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Aircraft replacement strategy: Model and analysis
Journal of Air Transport Management 25 (2012) 26e29
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Note
Aircraft replacement strategy: Model and analysis Massoud Bazargan a, *, Joseph Hartman b a b
College of Business, Embry-Riddle Aeronautical University, 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114, USA Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
a b s t r a c t Keywords: Aircraft acquisition Aircraft replacement Aircraft purchasing Aircraft leasing
This study presents a model to help airlines plan their strategic fleet acquisitions and disposals. It minimizes the discounted costs of owning or leasing and operating a fleet by identifying which aircraft to buy, sell and lease over the planning horizon. The paper explains how the related cost data were compiled and analyzed. The model is applied to two US airlines with different business models and shows that aircraft leasing is generally the preferred alternative with benefits from having newer aircraft and less fleet diversity. 2012 Elsevier Ltd. All rights reserved.
1. Introduction Most aviation regulatory agencies and aircraft manufacturers foresee 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 decisions that impact all processes related to planning and operations within airlines, and involve when and how many aircraft of different types to purchase, lease and dispose of within an airline’s planning horizon. These decisions must support an airline’s short and longterm decisions affecting their financial, operational and competitive performance. Most prior work in this field addresses the problem in the context of fleet planning (e.g. Gao et al., 2009) and focus on short-term tactical decisions and utilizing the available fleet rather than consider long-term changes to the size or composition of the fleet. The limited aircraft replacement models include Hsu et al. (2011) who present modeling approach to aircraft replacement strategy with an application to an airline in Taiwan. One possible reason for such a limited work on aircraft replacement strategy is the reluctance of airlines to share their confidential financial data. 2. Mathematical model We adopt a binary-integer linear programming model to identify the number of aircraft to buy, lease or sell in an effort to minimize total discounted costs. The model makes use of: * Corresponding author. Tel.: þ1 386 226 6705. E-mail address: [email protected] (M. Bazargan). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2012.05.001
Index: k i j
l LH SH
Index for fleet type (k ¼ l,.., K); Index for age of the aircraft (i ¼ 0,..,N), N is the maximum aircraft age allowed; Index for period (j ¼ 0,..,T), T is the number of periods (years) in the planning horizon. Time 0 represents current year; Index for lease period (l ¼ 1,..., Lk), e Lk is the maximum lease period for fleet type k; Set of aircraft in the long-haul fleet (typically wide-body fleet); Set of aircraft in the short haul fleet (typically narrowbody fleet).
Decision variables: Bki ðjÞ Lki;l ðjÞ Ski ðjÞ ZBk(j) XOki ðjÞ XLki ðjÞ
Number of aircraft to buy of fleet type k, age i, ordered in period j; Number of leased aircraft of fleet type k, age i, ordered in j for a lease period of l; Number of owned aircraft of fleet type k, age i, sold in period j; A binary variable taking a value of 1 if the airline has aircraft of fleet type k in j and zero otherwise; Number of owned aircraft in operation of fleet type k, age i, in j; Number of leased aircraft in operation of fleet type k, age i, in j.
Parameters: Unit purchase price for aircraft of fleet type k, age i, PBki ðjÞ ordered in j. (For ordering new aircraft i ¼ 0);
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
PLki;l ðjÞ
Unit annual lease price for aircraft of fleet type k, age i, ordered in j, for a lease period of I; d(j) Discount factor for period j; Fixed cost for introducing/keeping aircraft of fleet type k FBk(J) in j; Unit annual operating and maintenance cost for owned COki ðjÞ aircraft of fleet type k, age i, in j; Unit annual operating and maintenance cost for leased CLki ðjÞ aircraft of fleet type k, age i, in period j; Unit salvage value for owned aircraft of fleet type k, age i, in j; Rki ðjÞ Average seat capacity for aircraft fleet type k; capk dLH(j) Demand for seats on long-haul (wide-body) flights in j; dSH(j) Demand for seats on short haul (narrow-body) flights in j; min_AC_reqk (j) Minimum number of aircraft of fleet type k needed in j; max_AC_reqk (j) Maximum number of aircraft of fleet type k needed in j; Average waiting time for delivery of a new aircraft of fleet lagk type k; Budget(J) Available budget for aircraft purchase and lease in period j; XOki ð0Þ Current number of owned aircraft in operation of fleet type k, age i; XLki ð0Þ Current number of leased aircraft in operation of fleet type k, age i. The model is then represented as:
Minimize
K X N X T X k¼1 i¼0 j¼0
þ þ
K X N X T X
dðjÞ
dðjÞ PBki ðjÞ$Bki ðjÞ
Lk X
k¼0 i¼0 j¼0
l¼1
K X N X T X
PLki;l ðjÞ$Lki;l ðjÞ
dðjÞ XOki ðjÞ$COki ðjÞ
(1)
k¼1 i¼0 j¼0 K X N X T X dðjÞ Ski ðjÞ$Rki ðjÞ þ XLki ðjÞ$CLki ðjÞ k¼1 i¼0 j¼0
þ
K X T X
dðjÞ FBk ðjÞ$ZBk ðjÞ
k¼1 j¼0
Subject to:
X
capk
XOki ðjÞ þ XLki ðjÞ dLHðjÞ
cj
(2)
cj
(3)
i¼0
k˛LH
X
N X
capk
k˛SH
N X
XOki ðjÞ þ XLki ðjÞ dSHðjÞ
i¼0
XOk0 ðjÞ ¼ Bk0 j lagk Sk0 ðjÞ ck and j 1 and j lagk
(4)
XOki ðjÞ ¼ XOki1 ðj 1Þ þ Bki ðjÞ Ski ðjÞ
(5)
XLk0 ðjÞ ¼
Lk X l¼1
Lk0;l j lagk
XLki ðjÞ ¼ XLki1 ðj 1Þ þ
Lk P i¼1
XOki ðjÞ þ XLki ðjÞ M$ZBk ðjÞ
cj; k
(8)
i¼0
Ski ðjÞ XOki1 ðj 1Þ K X N X k¼1 i¼0
ck and i; j 1
(9)
Lk K X N X X PBki ðjÞ$Bki ðjÞ þ
PLki;l ðjÞ$Lki;l ðjÞ
(10)
k¼0 i¼0 l¼1
budjetðjÞ
min AC reqk ðjÞ
N P i¼0
max AC reqk ðjÞ
cj
XOki ðjÞ þ XLki ðjÞ
(11)
cj and k
Bki ðjÞ; Lki;l ðjÞ; Ski ðjÞ; XOki ðjÞ; XLki ðjÞ˛Z þ ZBk ðjÞ˛f0; 1g
ci; j; k
(12) (13)
The objective function (1) minimizes the total discounted cost over the planning horizon. The first three terms in the objective function represent the total purchasing, leasing and operating and maintenance costs over the planning horizon, respectively. The fourth term is the discounted revenue generated from the sales of owned aircraft and finally the last term in this function represents the discounted cost of keeping fleet in the airline’s network. This term includes costs such as hangers, crew training, spare parts, etc. The set of constraints 2 and 3 insure that the demand for wide- and narrow-body aircraft are met each year within the planning horizon. Constraints 4 through 7 maintain the balance on the number of aircraft for new (age ¼ 0) and old (age > 0) for both owned and leased aircraft for each year respectively. Constraint 8 ensures a cost associated with a fleet type is incurred if an aircraft of that fleet type is in the airline’s network for each year. M is a sufficiently large positive number. Constraint 9 limits the number of salvaged aircraft from each fleet to the available number of owned aircraft in that fleet for each year. Constraint 10 imposes a budget restriction for purchasing and leasing aircraft in each year. For operational, marketing and strategic purposes, the airlines may impose a minimum and/or maximum number of aircraft of a specific fleet type within their network. Constraint 11 imposes these limits for each year. Constraints 12 and 13 impose integer and binary status on the model’s decision variables. This model does not attempt to dispose of nor enforce the lease expiry of all aircraft at the end of planning horizon T. The airline continues to operate at year T þ 1, where there are the same number of aircraft, both owned and leased, as the number of planning horizon T. 3. Model parameters
ck and i; j 1
ck and j 1 and j lagk
Lki;l ðjÞ
N X
27
Lk K N P P P u¼0 v¼1 l¼1
Lku;l ðvÞ
ck; i and j 1; u þ j ¼ v þ i; and l þ v ¼ j
(6)
(7)
The airlines typically do not have or do not wish to disclose the relevant parameters. We thus initiated an alternative search. Aircraft values including purchase and salvage prices (PBki ðjÞ and k Ri ðjÞ) for each fleet were compiled from Collateral Verification (2010) and Airfinance Journal (2010) databases. These databases provide both the aircraft book and market values with respect to their ages. We adopted a series of regression analyses to identify the relationships between aircraft market values and their ages for each fleet. We found that the following equation provides a valid
28
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
estimate with an R2 0.968 for aircraft market values with respect to their ages for all fleet.
aircraftðageÞ ¼ new aircraftðage ¼ 0Þ$eexponent$age The aircraft annual lease prices (PLki;l ðjÞ) vary depending on the leasing company and the airline’s network. Again, Collateral Verification (2010) was used to determine the lease payments. A logarithmic equation was found to provide a good estimate for annual aircraft lease prices with respect to their market values with an R2 0.968
Aircraft annual lease price ¼ coefficient$lnðmarket valueÞ þ constant Fig. 1. Aircraft replacement strategy for AirTran Airways.
The operating and maintenance cost estimates (CLkl ðjÞ) were obtained from the Airline Monitor (2010). The operating cost of a fleet tends to be stable and does not depend on the age of the aircraft (Dixon, 2006). The RAND Corporation (2010) has conducted research on maintenance costs for both commercial and military aircraft 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 6e12 years, an increase of 3.5% and for ‘aging’ aircraft (after 12 years) this increase rate is 0.7% per year. We adopt Conklin and Decker (2010) to determine the cost associated with introducing a new fleet, US Bureau of Transportation Statistics for current fleet sizes and International Air Transport Association for nominal discount factor. Clark (2007) indicates that major technological change in aircraft manufacturing occurs every decade. Accordingly, we set the planning as 2011 to 2020.
Fig. 2. Aircraft replacement strategy for Continental Airlines.
4. Analysis We examine AirTran Airways, a low cost carrier and Continental Airlines, a major airline operating within the US. The rationale for selecting these two airlines was to investigate if the aircraft replacement strategies vary with fleet diversity, network size and/ or business models. In 2010, AirTran Airways operated only two types of narrow-body fleet, with 138 aircraft and more than 600 daily flights while Continental Airlines operated more than ten types of narrow and wide-body fleet, with 352 aircraft and more than 2200 daily short and long-haul flights. The models for the two airlines were solved using Cplex Solver.1 Figs. 1 and 2 present the solutions for the aircraft replacement strategies for the two airlines between 2011 and 2020. The discounted costs over the ten years are $3.45 billion and $53.50 billion for AirTran and Continental airlines respectively. These figures provide the fleet type, number of aircraft to buy, lease, and sell. It should be noted that these solutions also include current airlines’ orders for owned and leased aircraft to be delivered between 2011 and 2020 as reported by the US Bureau of Transportation Statistics. To avoid clutter, the figures do 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 fleet diversity; Leasing aircraft over buying them.
These recommendations are similar for both airlines, which have different network sizes and fleet diversity. Other studies (see for
1
http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.
Fig. 3. Solutions for percentages of leased aircraft for AirTran and Continental airlines from 2010 to 2020.
example Hsu, et al., 2011 and Oum, et al., 2000) also show a growing interest for leasing over buying among airlines. Based on the solutions, Fig. 3 presents the percentage of leased aircraft out of total aircraft in their networks for the two airlines from 2010 to 2020. 5. Sensitivity analysis In this section we further explore the sensitivity of the solutions presented in Section 4. In particular, we examine how the strategies of lease/buy are affected as we change their prices and identify major cost drivers and their roles. To determine how sensitive the solutions are to lease/buy prices, we let the prices fluctuate between 50% and þ50% of their current values. The strategy started to favor buy over lease when the lease prices went up by 30% and purchase prices are reduced by 40% which are unlikely events. We made fluctuations to other parameters such as annual demand and planning horizon. The strategy still continued to favor lease over buy. The solutions in Section 4 presented the total discounted costs for the two airlines over ten years. These costs include purchase, lease, operation, maintenance and depreciation costs minus
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
29
costs. This figure presents the aircraft market value and cumulative operating and maintenance cost for a sample fleet over ten years. As the figure suggests, the airlines spend more money on operation and maintenance in the first years of operating this new aircraft than what the aircraft is worth at the end of three years. Further analyses with other fleet also confirmed that no aircraft was worth more than what it was spent on within their first four years of operations.
6. Conclusion Fig. 4. Percentages of cost components for the two airlines over 10 years.
This study introduced a model to highlight major factors in aircraft replacement strategy for the airlines. The model minimizes the total discounted cost by identifying the number of aircraft to lease, buy and sell over a planning horizon. The study explores how cost data were compiled and analyzed from aviation databases. The model was applied to two US airlines with different network sizes and business models. The suggested strategy favors new aircraft to be leased over short-term periods. This strategy discourages fleet diversity. Various sensitivity analyses tend to imply that leasing aircraft is preferred to buying them. The analyses also suggest that airlines will benefit from operating more efficient fleet, even if they cost more to acquire.
References Fig. 5. Aircraft market value and cumulative operations and maintenance cost over 10 years.
revenue generated from sales of aircraft. Fig. 4 presents the percentages of each of these cost components over 10 year period for each airline. As this figure suggests the major cost drivers are operation and maintenance costs. These two components make up more than 90% of incurred cost over the decade planning horizon. In fact, as the figure shows, the lease/purchase costs are insignificant compared to operation and maintenance cost figures. Fig. 5 provides a comparison between lease/buy and operations and maintenance
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 fleet and crew robust planning. Transportation Science 43, 2e16. 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, 17e29. Rand, 2010. Rand Corporation. Available from: http://www.rand.org/topics/ maintenance-repair-and-overhaul.html.
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Note
Aircraft replacement strategy: Model and analysis Massoud Bazargan a, *, Joseph Hartman b a b
College of Business, Embry-Riddle Aeronautical University, 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114, USA Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
a b s t r a c t Keywords: Aircraft acquisition Aircraft replacement Aircraft purchasing Aircraft leasing
This study presents a model to help airlines plan their strategic fleet acquisitions and disposals. It minimizes the discounted costs of owning or leasing and operating a fleet by identifying which aircraft to buy, sell and lease over the planning horizon. The paper explains how the related cost data were compiled and analyzed. The model is applied to two US airlines with different business models and shows that aircraft leasing is generally the preferred alternative with benefits from having newer aircraft and less fleet diversity. 2012 Elsevier Ltd. All rights reserved.
1. Introduction Most aviation regulatory agencies and aircraft manufacturers foresee 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 decisions that impact all processes related to planning and operations within airlines, and involve when and how many aircraft of different types to purchase, lease and dispose of within an airline’s planning horizon. These decisions must support an airline’s short and longterm decisions affecting their financial, operational and competitive performance. Most prior work in this field addresses the problem in the context of fleet planning (e.g. Gao et al., 2009) and focus on short-term tactical decisions and utilizing the available fleet rather than consider long-term changes to the size or composition of the fleet. The limited aircraft replacement models include Hsu et al. (2011) who present modeling approach to aircraft replacement strategy with an application to an airline in Taiwan. One possible reason for such a limited work on aircraft replacement strategy is the reluctance of airlines to share their confidential financial data. 2. Mathematical model We adopt a binary-integer linear programming model to identify the number of aircraft to buy, lease or sell in an effort to minimize total discounted costs. The model makes use of: * Corresponding author. Tel.: þ1 386 226 6705. E-mail address: [email protected] (M. Bazargan). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2012.05.001
Index: k i j
l LH SH
Index for fleet type (k ¼ l,.., K); Index for age of the aircraft (i ¼ 0,..,N), N is the maximum aircraft age allowed; Index for period (j ¼ 0,..,T), T is the number of periods (years) in the planning horizon. Time 0 represents current year; Index for lease period (l ¼ 1,..., Lk), e Lk is the maximum lease period for fleet type k; Set of aircraft in the long-haul fleet (typically wide-body fleet); Set of aircraft in the short haul fleet (typically narrowbody fleet).
Decision variables: Bki ðjÞ Lki;l ðjÞ Ski ðjÞ ZBk(j) XOki ðjÞ XLki ðjÞ
Number of aircraft to buy of fleet type k, age i, ordered in period j; Number of leased aircraft of fleet type k, age i, ordered in j for a lease period of l; Number of owned aircraft of fleet type k, age i, sold in period j; A binary variable taking a value of 1 if the airline has aircraft of fleet type k in j and zero otherwise; Number of owned aircraft in operation of fleet type k, age i, in j; Number of leased aircraft in operation of fleet type k, age i, in j.
Parameters: Unit purchase price for aircraft of fleet type k, age i, PBki ðjÞ ordered in j. (For ordering new aircraft i ¼ 0);
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
PLki;l ðjÞ
Unit annual lease price for aircraft of fleet type k, age i, ordered in j, for a lease period of I; d(j) Discount factor for period j; Fixed cost for introducing/keeping aircraft of fleet type k FBk(J) in j; Unit annual operating and maintenance cost for owned COki ðjÞ aircraft of fleet type k, age i, in j; Unit annual operating and maintenance cost for leased CLki ðjÞ aircraft of fleet type k, age i, in period j; Unit salvage value for owned aircraft of fleet type k, age i, in j; Rki ðjÞ Average seat capacity for aircraft fleet type k; capk dLH(j) Demand for seats on long-haul (wide-body) flights in j; dSH(j) Demand for seats on short haul (narrow-body) flights in j; min_AC_reqk (j) Minimum number of aircraft of fleet type k needed in j; max_AC_reqk (j) Maximum number of aircraft of fleet type k needed in j; Average waiting time for delivery of a new aircraft of fleet lagk type k; Budget(J) Available budget for aircraft purchase and lease in period j; XOki ð0Þ Current number of owned aircraft in operation of fleet type k, age i; XLki ð0Þ Current number of leased aircraft in operation of fleet type k, age i. The model is then represented as:
Minimize
K X N X T X k¼1 i¼0 j¼0
þ þ
K X N X T X
dðjÞ
dðjÞ PBki ðjÞ$Bki ðjÞ
Lk X
k¼0 i¼0 j¼0
l¼1
K X N X T X
PLki;l ðjÞ$Lki;l ðjÞ
dðjÞ XOki ðjÞ$COki ðjÞ
(1)
k¼1 i¼0 j¼0 K X N X T X dðjÞ Ski ðjÞ$Rki ðjÞ þ XLki ðjÞ$CLki ðjÞ k¼1 i¼0 j¼0
þ
K X T X
dðjÞ FBk ðjÞ$ZBk ðjÞ
k¼1 j¼0
Subject to:
X
capk
XOki ðjÞ þ XLki ðjÞ dLHðjÞ
cj
(2)
cj
(3)
i¼0
k˛LH
X
N X
capk
k˛SH
N X
XOki ðjÞ þ XLki ðjÞ dSHðjÞ
i¼0
XOk0 ðjÞ ¼ Bk0 j lagk Sk0 ðjÞ ck and j 1 and j lagk
(4)
XOki ðjÞ ¼ XOki1 ðj 1Þ þ Bki ðjÞ Ski ðjÞ
(5)
XLk0 ðjÞ ¼
Lk X l¼1
Lk0;l j lagk
XLki ðjÞ ¼ XLki1 ðj 1Þ þ
Lk P i¼1
XOki ðjÞ þ XLki ðjÞ M$ZBk ðjÞ
cj; k
(8)
i¼0
Ski ðjÞ XOki1 ðj 1Þ K X N X k¼1 i¼0
ck and i; j 1
(9)
Lk K X N X X PBki ðjÞ$Bki ðjÞ þ
PLki;l ðjÞ$Lki;l ðjÞ
(10)
k¼0 i¼0 l¼1
budjetðjÞ
min AC reqk ðjÞ
N P i¼0
max AC reqk ðjÞ
cj
XOki ðjÞ þ XLki ðjÞ
(11)
cj and k
Bki ðjÞ; Lki;l ðjÞ; Ski ðjÞ; XOki ðjÞ; XLki ðjÞ˛Z þ ZBk ðjÞ˛f0; 1g
ci; j; k
(12) (13)
The objective function (1) minimizes the total discounted cost over the planning horizon. The first three terms in the objective function represent the total purchasing, leasing and operating and maintenance costs over the planning horizon, respectively. The fourth term is the discounted revenue generated from the sales of owned aircraft and finally the last term in this function represents the discounted cost of keeping fleet in the airline’s network. This term includes costs such as hangers, crew training, spare parts, etc. The set of constraints 2 and 3 insure that the demand for wide- and narrow-body aircraft are met each year within the planning horizon. Constraints 4 through 7 maintain the balance on the number of aircraft for new (age ¼ 0) and old (age > 0) for both owned and leased aircraft for each year respectively. Constraint 8 ensures a cost associated with a fleet type is incurred if an aircraft of that fleet type is in the airline’s network for each year. M is a sufficiently large positive number. Constraint 9 limits the number of salvaged aircraft from each fleet to the available number of owned aircraft in that fleet for each year. Constraint 10 imposes a budget restriction for purchasing and leasing aircraft in each year. For operational, marketing and strategic purposes, the airlines may impose a minimum and/or maximum number of aircraft of a specific fleet type within their network. Constraint 11 imposes these limits for each year. Constraints 12 and 13 impose integer and binary status on the model’s decision variables. This model does not attempt to dispose of nor enforce the lease expiry of all aircraft at the end of planning horizon T. The airline continues to operate at year T þ 1, where there are the same number of aircraft, both owned and leased, as the number of planning horizon T. 3. Model parameters
ck and i; j 1
ck and j 1 and j lagk
Lki;l ðjÞ
N X
27
Lk K N P P P u¼0 v¼1 l¼1
Lku;l ðvÞ
ck; i and j 1; u þ j ¼ v þ i; and l þ v ¼ j
(6)
(7)
The airlines typically do not have or do not wish to disclose the relevant parameters. We thus initiated an alternative search. Aircraft values including purchase and salvage prices (PBki ðjÞ and k Ri ðjÞ) for each fleet were compiled from Collateral Verification (2010) and Airfinance Journal (2010) databases. These databases provide both the aircraft book and market values with respect to their ages. We adopted a series of regression analyses to identify the relationships between aircraft market values and their ages for each fleet. We found that the following equation provides a valid
28
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
estimate with an R2 0.968 for aircraft market values with respect to their ages for all fleet.
aircraftðageÞ ¼ new aircraftðage ¼ 0Þ$eexponent$age The aircraft annual lease prices (PLki;l ðjÞ) vary depending on the leasing company and the airline’s network. Again, Collateral Verification (2010) was used to determine the lease payments. A logarithmic equation was found to provide a good estimate for annual aircraft lease prices with respect to their market values with an R2 0.968
Aircraft annual lease price ¼ coefficient$lnðmarket valueÞ þ constant Fig. 1. Aircraft replacement strategy for AirTran Airways.
The operating and maintenance cost estimates (CLkl ðjÞ) were obtained from the Airline Monitor (2010). The operating cost of a fleet tends to be stable and does not depend on the age of the aircraft (Dixon, 2006). The RAND Corporation (2010) has conducted research on maintenance costs for both commercial and military aircraft 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 6e12 years, an increase of 3.5% and for ‘aging’ aircraft (after 12 years) this increase rate is 0.7% per year. We adopt Conklin and Decker (2010) to determine the cost associated with introducing a new fleet, US Bureau of Transportation Statistics for current fleet sizes and International Air Transport Association for nominal discount factor. Clark (2007) indicates that major technological change in aircraft manufacturing occurs every decade. Accordingly, we set the planning as 2011 to 2020.
Fig. 2. Aircraft replacement strategy for Continental Airlines.
4. Analysis We examine AirTran Airways, a low cost carrier and Continental Airlines, a major airline operating within the US. The rationale for selecting these two airlines was to investigate if the aircraft replacement strategies vary with fleet diversity, network size and/ or business models. In 2010, AirTran Airways operated only two types of narrow-body fleet, with 138 aircraft and more than 600 daily flights while Continental Airlines operated more than ten types of narrow and wide-body fleet, with 352 aircraft and more than 2200 daily short and long-haul flights. The models for the two airlines were solved using Cplex Solver.1 Figs. 1 and 2 present the solutions for the aircraft replacement strategies for the two airlines between 2011 and 2020. The discounted costs over the ten years are $3.45 billion and $53.50 billion for AirTran and Continental airlines respectively. These figures provide the fleet type, number of aircraft to buy, lease, and sell. It should be noted that these solutions also include current airlines’ orders for owned and leased aircraft to be delivered between 2011 and 2020 as reported by the US Bureau of Transportation Statistics. To avoid clutter, the figures do 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 fleet diversity; Leasing aircraft over buying them.
These recommendations are similar for both airlines, which have different network sizes and fleet diversity. Other studies (see for
1
http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.
Fig. 3. Solutions for percentages of leased aircraft for AirTran and Continental airlines from 2010 to 2020.
example Hsu, et al., 2011 and Oum, et al., 2000) also show a growing interest for leasing over buying among airlines. Based on the solutions, Fig. 3 presents the percentage of leased aircraft out of total aircraft in their networks for the two airlines from 2010 to 2020. 5. Sensitivity analysis In this section we further explore the sensitivity of the solutions presented in Section 4. In particular, we examine how the strategies of lease/buy are affected as we change their prices and identify major cost drivers and their roles. To determine how sensitive the solutions are to lease/buy prices, we let the prices fluctuate between 50% and þ50% of their current values. The strategy started to favor buy over lease when the lease prices went up by 30% and purchase prices are reduced by 40% which are unlikely events. We made fluctuations to other parameters such as annual demand and planning horizon. The strategy still continued to favor lease over buy. The solutions in Section 4 presented the total discounted costs for the two airlines over ten years. These costs include purchase, lease, operation, maintenance and depreciation costs minus
M. Bazargan, J. Hartman / Journal of Air Transport Management 25 (2012) 26e29
29
costs. This figure presents the aircraft market value and cumulative operating and maintenance cost for a sample fleet over ten years. As the figure suggests, the airlines spend more money on operation and maintenance in the first years of operating this new aircraft than what the aircraft is worth at the end of three years. Further analyses with other fleet also confirmed that no aircraft was worth more than what it was spent on within their first four years of operations.
6. Conclusion Fig. 4. Percentages of cost components for the two airlines over 10 years.
This study introduced a model to highlight major factors in aircraft replacement strategy for the airlines. The model minimizes the total discounted cost by identifying the number of aircraft to lease, buy and sell over a planning horizon. The study explores how cost data were compiled and analyzed from aviation databases. The model was applied to two US airlines with different network sizes and business models. The suggested strategy favors new aircraft to be leased over short-term periods. This strategy discourages fleet diversity. Various sensitivity analyses tend to imply that leasing aircraft is preferred to buying them. The analyses also suggest that airlines will benefit from operating more efficient fleet, even if they cost more to acquire.
References Fig. 5. Aircraft market value and cumulative operations and maintenance cost over 10 years.
revenue generated from sales of aircraft. Fig. 4 presents the percentages of each of these cost components over 10 year period for each airline. As this figure suggests the major cost drivers are operation and maintenance costs. These two components make up more than 90% of incurred cost over the decade planning horizon. In fact, as the figure shows, the lease/purchase costs are insignificant compared to operation and maintenance cost figures. Fig. 5 provides a comparison between lease/buy and operations and maintenance
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