figure 2. Scheduling of flights for each aircraft on a route.


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387A FUEL TANKERING MODEL

the destination is exactly the fuel required by regulations for the next sector, calculated according to the

regulatory minimum fuel reserves.

In addition, due to the additional weight the operation imposes on the aircraft, some requirements

must be respected in each sector where the extra fuel is tankered: the maximum takeoff weight

(MTOW) at the airport of origin cannot be exceeded, the maximum landing weight (MLW) at

the destination airport cannot be exceeded, and the aircraft’s maximum fuel capacity on tanks cannot be

exceeded. Another important aspect, generally not considered by airlines, is the deterioration of other

aircraft systems with regard to the heavier landing weight this technique imposes. Studies carried out by

Boeing [3] mention the wearing of brakes, tires and engine reversing systems, which can be aggravated if

these systems are used more intensely when the aircraft operate at weights close to the Maximum

Structural Landing Weight (MSLW). In this work, we have not considered such deterioration.

In Brazil fuel tankering is a very common practice as there is a large variation in the tax rate on

aviation fuel amongst the States (a variation of between 4 and 25% is expected). The airlines generally use

sector-by-sector analysis to study the viability of fuel tankering. Network effects, such as theminimization

of costs for all the supplies throughout the planning for an aircraft on a route, in an integrated and

simultaneous form, are not yet evaluated. Very often, analysis of the break-even price is not systematized,

and is fuel tankering is normally simplified only executed where fuel prices are cheaper. Some operators

ignore concerns over additional consumption due to higher takeoff weights produced by this practice.

3. BIBLIOGRAPHICAL OVERVIEW

EMBRAER [4] suggests the analysis of economic viability for fuel tankering in one single sector,

comparing the break-even price (Pdeq), determined through charts and tables in the aircraft operating

manual, with the real price of fuel at the destination (Pd). If the real price of the fuel at the destination

is higher than the break-even price, extra fuel tankering is feasible at the airport of origin. It is

suggested that the quantity supplied at the origin be such that on landing at the destination, the fuel

remaining be exactly the minimum required by regulations for the following sector. The following

relations determine the break-even price at the destination:

Pdeq ¼ Po

ð1�f Þ (1)

f ¼ dWf

dW(2)

where Pdeq is the ‘‘Break-even’’ price at the destination. This represents the minimum fuel price on

destination station that turns the transportation of extra fuel from origin station economically feasible,

Po the Fuel price at the origin, f the Fuel consumption factor, dWf the Variation of fuel consumed (kg),

and dW is the Variation of aircraft weight (kg).

Factor f is sensitive to the length of the sector, its cruising altitude and speed, and its average wind

speed. Generally it is a factor informed by computerized navigational planning systems, such as

fuel burn adjustment expressed as a percentage. Values between 3 and 5% are expected for short

and medium sectors (up to 1000 nm) for regional aircraft with capacities of 70–110 seats. Charts are

found in these aircrafts’ flight manuals to determine factor f, as well as Pdeq.

Saboya [5] suggests comparing break-even prices and real fuel prices at the destination, in a manner

identical to the aircraft manufacturer, which is to say sector by sector. However, he develops

an algorithm to produce factor f from the information available in the flight manuals of any kind of

aircraft. This algorithm involves the determination of the average additional percentage of

consumption in relation to a reference landing weight, determined at about 4000 kg less than the

MSLW for a certain sector. To this end, it suggests the hypothesis that the additional percentage

consumption ion this weight band is approximately constant. This consumption is calculated

from the simplified planning charts for the sector (consumption calculation) in the aircraft operating

manuals. Next, the average percentage consumption deviation for each combination of predetermined

distances and cruising altitudes is calculated. The percentages obtained will be the values of factor

f. Stroup and Lackey [6] provide a decision model to indicate where to execute fuel tankering along a


DOI: 10.1002/atr

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388 388 J. A. T. GUERREIRO FREGNANI ET AL.

route. They consider location and supplier restrictions, as well as the price of fuel. They use a constant

factor f in their analysis.

Darnell and Loflin [7] drew up a great strategy for fueling to be used in the short and medium term. They

developed a choice model that supplies the best places and suppliers for each sector based on: price,

availability, consumption, tankering costs (considering a constant factor f), and real data from the flights in

question. Stroup and Wollmer [8] present a generic model that minimizes fuel supply costs for a route

supplied by various kinds of aircraft, through a linear programmingmodel, assuming a constant factor f. The

fuel supply decisions are based fuel prices and two network restrictions: airport restrictions: total fuel the

airport could supply to all its flights and total fuel contracted from a supplier. If the problem is limited to just

fuel prices, it may be transformed into a pure network problem. In this model, they estimate 5–6% savings in

fuel supply using this kind of resolution. This model was executed to minimize fuel supply costs in planning

for a single aircraft on two routes involving 10 distinct sectors. A saving of 5.69% was achieved.

Zouein et al. [9] present the decision model to determine the quantity of fuel to be supplied to an

aircraft at each airport on its schedule, considering a certain planning horizon in time, so as to minimize

total fuel supply costs. Such a problem is modeled as a multiple period inventory problem and solved

using linear programming. The applied the model to Middle East Airlines (MEA) routes. The weight

and capacity restrictions considered on each sector are the following: MTOW,MLWat the destination,

total fuel capacity and minimum security fuel (remaining at the destination). Analysis is done for each

aircraft in the fleet throughout the sectors in the daily schedule. Factor f is determined as a linear weight

function for each sector. Abdelghany et al. [10] developed the linear programming model for fuel

supply in multiple locations, considering a constant factor f and applying it to various price scenarios.

They analyzed multiple fuel supply scenarios and the sector-to-sector scenario. They achieved savings

in the range of 0.5% for the sector-to-sector analysis, and 3% to multiple sector analysis.

This paper presents the research results as an improvement to Zouein’s model, which includes the

MTOW and MLW restrictions. On the proposed model restrictions regarding Maximum Fuel Capacity,

local regulations and common operational policies are included. Additionally the factor f, estimated as

a fixed constant on previous studies, is now proposed to be evaluated as function of altitude and distance on

a bi-dimensional polynomial model. This turns the solution closer to the operational environment

(for example avoiding the solution where the remaining fuel on a sector scheduled to be zero).

4. MODEL PROPOSED

The model proposed is applied to the daily schedule for a group of aircraft on one network flight

sequence. Each aircraft is scheduled for i sectors (where i¼ 1, . . ., N� 1 and N is the total number of

stations). It is also considered that for each airport the price of fuel is predefined as Pi (kg). The problem

involves determining what quantity of fuel must be supplied at each airport in order to minimize

the total cost of the operation for each aircraft.

The following operating restrictions must be obeyed:

� MTOW at airports of origin must not be exceeded.

� MLW at destination airports must not be exceeded.

� Maximum Fuel Capacity for the aircraft must not be exceeded.

� Fuel supplied must not be less than the minimum required by regulation.

� Remaining fuel at the destinations must not be less than the minimum reserve defined by the

company’s operating policy.

We have also considered the following hypotheses:

� There shall be one single fuel supplier, established in contract, at each location. Such a hypothesis

is very reasonable, given that airlines always opt for the cheapest supplier.

� There shall be no contractual restrictions on the total volume of fuel bought along the routes for

a certain supplier. That is to say, the sale of fuel is unlimited.

� All the locations will be capable of providing the necessary fuel quantity for all the flights. That is to

say, there shall be no restrictions on fuel storage capacity to supply all the aircraft passing through

each location.


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A FUEL TANKERING MODEL 389

In this way, fuel supply for each aircraft does not interfere with the supply for others along the route.

This allows each aircraft to be dealt with separately on its schedule. The total fuel supply cost for the

routes shall be the sum of the fuel supply costs for each aircraft. This problem shall be solved through

the linear programming model to minimize the total fuel supply cost along the N locations for the daily

schedule for each aircraft. The decision variable is the quantity of fuel to be supplied (Xi) for each

sector i, at location i, with i¼ 1, . . ., N� 1. For each aircraft in its daily schedule, the following linear

programming model can be formulated:

� Objective function:

MinZ ¼XN�1

i¼1

PiXi (3Þ

� Restrictions:

i. MTOW Restriction:

ZFWi þ FOBi ¼ MTOWi for i ¼ 1; . . .;N�1 (4Þii. MLW Restriction:

TOWi�TRIPi � MLWi for i ¼ 1; . . .;N�1 (5Þiii. Maximum aircraft fuel capacity restriction:

REMi þ Xi � MAXF for i ¼ 1; . . .;N�1 (6Þiv. Minimum fuel regulation for sector i:

REMi þ Xi � FOB0i for i ¼ 1; . . .;N�1 (7Þv. Minimum remaining fuel at destination:

FOBi�1 þ TRIPi�1 � MINFi for i ¼ 2; . . .;N (8Þvi. Consumption adjustment by factor f:

fi ¼ dWf

dW� TRIPi�TRP0i

FOBi�FOB0i

� �for i ¼ 1; . . .;N�1 (9Þ

vii. Definition of fuel aboard at origin:

FOBi ¼ REMi þ Xi fori ¼ 1; . . .;N�1 (10Þviii. Definition of remaining fuel at destination:

REMi ¼ FOBi�1�TRIPi�1 for i ¼ 1; . . .;N�1 (11Þix. Positive fuel supply values:

Xi � 0 (12Þwhere fi is the fuel Adjustment Constant, FOB0i the regulation minimum fuel on sector I

(according to RBHA 121.645) (kg), FOBi the total fuel aboard on sector i (kg), MAXF the

maximum fuel capacity in tanks (kg), MINFi the fuel remaining from sector i (kg), TOWi the

takeoff weight on sector i in (kg), Pi the price of fuel at airport of origin on sector i (US$/kg),

MTOWi the maximum structural takeoff weight (kg), MSLWi the maximum structural landing

weight (kg), MZFWi the maximum zero fuel weight (kg), LWi the landing weight on sector i

(kg), ZFWi the zero fuel weight on sector i (kg), REMi the remaining fuel after landing on

sector i (kg), TRIP0i the consumption from sector i with minimum regulation fuel (kg), and

TRIPi is the Consumption from sector i (kg).

The equations regarding one sector i are linear combinations of the equations regarding the sector

before (i� 1), lending the model a recursive nature. Also, the number of restrictions is a function of the

number of locations involved: for N locations, 5(N� 1) restrictions are generated, considering

Equations (4)–(8). For Equations (9)–(11), these just define some of the variables involved in these

restrictions.


DOI: 10.1002/atr

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J. A. T. GUERREIRO FREGNANI ET AL.390

Considering that domestic and regional routes typically have 4–12 daily sectors for each aircraft, the

linear programming model proposed has 20–60 restriction equations. This leads us to conclude that

a robust resolution algorithm is necessary. In the model proposed, the new feature in regard to the

others found in the literature shall be the form with which factor f shall be modeled: a polynomial

relation as function of the distance and cruising altitude for a certain profile of speeds in each sector

considered. The influence of the weight of the aircraft shall be built into such modeling.

5. MODEL RESTICTIONS

Due to operational reasons, such as badweather forecasts en-route or expected delays and holdings at peak

times on destination, sometimes pilots request to uplift more fuel than the minimum required on the

departure station (as per predicted on the flight plan) regardless of the fuel price analysis. This ‘‘forced’’

fuel tankering procedure is the so-called ‘‘captain extra fuel’’ and it is not considered on the present model.

It is also valid to comment that the fuel tankering technique is only feasible on short/medium range

flights where takeoffs are generally limited by MLW on destination or MZFW. International Long

Range flights, typically above 3000 nm sector length, where most of the times are limited by MTOWs,

are not appropriate for this kind of procedure since every increment of additional fuel may represent

payload or range shortening. Therefore Long Range flights are generally not adequate to this technique

and are not evaluated on this study.

6. APPLICATION OF THE MODEL

From a route supplied by a Brazilian domestic airline and its respective scheduling for one aircraft for one

day, we have used the proposedmodel to determine supply in 12 sectors. The prices of fuel at each basewere

also supplied, converted to cost per kg, using a density of 0.785kg/L. The values were given in US dollars.

We used a single regional aircraft model with a 108-seat capacity, equipped with GE CF34-10E6

engines developing 18 500 lbf of maximum takeoff thrust at sea level in international standard

atmosphere (ISA) conditions. The Advanced Integrated Multidimensional Modeling Software

(AIMMS) was used to solve the linear programming problem, due to its recursive nature. Total fuel

cost obtained (extrapolated for a month) was compared with the total cost of conventional fuel supply,

where each location is supplied with a minimum regulation quantity of fuel. The following input data

sources were used:

� Airport information: From the Brazilian Airport Information Publication (AIP).

� Aircraft characteristics: Taken from the operating manual: MSZFW, takeoff (MSTOW), landing

(MSLW), and maximum fuel capacity (MAXF). The Simplified Long Range Cruise Fuel Con-

sumption Planning Chart (Annex I) was used to ascertain consumption involved in calculation of

factor f.

� ZFWi: Estimated through the average load factor of 65% and 500 kg of load in the hold in all sectors.

The average passenger weight of 85 kg was adopted, with 5 kg of hand baggage, and 20 kg of stowed

bagged and a BOP of 27 400 kg. The ZFW considered for all the sectors was 35 600 kg.

� MTOWi and MLWi: Ascertained through specific software for calculating takeoff and landing

performance produced by the aircraft manufacturer. For this calculation, reference temperatures,

calm wind, and the statistically most commonly used parameters in each airport were considered.

� Consumption without Tankering (TRIP0i) and minimum regulation fuel (FOB0i): Ascertained

through specific software for calculating navigation plans produced by the aircraft manufacturer.

For the purpose of flight planning, the following premises were considered:

(i) Cruising altitudes, as far as possible, corresponded to those for lesser specific consumption.

However, the most appropriate altitudes were respected for the upper limits of flight paths used,

as well as maximum altitudes allowed by the performance of the aircraft.

(ii) The minimum fuel reserves were calculated according to the Brazilian regulations referent to

flights on instruments in regular passenger transport airlines o domestic flights.

(iii) The alternative airports were considered at a maximum distance of 200 nm from the destination

airport.


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(iv) For each sector considered winds and temperatures at cruising were considered at 85% of the

annual statistics.

(v) The flight path distances were taken from instrument navigation charts published by the

Brazilian Airspace Control Department for higher and lower airspace.

� Remaining Fuel: The minimum fuel on landing at the destination (MINFi) was considered to be

2000 kg on all sectors. This value was also adopted in the first sector (REM1).It is essential to

ascertain factor f for each sector i considered for the resolution of the problem. Hence, we adopted

the methodology cited by Saboya [5]:

(i) Choosing a landing weight reference. 36 000 kg, corresponding approximately to the ZFW in

the study.

(ii) Using the Simplified Long Range Cruise Fuel Consumption Planning Chart in the aircraft

Operating Manual, calculating the consumption for each combination of landing weights,

altitudes, and distances established beforehand. The following intervals were considered:

� Distances: 200, 400, 600, 800, 1000, and 1200 nm.

� Altitudes: 15 000, 20 000, 25 000, 30 000, 35 000, 39 000, and 41 000 ft.

� Weights: 36 000 (reference weight), 38 000, 40 000, 42 000, and 43 000 (MSLW) kg.

(iii) For each set of weights for a given distance and altitude pair, the percentage difference of

consumption is calculated in regard to the reference weight in this set. The average percentage

deviation shall be the factor f referent to the respective combination of altitude and distance.

Note that in this form, the variable weight no longer has a direct role in the calculations for f.

This methodology assumes the hypothesis that the influence of the weight has a lesser magnitude

than the influence of the distance and/or altitude on additional fuel consumption. Thus, an average

value can be adopted for factor f for a set of weights near to the MLW, given the combination of altitude

and distance. In Table I we present the complete result for all suitable altitudes. Maximum altitudes for

the referred distances are selected considering three minutes of minimum cruise time.

In order to make the exact calculation of factor f more executable from the computational

standpoint, Table III can be conveniently modeled in a polynomial form (cubic) through the following

set of equations:

f ¼ A0 þ A1di þ A2d2i þ A3d

3i (14)

A0 ¼ A00 þ A01Hi þ A02H2i þ A03H

3i (15)


3i (16)


3i (17)


3i (18)

Table I. Analysis of factor f.

Dist (nm) Altitude (ft)

15 000 20 000 25 000 30 000 35 000 37 000 39 000 41 000

200 1.30% 1.19% 1.07% 0.99% 0.94% — — —400 2.94% 2.68% 2.43% 2.24% 2.12% 2.10% 2.10% —600 — 4.19% 3.81% 3.50% 3.30% 3.26% 3.24% 3.26%800 — — 5.19% 4.77% 4.51% 4.45% 4.43% 4.45%1000 — — — 6.06% 5.75% 5.71% 5.72% 5.78%1200 — — — — 7.05% 7.05% 7.14% 7.32%


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For i¼ 1, . . ., N� 1where di is the distance in sector i (nm), Hi the Cruising altitude in sector i (ft),

Amn the adjustment coefficients. For m¼ [0, . . ., 3] and n¼ [0, . . ., 3].Applying the minimum square method for two-dimensions, the values for Amn for the case analyzed

can be ascertained. Table II shows the values. The correlation coefficient (R2) considering these

coefficients is 0.9998, which we deem adequate to solve the problem proposed.

According to Boeing [11], if we consider the effect of the wind along the route, the distance (di)

considered in the tables above should be interpreted as being the distance traveled by the aircraft in

a mass of air, which is different from the distance traveled by the aircraft on the ground because of the

wind. A correction is required in the distance traveled in relation to the ground (or total route distance)

in order to provide an equivalent value ‘‘d,’’ bearing in mind the average wind vector forecast along

the longitudinal axis of the aircraft (Vw) and the true air speed (TAS) along the route. The following

relation is applicable:

di ¼ Di

TASi

TASi þ Vwi

� �(19)

where TASi is the true airspeed speed of the aircraft for sector i (kt) and Vwi is the average cruising

wind vector component forecast for the longitudinal axis of the aircraft for sector i (kt). Negative values

represent headwinds and positive values represent tailwinds. Di is the distance traveled on the ground

(or flight path) in nm for sector i. We adopted the values published in the navigation charts for

instrument flights.

The TAS value must be provided by the navigation planning system produced by the aircraft

manufacturer. In addition, it is necessary to adjust consumption to average temperature conditions on

a route different from the standard. Standard temperature is defined as static temperature of the air at

the altitude referred to according to the ISA model defined by the ICAO. Further details can be found

at Padilla [12] and Boeing [11]. According to the Flight Planning section of the Aircrafts Operating

Manual (EMBRAER [13]), for every 1 8C above the ISA temperature, 0.4% is added to hourly aircraft

consumption. As factor f is directly proportional to total consumption (which is the integration of

hourly consumption), then it can also be adjusted for this deviation with reasonable approximation

through the following equation:

f �i ¼fi 1þ 0:004 � DELTA ISAið Þ (20)

where f �i is the fuel consumption adjustment factor in temperature conditions other than the standard

static air temperature for sector i. DELTA_ISAi is the temperature deviation at cruising altitude in

relation to the ISA static air temperature for sectors i (8C).For the calculation of di andf

�1 , statistical annual static standard temperature deviations and winds

are used in each route, with a significance of 85%.

7. RESULTS

It was considered that at the beginning of the schedule the aircraft carried 2000 kg of fuel, generally the

minimum quantity of fuel on board according to airline operating policy. Table III shows all the input

data necessary to solve the problem. Table IV shows the results with the conventional fuel supply

Table II. Interpolation coefficients (Amn) for the function f¼ f (d, H).

Amn m

0 1 3 3

n0 �6.5862E�03 3.1845E�07 �8.4929E�12 8.0717E�171 9.8221E�05 �1.3562E�10 �8.8946E�14 1.7485E�182 2.1868E�08 �3.6676E�12 1.9498E�16 �3.1524E�213 �8.3698E�12 1.5333E�15 �8.6796E�20 1.5039E�24


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Table

III.

Inputdata.

IFrom

To

Pi

(US$/kg)

D(nm)

ALT

CRZ(ft)

ISA

Dev

CRZ(8C)

WIN

DCRZ(K

t)TAS

(kt)

d(nm)

f�(%

)ZFW

i

(kg)

MTW

i

(kg)

MLW

i

(kg)

MFOB0i

(kg)

TRIP0i(kg)

1FOR

REC

1.26

339

39000

4�1

1404

348

1.80

35600

50300

43000

4870

1957

2REC

MCZ

1.01

98

15000

17

�5310

100

0.46

35600

50300

43000

2639

1143

3MCZ

AJU

1.16

116

20000

17

�9330

119

0.57

35600

50198

43000

2841

964

4AJU

SSA

1.16

137

24000

16

�9347

141

0.67

35600

50300

43000

3093

1085

5SSA

GRU

1.05

846

38000

6�4

4439

940

5.31

35600

50300

43000

6818

4395

6GRU

CWB

0.96

194

30000

12

�52

386

224

1.13

35600

50300

43000

3707

1400

7CWB

GRU

0.93

221

31000

12

5377

218

1.07

35600

46971

43000

3520

1382

8GRU

SSA

0.96

787

39000

42

432

783

4.33

35600

50300

43000

5941

3675

9SSA

AJU

1.05

137

25000

16

�17

353

144

0.68

35600

50300

43000

3093

1098

10

AJU

MCZ

1.16

116

19000

17

�10

325

120

0.58

35600

50300

43000

2750

973

11

MCZ

REC

1.16

98

18000

17

�10

319

101

0.45

35600

50198

43000

2633

867

12

REC

FOR

1.01

337

38000

6�2

2408

356

1.84

35600

50300

43000

4875

1986


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J Adv Transp 2013; 47:386–398


strategy, where takeoff is donewith the minimum possible fuel according to regulations. One exception

is made in sector REC–MCZwhere the minimum regulation fuel required was less than that remaining

from the sector. The table also shows the amounts of fuel supplied in each base (Xi), as well as the costs

associated to each supply according to fuel prices given.

Table V shows the supply values obtained from the application of the model proposed.

Table VI summarizes the main impacts of the proposed model since it presents a comparative

analysis of the results between the conventional and the proposed approach. The monthly and annual

estimates are forecasted for one single aircraft running this schedule 6 days a week. It is noticeable that,

although more fuel is effectively burnt daily with the new tankering strategy, substantial economic

gains are obtained annually considering only 12 sectors.

Table V. Supply strategy using the model proposed.

I From To REMi (kg) Xi (kg) FOBi (kg) Twi (kg) TRIPi (kg) Lwi (kg) COST (US$)

1 FOR REC 2 000 2 870 4 870 40 470 1 957 38 513 $3.604,532 REC MCZ 2 913 5 657 8 570 44 170 1 170 43 000 $5.737,213 MCZ AJU 7 400 0 7 400 43 000 990 42 010 —4 AJU SSA 6 410 0 6 410 42 010 1 107 40 903 —5 SSA GRU 5303 1 515 6 818 42 418 4 395 38 023 $1.588,566 GRU CWB 2423 1 284 3 707 39 307 1 400 37 907 $1.227,577 CWB GRU 2307 6 532 8 839 44 439 1 439 43 000 $6.052,708 GRU SSA 7 400 1 355 8 755 44 355 3 797 40 558 $1.295,409 SSA AJU 4 958 0 4 958 40 558 1 111 39 447 —10 AJU MCZ 3 847 0 3 847 39 447 979 38 468 —11 MCZ REC 2 868 0 2 868 38 468 868 37 600 —12 REC FOR 2 000 2 875 4 875 40 475 1 986 38 489 $2.915,62Total 21 199 $22,421.60

Table VI. Final comparative results.

Final results (per aircraft)

Item Daily Monthlyforecast

Annualforecast

Saving (US$) 751,41 (3.24%) 19.322,08 231.865,00Average saving per sector (US$) $62,62Extra consumption (kg) 1096 (1,31%) 28.191 338.294Extra consumption per sector (kg) 23

Table IV. Conventional tankering strategy.

i From To REMi (kg) Xi (kg) FOBi (kg) Twi (kg) TRIPi (kg) Lwi (kg) COST (US$)

1 FOR REC 2 000 2 870 4 870 40 470 1 957 38 513 $3.604,532 REC MCZ 2 913 0 2 913 38 513 1 143 37 370 —3 MCZ AJU 1 770 1 071 2 841 38 441 964 37 477 $1.243,644 AJU SSA 1 877 1 216 3 093 38 693 1 085 37 608 $1.407,175 SSA GRU 2008 4 810 6 818 42 418 4 395 38 023 $5.042,846 GRU CWB 2423 1 284 3 707 39 307 1 400 37 907 $1.227,577 CWB GRU 2307 1 213 3 520 39 120 1 382 37 738 $1.124,018 GRU SSA 2 138 3 803 5 941 41 541 3 675 37 866 $3.635,869 SSA AJU 2 266 827 3 093 38 693 1 098 37 595 $867,0310 AJU MCZ 1 995 755 2 750 38 350 973 37 377 $873,6911 MCZ REC 1 777 856 2 633 38 233 867 37 366 $993,7412 REC FOR 1 766 3 109 4 875 40 475 1 986 38 489 $3.152,93Total 20 925 $23.173,01


DOI: 10.1002/atr

J Adv Transp 2013; 47:386–398


Finally on Figure 3 it is shown the fuel uplift strategies (quantity supplied – Xi) regarding the

conventional flight planning and the optimized fuel uplift predicted by the tankering model. It is

noticeable the larger quantity of fuel uplifted at departure stations where fuel price are cheaper. Origin

airport fuel prices are shown and expressed in US$/kg.

8. FINAL CONSIDERATIONS

The proposed model is shown to be consistent with the results found by Stroup and Wollmer [8] when

they applied their model without restrictions on fuel quantities supplied at the airports. All the results

found are valid, considering the premises adopted by the model. A gain of 3.24% was achieved for the

12 sectors analyzed, which is considered very satisfactory in the aeronautical industry, where operating

cost reductions of 1% are considered satisfactory. For the scenario analyzed, a fleet of 10 aircraft flying

six times a week would make annual savings estimated at US$2,318,650.00 if such a procedure where

adopted.

The proposed model is very sensitive to fuel prices and generally distributes larger fuel uplifts at

stations presenting lower fuel prices. As expected through the linear model restrictions, on stations

where fuel is more expensive uplift is scheduled to zero and minimum fuel is exactly the remaining fuel

from the previous sector.

Although the model was evaluated for a Brazilian domestic airline network, results may be

extrapolated to any airline operating under equivalent domestic FAR or JAR-OPS regulations, since

minimum fuel requirements are similar.

However, it must be stressed that fuel tankering causes, besides economic gains, significant

environmental impacts. In the example analyzed, there is an additional average fuel consumption

of 23 kg per sector flown, or 338 tons a year per aircraft. This additional consumption also implies the

emission of pollutants into the higher layers of the troposphere and tropopause, where commercial

jet aircraft generally fly.

According to recent studies by the FAA [14], for every 1000 kg of JET-A1 fuel burned, the aircraft/

engine in question produces, in average, 3.155 kg of CO2. That is to say, considering only this pollutant,

this operation would involve the emission of 1067 additional tons a year into the atmosphere, for

one single aircraft.

Figure 3. Difference in quantity supplied (Xi) along the routes between the conventional strategy and fueltankering.


DOI: 10.1002/atr

J Adv Transp 2013; 47:386–398


Currently, the influence on global warming caused by gases emitted by human activity is being

fiercely debated. Analysis of the contribution made by the airline business on the greenhouse effect

is gaining pace, estimating that it is currently responsible for approximately 2.5% of total CO2

emissions, or 12% of emissions from the means of transport that use fossil fuels.

According to the ICAO [15], the possibility is being studied of adopting landing and parking fees

based on aircraft emission levels, as is nowadays practiced in terms of airport noise in some places

in the world. International airports in Zurich and Stockholm were the first ones to test such measures.

In the years to come it is expected that Annex XIVof the ICAO will contain recommendations on such

fees and the classification of polluting aircraft groups. Airlines operating aircraft with high emissions

levels will very soon pay more for their ecological damage. One example of this concern is the

European Union Emissions Trading Scheme (EU ETS), held by the European Parliament, which

included in January 2008 by the first time the aviation activity on specific regulations for carbon trading

schemes in Europe (to be starting at 2010). According to IATA, these initiatives are expected to be

followed by aviation regulation authorities worldwide in order to stabilize aviation emissions

share facing of the predicted traffic growth in next decades.

Since fuel uplift means also more fuel consumption (and therefore more emissions), although the

fuel tankering practice has significant potential to provide expressive economic gains, environmental

sustainability seems to be the main limitation to this operational procedure.

The main challenge for future investigations will be the evaluation of fuel tankering in the light

of the impact caused by this technique on the environment.

REFERENCES

1. International Air Transport Association – IATA. Guidance material and best practices for fuel and environmental

management, 1st edn IATA-International Air Transportation Association: Montreal, 2004.

2. Embraer. Embraer 170/190 fuel conservation, Sao Jose dos Campos, 2005.

3. Boeing Company. Fuel conservation News Letters, Seattle, 1992.

4. Embraer. Embraer 190 operations manual Vol. 1 – Chapter 6 – Flight Planning, Sao Jose dos Campos, 2006.

5. Saboya EW. Airline flight operations handbook. Varig Airlines: VARIG, Porto Asectorre, 1992.

6. Stroup JW, Lackey WJ. Fuel management model (for aircraft fuel costs and requirements). Operations Research

Society of America and Institute of Management Sciences, Joint National Meeting: Las Vegas, Nevada, 1975.

7. Darnell DW, Loflin C. National Airlines Fuel Management and Allocation Model. Interfaces 1977; 7: 1–16.8. Stroup JS,Wollmer RD. A Fuel Management Model for the Airline Industry.Operations Research 1991; 40(2): 229–

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9. Zouein PP, Abillama WR, Tohme E. A multiple period capacitated inventory model for airline fuel management: A

case study. Lebanese American University: Beirut, Lebanon, 2002.

10. Abdelghany K, Abdelghany A, Raina S. A model for the airlines’ fuel management strategies. Journal of Air

Transport Management 2004; 11: 199–206.11. Boeing Company. Jet transport performance Methods, Seattle, 1998.

12. Padilla CE. Optimizing jet transport efficiency – performance, operations and economics. McGraw-Hill: New York,

1996.

13. Embraer. Embraer 170/190 flight operations engineering course notes, Sao Jose dos Campos, 2006.

14. FAA. Sage – Appendix ‘‘D’’ – Modal Aircraft Fuel Burn and Emissions for 2004, Seattle. 2004.

15. International Civil Aviation Organization – ICAO. Cost effectiveness on local Air quality charges. CAEP - Issue

Paper No.7, Montreal. 2006.


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ANNEX I: SIMPLIFIED LONG RANGE CRUISE FUEL CONSUMPTION PLANNING

CHART [7].


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a fuel tankering model applied to a domestic airline network

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