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Note

Aircraft replacement strategy: Model and analysis

Massoud Bazargan a , *, Joseph Hartman ba College of Business, Embry-Riddle Aeronautical University, 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114, USAb Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA

Keywords:Aircraft acquisitionAircraft replacementAircraft purchasingAircraft leasing

a b s t r a c t

This study presents a model to help airlines plan their strategic eet acquisitions and disposals. It

minimizes the discounted costs of owning or leasing and operating a eet by identifying which aircraft tobuy, sell and lease over the planning horizon. The paper explains how the related cost data werecompiled and analyzed. The model is applied to two US airlines with different business models andshows that aircraft leasing is generally the preferred alternative with bene ts from having newer aircraftand less eet diversity.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

Most aviation regulatory agencies and aircraft manufacturersforesee that demand for air transport will rise in the next 20 years.Airlines seek to strategically position themselves to meet this rise in

demand. Aircraft replacement strategies are important decisionsthat impact all processes related to planning and operations withinairlines, and involve when and how many aircraft of different typesto purchase, lease and dispose of within an airline s planninghorizon. These decisions must support an airline s short and long-term decisions affecting their nancial, operational and competi-tive performance.

Most prior work in this eld addresses the problem in thecontext of eet planning (e.g. Gao et al., 2009 ) and focus onshort-term tactical decisions and utilizing the available eetrather than consider long-term changes to the size or composi-tion of the eet. The limited aircraft replacement models includeHsu et al. (2011) who present modeling approach to aircraftreplacement strategy with an application to an airline in Taiwan.One possible reason for such a limited work on aircraft replace-ment strategy is the reluctance of airlines to share their con -dential nancial data.

2. Mathematical model

We adopt a binary-integer linear programming model to iden-tify the number of aircraft to buy, lease or sell in an effort tominimize total discounted costs. The model makes use of:

Index:k Index for eet type ( k l,.., K );i Index for age of the aircraft ( i 0,..,N ), N is the maximum

aircraft age allowed; j Index for period ( j 0,..,T ), T is the number of periods

(years) in the planning horizon. Time 0 represents currentyear;l Index for lease period ( l 1,..., Lk), e Lk is the maximum

lease period for eet type k;LH Set of aircraft in the long-haul eet (typically wide-body

eet);SH Set of aircraft in the short haul eet (typically narrow-

body eet).

Decision variables:Bki j Number of aircraft to buy of eet type k, age i, ordered in

period j;Lki;l j Number of leased aircraft of eet type k, age i, ordered in j

for a lease period of l;

S ki j Number of owned aircraft of eet type k, age i, sold inperiod j;

ZBk( j) A binary variable taking a value of 1 if the airline hasaircraft of eet type k in j and zero otherwise;

XOki j Number of owned aircraft in operation of eet type k,age i, in j;

XL ki j Number of leased aircraft in operation of eet type k,age i, in j.

Parameters:PBki j Unit purchase price for aircraft of eet type k, age i,

ordered in j. (For ordering new aircraft i 0);* Corresponding author. Tel.: 1 386 226 6705.

E-mail address: bazargam@erau.edu (M. Bazargan).

Contents lists available at SciVerse ScienceDirect

Journal of Air Transport Management

j o u rn a l h o mep ag e : www.e l sev i e r. co m/ l o ca t e / j a i r t r aman

0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved.

doi: 10.1016/j.jairtraman.2012.05.001

Journal of Air Transport Management 25 (2012) 26 e 29

mailto:bazargam@erau.eduhttp://www.sciencedirect.com/science/journal/09696997http://www.elsevier.com/locate/jairtramanhttp://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://dx.doi.org/10.1016/j.jairtraman.2012.05.001http://www.elsevier.com/locate/jairtramanhttp://www.sciencedirect.com/science/journal/09696997mailto:bazargam@erau.edu

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PL ki;l j Unit annual lease price for aircraft of eet type k, age i,ordered in j, for a lease period of I ;

d( j) Discount factor for period j;FBk( J ) Fixed cost for introducing/keeping aircraft of eet type k

in j;COki j Unit annual operating and maintenance cost for owned

aircraft of eet type k, age i, in j;CL k

i j Unit annual operating and maintenance cost for leased

aircraft of eet type k, age i, in period j;Rki j Unitsalvagevalue forowned aircraft of eettype k,age i, in j;cap k Average seat capacity for aircraft eet type k;dLH( j) Demand for seats on long-haul (wide-body) ights in j;dSH( j) Demand for seats on short haul (narrow-body) ights in j;min _AC_req k ( j) Minimum number of aircraft of eettype k needed

in j;max _AC_req k ( j) Maximum number of aircraft of eet type k

needed in j;lag k Average waiting time for delivery of a new aircraft of eet

type k;Budget( J )Available budget for aircraft purchase and lease in

period j;XOki 0 Current number of owned aircraft in operation of eet

type k, age i;XL ki 0 Current number of leased aircraft in operation of eet

type k, age i.The model is then represented as:

Minimize XK

k 1X

N

i 0X

T

j 0

d j PBki j$Bki j

XK

k 0X

N

i 0X

T

j 0

d jXLk

l 1PL ki;l j$L

ki;l j

XK

k 1X

N

i 0X

T

j 0

d j XOki j$COki j

XL ki j$CL ki j XK

k 1 XN

i 0 XT

j 0

d j S ki j$Rki j

XK

k 1X

T

j 0

d j FBk j$ZBk j

(1)

Subject to:

Xk LH

cap k XN

i 0XOki j XL

ki j dLH j c j (2)

Xk SH

cap k XN

i 0XOki j XL

ki j dSH j c j (3)

XOk0 j Bk0 j lag

k S k0 j c k and j 1 and j lagk (4)

XOki j XOki 1 j 1 B

ki j S

ki j c k and i; j 1 (5)

XL k0 j XLk

l 1Lk0 ;l j lag

k c k and j 1 and j lag k (6)

XL ki j XL ki 1 j 1 P

Lk

i 1Lki;l j P

K

u 0 PN

v 1 PLk

l 1Lku ;lv

c k; i and j 1; u j v i; and l v j(7)

XN

i 0XOki j XL

ki j M $ZB

k j c j; k (8)

S ki j XOki 1 j 1 c k and i; j 1 (9)

XK

k 1 XN

i 0PBki j$Bki j X

K

k 0 XN

i 0 XLk

l 1

PL ki;l j$Lki;l j budjet j c j

(10)

min AC req k j PN

i 0XOki j XL

ki j

max AC req k j c j and k(11)

Bki j; Lki;l j; S

ki j; XO

ki j; XL

ki j Z

c i; j; k (12)

ZBk j f 0 ; 1g (13)

The objective function (1) minimizes the total discounted costover the planning horizon. The rst three terms in the objectivefunction represent the total purchasing, leasing and operatingand maintenance costs over the planning horizon, respectively.The fourth term is the discounted revenue generated from thesales of owned aircraft and nally the last term in this functionrepresents the discounted cost of keeping eet in the airline snetwork. This term includes costs such as hangers, crew training,spare parts, etc. The set of constraints 2 and 3 insure that thedemand for wide- and narrow-body aircraft are met each yearwithin the planning horizon. Constraints 4 through 7 maintainthe balance on the number of aircraft for new (age 0) and old(age > 0) for both owned and leased aircraft for each yearrespectively. Constraint 8 ensures a cost associated with a eettype is incurred if an aircraft of that eet type is in the airline snetwork for each year. M is a suf ciently large positive number.Constraint 9 limits the number of salvaged aircraft from each eetto the available number of owned aircraft in that eet for eachyear. Constraint 10 imposes a budget restriction for purchasing andleasing aircraft in each year. Foroperational,marketing and strategicpurposes, the airlines may impose a minimum and/or maximumnumber of aircraft of a speci c eet type within their network.Constraint 11 imposes these limits for each year. Constraints 12and 13 impose integer and binary status on the model s decisionvariables.

This model does not attempt to dispose of nor enforce the leaseexpiry of all aircraft at the end of planning horizon T . The airlinecontinues to operate at year T 1, where there are the samenumber of aircraft, both owned and leased, as the number of planning horizon T .

3. Model parameters

The airlines typically do not have or do not wish to disclose therelevant parameters. We thus initiated an alternative search.

Aircraft values including purchase and salvage prices (PB ki jandRki j) for each eet were compiled from Collateral Veri cation(2010) and Air nance Journal (2010) databases. These databasesprovide both the aircraft book and market values with respect totheir ages. We adopted a series of regression analyses to identifythe relationships between aircraft market values and their ages for

each

eet. We found that the following equation provides a valid

M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26 e 29 27

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estimate with an R2 0.968 for aircraft market values with respectto their ages for all eet.

aircraft age new aircraft age 0$eexponent $age

The aircraft annual lease prices (PL ki;l j) vary depending on theleasing company and the airline s network. Again, Collateral Veri-

cation (2010) was used to determine the lease payments. A log-

arithmic equation was found to provide a good estimate for annualaircraft lease prices with respect to their market values with anR2 0.968

Aircraft annual lease price coefficient $ln market value constant

The operating and maintenance cost estimates (CL kl j) wereobtained from the Airline Monitor (2010). The operating cost of a eet tends to be stable and does not depend on the age of theaircraft ( Dixon, 2006 ). The RAND Corporation (2010) has conductedresearch on maintenance costs for both commercial and militaryaircraft as they age (e.g. Keating and Dixon, 2003 ) that shows that new aircraft have 17.6% annual rate of increase in maintenance

cost. For

mature

aircraft, ages 6 e 12 years, an increase of 3.5% andfor aging aircraft (after 12 years) this increase rate is 0.7% per year.We adopt Conklin and Decker (2010) to determine the cost asso-ciated with introducing a new eet, US Bureau of TransportationStatistics for current eet sizes and International Air TransportAssociation for nominal discount factor. Clark (2007) indicates thatmajor technological change in aircraft manufacturing occurs everydecade. Accordingly, we set the planning as 2011 to 2020.

4. Analysis

We examine AirTran Airways, a low cost carrier and ContinentalAirlines, a major airline operating within the US. The rationale forselecting these two airlines was to investigate if the aircraft

replacement strategies vary with eet diversity, network size and/or business models. In 2010, AirTran Airways operated only twotypes of narrow-body eet, with 138 aircraft and more than 600daily ights while Continental Airlines operated more than tentypes of narrow and wide-body eet, with 352 aircraft and morethan 2200 daily short and long-haul ights.

The models for the two airlines were solved using Cplex Solver. 1

Figs. 1 and 2 present the solutions for the aircraft replacement strat-egies for the two airlines between 2011 and 2020. The discountedcosts over the tenyears are$3.45 billionand$53.50billionforAirTranand Continental airlines respectively. These gures provide the eettype, number of aircraft to buy,lease, andsell. It should be noted thatthese solutions also include current airlines orders for owned andleased aircraft to be delivered between 2011 and 2020 as reported by

theUS Bureauof Transportation Statistics. Toavoidclutter, the guresdo not present the ages of the aircraft to buy, sell or lease.

The solutions for both airlines favor:

Brand new aircraft for both buying and leasing; Short-term leases; Selling older aircraft with ages of 12 years and older; Discouraging eet diversity; Leasing aircraft over buying them.

Theserecommendations are similar for bothairlines, whichhavedifferent network sizes and eet diversity. Other studies (see for

example Hsu, et al., 2011 and Oum,et al.,2000 ) also showa growinginterest for leasing over buying among airlines. Based on the solu-tions, Fig. 3 presents the percentage of leased aircraft out of totalaircraft in their networks for the two airlines from 2010 to 2020.

5. Sensitivity analysis

In this section we further explore the sensitivity of the solutionspresented in Section 4. In particular,we examine howthe strategiesof lease/buy are affected as we change their prices and identifymajor cost drivers and their roles.

To determine howsensitive the solutionsare to lease/buy prices,we let the prices uctuate between 50% and 50% of their currentvalues. The strategy started to favor buy over lease when the leaseprices went up by 30% and purchase prices are reduced by 40%which are unlikely events. We made uctuations to other param-eters such as annual demand and planning horizon. The strategystill continued to favor lease over buy.

The solutions in Section 4 presented the total discounted costsfor the two airlines over ten years. These costs include purchase,

lease, operation, maintenance and depreciation costs minus

Fig. 1. Aircraft replacement strategy for AirTran Airways.

Fig. 2. Aircraft replacement strategy for Continental Airlines.

Fig. 3. Solutions for percentages of leased aircraft for AirTran and Continental airlinesfrom 2010 to 2020.

1

http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/ .

M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26 e 2928

http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/

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revenue generated from sales of aircraft. Fig. 4 presents thepercentages of each of these cost components over 10 year periodfor each airline.

As this gure suggests the major cost drivers are operation andmaintenance costs. These two components make up more than 90%of incurred cost over the decade planning horizon. In fact, as the

gure shows, the lease/purchase costs are insigni cant comparedto operation and maintenance cost gures. Fig. 5 providesa comparison between lease/buy and operations and maintenance

costs. This gure presents the aircraft market value and cumulativeoperating and maintenance cost for a sample eetover tenyears. Asthe gure suggests, the airlines spend more money on operationand maintenance in the rst years of operating this new aircraftthan what the aircraft is worth at the end of three years. Furtheranalyses with other eet also con rmed that no aircraft was worthmore than what it was spent on within their rst four years of operations.

6. Conclusion

This study introduced a model to highlight major factors inaircraft replacement strategy for the airlines. The model minimizesthe total discounted cost by identifying the number of aircraft tolease, buy and sell over a planning horizon. The study explores howcost data were compiled and analyzed from aviation databases. Themodel was applied to two US airlines with different network sizesand business models. The suggested strategy favors new aircraft tobe leased over short-term periods. This strategy discourages eetdiversity. Various sensitivity analyses tend to imply that leasingaircraft is preferred to buying them. The analyses also suggest thatairlines will bene t from operating more ef cient eet, even if theycost more to acquire.

References

Clark, P., 2007. Buying the Big Jets e Fleet Planning for Airlines, second ed. Ashgate,Farnham.

Conklin, Decker, 2010. http://www.conklindd.com/ .Dixon, M., 2006. The Maintenance Costs of Aging Aircraft e Insights From

Commercial Aviation. RAND Corporation, Santa Monica, Calif. UG1243.D568.Gao, C., Johnson, E., Smith, B., 2009. Integrated airline eet and crew robust plan-

ning. Transportation Science 43, 2 e 16.Hsu, C., Li, H., Liu, S., Chao, C., 2011. Aircraft replacement scheduling: a dynamic

programming approach. Transportation Research E 47, 41.Keating, E., Dixon, M., 2003. Investigating Optimal Replacement of Aging Air Force

Systems. RAND Corporation, Santa Monica, Calif. MR-1763-AF.Oum, T.H., Zhang, A., Zhang, Y., 2000. Optimal demand for operating lease of

aircraft. Transportation Research B, 17 e 29.Rand, 2010. Rand Corporation. Available from: http://www.rand.org/topics/

maintenance-repair-and-overhaul.html .

Fig. 5. Aircraft market value and cumulative operations and maintenance cost over 10years.

Fig. 4. Percentages of cost components for the two airlines over 10 years.

M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26 e 29 29

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