- Email: [email protected]
Impact of landing fees on airlines’ choice of aircraft size and service frequency in duopoly markets
ARTICLE IN PRESS
Journal of Air Transport Management 12 (2006) 288–292 www.elsevier.com/locate/jairtraman
Impact of landing fees on airlines’ choice of aircraft size and service frequency in duopoly markets Wenbin Wei a
Department of Aviation and Technology, San Jose State University, One Washington Square, San Jose, CA 95192-0061, USA
Abstract A one-shot simultaneous game-theoretic model is applied in a duopoly market to investigate how airport landing fees could influence airlines’ decisions on aircraft size and service frequency. It is found that higher landing fees will force airlines to use larger aircraft and less frequency, with higher load factor for the same number of passengers. It is also found that airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft, which consequently reduces airport congestion. r 2006 Elsevier Ltd. All rights reserved. Keywords: Landing fee; Aircraft size; Airport congestion; Airline competition
1. Introduction Delays caused congestion are a major problem at many airports. The traditional method of dealing with the problem focused on airport capacity expansion, but this is expensive and often only generates more traffic. Installing more advanced air traffic control systems can also enhance capacity, but this tends to be marginal compared with costs involved. Therefore, more attention has been paid to applying administrative and economic methods to the reduction of airport congestion without large investments. Concepts of slot (i.e. right of departure or arrival during a specific period at an airport) and congestion pricing (i.e. using price to ration capacity and divert traffic from peak periods to off-peak periods) are forms of administrative and economic controls. To this end, Geisinger (1989) proposes an administrative method to allocate airport runway slots among airlines and Morrison (1982) examines a simple twopart pricing model for uncongested airports. Brander and Cook (1986) find that the airport will be more efficiently operated and social costs will be reduced under congestion management, and argue that the slot auction approach— each slot goes to the highest bidder—would solve the slot Tel.: +1 4089243206; fax: +1 4089243198.
E-mail address: [email protected]. 0969-6997/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2006.07.008
shortage problem. In practice, the principal part of the landing fee in all major international airports is based on aircraft weight, and no airport in the US has adopted the time-varying landing fee policy (de Neufville and Odoni 2003). London Heathrow has in the past adopted ‘punitive peak-hour tariffs’ to encourage airlines to transfer operations from Heathrow to Gatwick and to move operations from the peak period. Given the particular situation at Heathrow and Gatwick this approach did not prove very successful (Ashford et al., 1995). Some of the more recent work has focused on applying pricing regulation and landing fee policies at airports to optimize social benefits.1 Most of these theoretical studies develop airport pricing policies from the airport’s perspective and consider the airport as a public entity that maximizes social benefits. In reality, airlines, the users of airports, play a very important role in airport pricing policy, since the structure of landing fees influences airlines’ operational and management decisions. Lack of consideration of airlines’ perspectives on such issues as practical scheduling constraints and influence on their competitive 1 Forsyth (1997) incorporates principles of efficient pricing into a pricecap regulatory framework, and Martin-Cejas (1997) proposes Ramsey pricing models for Spanish Airports. Starkie (2001), Zhang and Zhang (1997) and Oum et al. (2004) argue that the dual-till or two-till (considering both the runways and retailing) regulation is better than the single-till price-cap regulation for airport management.
ARTICLE IN PRESS W. Wei / Journal of Air Transport Management 12 (2006) 288–292
situations makes airport congestion management policy difficult to implement. Allen (1994) finds that congestion pricing policy may alter aircraft mix which favors larger aircraft and large airlines. Pels et al. (1997) explore the implications of airport pricing as possible influence on the choice of hub location for airlines. Niemeier (2002) advocates that regulatory reform should be combined with reforms to intensify competition such as slot auctioning among airlines. New York’s LaGuardia Airport (LGA) has been a flagship airport in applying administrative and economic measures to restrict traffic in the US. Since 1968, LGA has applied the high-density rule (HDR) to limit hourly slots to reduce airport congestion and delay. With some minor adjustment, this policy has been implemented in practice at LGA for more than 30 years. In April 2000, the congress passed the Wendell H. Ford Aviation Investment and Reform Act for the 21st Century (AIR-21), which requires that the slot restrictions at LGA should be eliminated after January 1, 2007 and the exemption of slots should be granted immediately to some special flights such as those provided by regional jets with less than 72 seats. Very shortly after this new policy was taken into action, FAA believed that the elimination of slots would cause severe delay problem in LGA and the whole national airspace system, and therefore withdrew the slot exemption policy and redistributed the available slots through a lottery system on December 4, 2000 (Hansen and Zhang, 2005). But today, the US congress still requires that the current slot-based demand management policy adopted at LGA should end in January of 2007. Therefore, a set of new rules and ideas have been proposed to develop the next generation of policies for pricing and slot allocation at LGA. But the critical challenge in designing new pricing and slot allocation rules, such as ‘‘slot auction,’’ is the lack of a mechanism or model for predicting airlines’ behavior in response to various landing fee polices and this behavior’s consequences on airport congestion and delay. To fill in this gap, this paper uses a set of analytical models to study how landing fee policies may influence airlines’ choice of aircraft size and service frequency in a competitive environment. Setting aside political factors that might influence airport pricing policy, we study airport pricing policy from the operational and economic perspectives of airlines. Since airport throughput depends on both aircraft size and service frequency provided by airlines, if airlines choose, or are economically forced by the landing fee policy, to use larger aircraft, then an airport can serve more passengers without any physical expansion of airport capacity, and the congestions and delay at airport can be reduced. The analysis here differs from previous studies in several aspects: we investigate the relation between airport pricing and airline management under the deregulated civil aviation umbrella, and study how landing fees may influence airlines’ decision on both aircraft size and service frequency, which has a significant impact on airport
289
congestion and delay; we take into account competition among airlines, especially their choices of aircraft size and service frequency as competitive strategies. Since most of the US domestic markets are served by two or three major airlines, a game-theoretic model is applied to predict airlines’ behavior in response to changes of landing fees in duopoly markets; and this study is based on previous empirical studies of airlines’ cost function and market share model, both of which are derived by using the real data of the airline industry in the US. 2. Research methodology We investigate if different landing fees per flight are charged to airlines, how the airlines may adjust their service frequency and aircraft size in a duopoly market, and whether it is possible that airlines may choose to use larger aircraft and less service frequency so that airport congestion and delay could be alleviated. Our research is confined to airlines’ strategic decisions at a market level, which is different from airlines’ decisions for daily operations in the network level.2 Airlines are assumed to be profit maximizers—they make their own best operation decisions to achieve the maximum profit. We consider competition as an important factor, and build our model in a market setting with two airlines competing with each other. Our analysis framework is based on a game-theoretic competition model, which has two basis: the cost function and the market share model, together capturing the differences in cost and in market share for airlines using different aircraft size and service frequency when different landing fees are charged. The impact of landing fees on airlines’ decision of aircraft size and service frequency is determined by both the cost function and the market share model. We directly apply the cost function and the market share model derived from previous studies of the cost economics of aircraft size (Wei and Hansen, 2003) and of market share modeling (Wei and Hansen, 2005) for airlines that use different aircraft size and service frequency in a competitive environment. 2.1. Cost function and market share model A de-mean translog model is used by Wei and Hansen (2003) to specify the airline cost function, which relates airlines’ direct operation cost per flight to aircraft size, stage length, unit fuel cost and unit labor cost. The model is calibrated using the data from the first quarter of 1987 to the fourth quarter of 1998 for the 10 largest US airlines in 2 For daily operations, most airlines make decisions on aircraft size and service frequency for each segment based on the computer models of ‘‘fleet assignment’’ and ‘‘capacity planning’’. The core of ‘‘fleet assignment’’ is an optimization model for maximizing airlines’ profit constrained by aircraft availability and scheduling feasibility. The core of ‘‘capacity planning’’ is a forecasting model for airlines to evaluate the effect of their market share and revenue resulting from certain aircraft type, service frequency, and type of service (non-stop vs. connection) in each market.
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W. Wei / Journal of Air Transport Management 12 (2006) 288–292
the US domestic market. Based on the estimated parameters, Wei and Hansen (2003) claim that, at the mean values of the data, there are economies of aircraft size, and that the elasticity of direct operating cost with respect to aircraft size increases with aircraft size. They also claim that, as stage length increases, cost elasticity decreases, and there are stronger scale economies in aircraft operating cost at longer distances. For any given stage length, they find that there is consequently an optimal (least cost) aircraft size, that increases with stage length. According to the data source (Form 41) used by Wei and Hansen (2003), airlines’ total operation costs are classified into two categories: direct operation cost and indirect operation cost. Landing fees are included in the category of ‘‘indirect operation cost’’, which is exogenous to direct operation cost. When airlines report ‘‘indirect operation cost’’ data to FAA, they do not differentiate the amount of ‘‘landing fees’’ from other aircraft service expense such as ‘‘line service expense’’ and ‘‘control expense.’’ Therefore, we do not know explicitly the amount of landings fees included in airlines’ indirect operation cost. But we can still find the impact of additional landing fees on airlines’ total cost and choice of aircraft size, without knowing the exact amount of landing fees currently charged to airlines at each specific airport. Based on the cost function in Wei and Hansen (2003), the least-cost aircraft size can be found under the current landing fee policy and under policies that charge airlines additional landing fees. Airlines need to consider not only the cost but also revenue to achieve maximum profit. Therefore, to find the optimal aircraft size, we need to analyze not only how operation cost changes with aircraft size but also how revenue, demand and market share change when different aircraft size and service frequency are provided in the market. We directly apply the nested logit model derived in Wei and Hansen (2005), which captures the roles of aircraft size, service frequency, and fare in airlines’ market share in non-stop duopoly markets. In this model, time series quarter data, in the database products of Onboard and O&D Plus, from the first quarter of 1989 to the fourth quarter of 1998 for six of ten largest US airlines are used to estimate the model coefficients. Wei and Hansen (2005) find that there is an S-curve effect of service frequency on airlines’ market share, and that airlines can obtain higher returns in market share from increasing service frequency than from increasing aircraft size. Therefore, they conclude that ‘‘airlines have no economic incentives to use aircraft larger than the least-cost aircraft, since for the same capacity provided in the market, increase of frequency can attract more passengers than increase of aircraft size’’. According to the market share model in Wei and Hansen (2005), one airline’s market share in the duopoly market depends on the airline’s own aircraft size, service frequency and ticket price and those of its competitor. If airport charges different landing fees, airlines may choose to use different aircraft size and service frequency due to properties revealed in the cost function of Wei and Hansen (2003),
and then airlines’ revenue resulted from using different combinations of aircraft size and service frequency can be quantitatively analyzed based on the market share model. Since one carrier’s market share and revenue depend not only on its own choice of aircraft size and service frequency but also on the choices made by its competitor in the market, the competition factor must be considered to study the influence of landing fees on airlines’ service decisions. We apply a one-shot simultaneous game-theoretic model for two airlines competing in a non-cooperative non-zero sum duopoly market to study whether different airport landing fees could influence airlines’ strategic decisions on aircraft size and service frequency, and how the changes could influence airlines’ profit, as well as congestion and delay at airport.
2.2. Game-theoretical competition model Since most US domestic markets are dominated by two or three major airlines, we concentrate on airlines’ competition in duopoly markets. But, the framework and the analytic model for two airlines can be easily extended for three airlines. We consider competition in local markets and assume that local passengers are served by direct nonstop flights. The game-theoretic analysis framework would be the same for cases in which local passengers could be served by connecting flights or cases in which there are connecting passengers in direct flights, but to explore indepth the analytical and empirical results for these cases, we need to have a more advanced and complex market share model for our analysis, which is not available in literature at present. In our game theoretic model, there are two players in the game: airlines 1 and 2. Each player has two decision variables: aircraft size and service frequency, and the player’s objective is to maximize its own profit. As in Wei (2000), we assume that the fare variable is an exogenous variable in the game, and is not a strategic decision variable in our study. In practice, airlines’ pricing rules and revenue management process are very complex, and are hard to be represented by a single aggregate fare variable as in the model specified in Wei and Hansen (2005). If we had sufficient pricing data and there were a more sophisticated market share model that could capture the ‘‘real’’ pricing process, we would incorporate a fare variable in our formulated game, which is actually not difficult to implement. As in Wei (2000), it is assumed that each airline will choose only one aircraft size and one service frequency, and therefore uncertainty in airlines’ decisions is not considered here. We formulate all the games for one period, and assume ‘‘complete information’’ for airlines to make decisions based on its own and its competitor’s information. We focus on pure strategy of the game and try to find Nash equilibrium (NE) for the game, which is defined as a set of strategies chosen by each player in the
ARTICLE IN PRESS W. Wei / Journal of Air Transport Management 12 (2006) 288–292
game, where no player has the incentive to change their own strategy given the other players’ strategy. The one-shot simultaneous game model is used in which two airlines in the market choose aircraft size and service frequency at the same time; both airlines know all the available choices for each other as well as profit resulted from each choice; and each airline makes an optimal choice to achieve the maximum profit for itself. Each airline’s optimal choice of aircraft size and frequency depends not only on its own cost function and market share function, but also on the choice of its competitor. There are two simultaneous optimization problems facing the airlines. As in Wei (2000), S1, F1, S2 and F2 represent the size and frequency used by airline 1 and airline 2; S 1 ; F 1 ; S2 and F 2 denote the optimal choices for corresponding variables of S1, F1, S2 and F2; Profit1ðS 1 ; F 1 ; S 2 ; F 2 Þ and Profit 2ðS 2 ; F 2 ; S 1 ; F 1 Þ represent the profit functions for airline 1 and airline 2 when airline 1 chooses S1 and F1, and airline 2 chooses S2 and F2; arg max ProfitðÞ denotes the arguments that make function ProfitðÞ achieve maximum. The airlines’ decision problem, under the one-shot simultaneous game, are formulated through two simultaneous optimization models: 8 profit1ðS 1 ; F 1 ; S2 ; F 2 Þ; < Maximize S 1 ;F 1 (1) : Maximize profit2ðS 2 ; F 2 ; S1 ; F 1 Þ; S 2 ;F 2
with the solutions: ðS1 ; F 1 Þ
¼ argmaxðS1 ;F 1 Þ Profit1ðS 1 ; F 1 ; S2 ; F 2 Þ,
(2)
ðS2 ; F 2 Þ ¼ argmaxðS2 ;F 2 Þ Profit2ðS 2 ; F 2 ; S1 ; F 1 Þ.
(3)
Since a general strategy for the airlines can be represented as [ðS 1 ; F 1 Þ, ðS 2 ; F 2 Þ], in which airline 1 chooses aircraft size and service frequency ðS 1 ; F 1 Þ, and airline 2 chooses ðS2 ; F 2 Þ, the NE strategy is [ðS 1 ; F 1 Þ, ðS2 ; F 2 Þ], in which airline 1’s optimal choice of aircraft size and frequency is ðS1 ; F 1 Þ, given airline 2’s optimal choice of ðS 2 ; F 2 Þ, and vice versa. 3. Case study Since the cost function and the market share model applied here are derived based on real data in the US domestic markets, an idealized US domestic market is defined based on the data of these markets. 1. The hypothetical market has a 1000-mile stage length (flight distance). Population and income data for the origin and destination that are needed for the demand model are based on the metropolitan areas of Albuquerque of New Mexico (ABQ) and Phoenix-Mesa of Arizona in 1998 (PHX). The ABQ–PHX market is one of those markets that are used to calibrate the market share and demand models in Wei and Hansen (2005). The populations were 680,439 and 2,933,542, and the average personal income was $23,819 and $25,302 for ABQ and PHX in 1998.
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2. There are two identical airlines operating in the market. Their operating characteristics and cost coefficients are assumed to be the same as those for an average airline in Wei and Hansen (2003). For example, airlines’ unit fuel cost and unit pilot cost are $0.46/gallon and $354/block hour. 3. Ticket fares charged by the two airlines are the same, fixed at $100 for one way. 4. The total demand in this market, 60,000 passengers per quarter, is assumed to be inelastic with airlines’ service decisions. 5. Each airline will choose one of 18 available sizes of aircraft: from 60 to 400 seats, increasing in step of 20 seats. 6. Each airline will choose one of 16 service frequencies per day: from 1 to 31, increasing in step of 2. 7. The flights in this market only serve local passengers. For the base case, it is assumed that airlines are only charged with the basic landing fees as what was included in the ‘‘indirect operation cost’’ in Wei and Hansen (2003), although we do not know the exact amount. We apply the one-shot simultaneous game model to find out airlines’ choices of aircraft size and service frequency in this base case without any additional landing fee. Since there are 18 choices of aircraft size and 16 choices of service frequency by the two airlines there are 82944 possible strategies available in the game. To find a NE strategy [ðs1 ; f 1 Þ, ðs2 ; f 2 Þ], a combination of ðs1 ; f 1 Þ and ðs2 ; f 2 Þ is needed from all the combinations that will solve the optimization problem (1), although there is no guarantee that we can find one. The solution is [ðs1 ¼ 160; f 1 ¼ 7Þ, ðs2 ¼ 160; f 2 ¼ 7Þ], i.e., both airlines will choose aircraft of 160 seats and operate seven times per day. Based on this solution, the cost, revenue, profit, and load factor for each airline can be calculated (Table 1). We now consider the scenarios that the airport charges airlines additional landing fees, so that airlines may use larger aircraft and reduce daily service frequency. The same cost model, market share model and the one-shot simultaneous game model are applied. We find that if airlines are charged $1000/flight extra landing fees, then both airlines will use 200-seat aircraft and operate five times per day; and if airlines are charged with $3000/flight extra landing fees, Table 1 Airlines’ operational indices and financial performance associated with different landing fees Additional charge ($/flight) Aircraft size (seats) Service frequency (daily) Load factor (%) Demand (no. of local passengers in thousands, quarterly) Cost ($ in millions, quarterly) Revenue ($ in millions, quarterly) Profit ($ in millions, quarterly)
0 160 7 58.2 60 2.76 6 3.24
1000 200 5 65.2 60 2.94 6 3.06
3000 260 3 83.6 60 3.32 6 2.68
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then both airlines will use 260-seat aircraft and operate three times per day. The load factors are 65.2% and 83.6%. The cost, revenue and profit for each airline under these two scenarios are summarized in Table 1. Comparing these results with those when airlines are not charged an additional landing fee, we notice that additional airport charges change the game equilibrium, and airlines’ choices of aircraft size and service frequencies are different if airlines were charged different landing fees. This is not surprising considering the properties of the cost function and market share model applied. Airlines will have different optimal choices of aircraft size and service frequency when the operation costs are different due to additional landing fees charged. Secondly, airlines will use larger aircraft and less frequency if charged higher landing fees. Being charged $1000 extra landing fees, airlines will use larger aircraft and less service frequency than without an additional landing fee; and being charged $3000 extra landing fees, airlines will use larger aircraft and less frequency than being charged $1000 in extra landing fees. Due to the cost economies of aircraft size determined by the cost model, higher landing fees will force airlines to use larger aircraft and less frequency for the same number of passengers in service. Also, if higher landing fee policy is employed, airlines will provide less capacity in the market for the same number of passengers, therefore, airlines’ load factor will be increased. Thirdly, since airport capacity depends on the size of aircraft in operations, using larger aircraft and less frequency to serve the same number of passengers will significantly reduce airport congestion and delay. Therefore, higher landing fees will provide incentives for airlines to use larger aircraft and less frequency, and thus reduce the number of aircraft operations and reduce airport congestion and delay at the airport. Fourthly, we also find that, very interestingly, airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft and consequently reducing airport congestion. From Table 1, one sees that airlines’ cost will go up and profit down if they are charged with higher landing fees. But if part of the higher landing fees collected by the airport are given back to the airlines, the airline will not lose any profit compared with the base case. For example, if 40% of $1000 additional landing fees are returned to the airlines, or 69% of $3000 additional landing fees are returned to the airlines, then the airlines being charged with additional landing fees will make the same profit as the base case. 4. Summary A one-shot simultaneous game-theoretic model for two airlines competing in a non-cooperative duopoly market is applied to study how the changes of airport landing fees could influence airlines’ decisions on aircraft size and service frequency, and how the changes could influence airlines’ profit, as well as airport congestion and delay. It is found
that airlines’ optimal aircraft size and service frequency are affected by landing fees, and higher landing fees will force airlines to use larger aircraft and less frequency, with higher load factor for the same number of passengers in service. It is also found that airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft and consequently contributing to airport congestion alleviation.
Acknowledgment The author started this project with suggestions from Professor Mark Hansen, and benefits from discussions with him.
References Allen, D., 1994. Social impacts of congestion pricing at airport facilities. Papers of Australasia Transportation Research Forum 19, 383–394. Ashford, N., Stanton, H.P.M., Moore, C.A., 1995. Airport Operations, second ed. McGraw-Hill, New York. Brander, J.R.G., Cook, B.A., 1986. Air transport deregulation and airport congestion: the search for efficient solutions. Transportation Research Record 1094, 18–23. de Neufville, R., Odoni, A., 2003. Airport Systems: Planning, Design and Management. McGraw-Hill, New York. Forsyth, P., 1997. Price regulation of airports: principles with Australian applications. Transportation Research, Part E: Logistics and Transportation Review 33, 297–309. Geisinger, K., 1989. Method of allocating airport runway slots. Transportation Research Record 768, 1–7. Hansen, M., Zhang, Y., 2005. Operational consequences of alternative airport demand management policies: the case of LaGuardia airport. Transportation Research Record 1915, 95–104. Martin-Cejas, R.R., 1997. Airport pricing systems in Europe and an application of Ramsey pricing to Spanish airports. Transportation Research, Part E: Logistics and Transportation Review 33, 321–327. Morrison, S.A., 1982. The structure of landing fees at uncongested airports: an application of Ramsey pricing. Journal of Transport Economics and Policy 16, 151–159. Niemeier, H., 2002. Regulation of airports: the case of Hamburg airport— a view from the perspective of regional policy. Journal of Air Transport Management 8, 37–48. Oum, T.H., Zhang, A., Zhang, Y., 2004. Alternative forms of economic regulation and their efficiency implications for airports. Journal of Transport Economics and Policy 38, 217–246. Pels, E., Nijkamp, P., Rietveld, P., 1997. Substitution and complementarity in aviation: airport vs. airlines. Transportation Research, Part E: Logistics and Transportation Review 33, 275–286. Starkie, D., 2001. Reforming UK airport regulation. Journal of Transport Economics and Policy 35, 119–135. Wei, W., 2000. Airlines’ choice of aircraft size in a competitive environment. Ph.D. Dissertation, Institute of Transportation Studies, University of California, Berkeley. Wei, W., Hansen, M., 2003. Cost economics of aircraft size. Journal of Transport Economics and Policy 37, 277–294. Wei, W., Hansen, M., 2005. Impact of aircraft size and seat availability on airlines’ demand and market share in duopoly markets. Journal of Transportation Research, Part E: Logistics and Transportation Review 41, 315–327. Zhang, A., Zhang, Y., 1997. Concession revenue and optimal airport pricing. Transportation Research, Part E: Logistics and Transportation Review 33, 287–296.
Journal of Air Transport Management 12 (2006) 288–292 www.elsevier.com/locate/jairtraman
Impact of landing fees on airlines’ choice of aircraft size and service frequency in duopoly markets Wenbin Wei a
Department of Aviation and Technology, San Jose State University, One Washington Square, San Jose, CA 95192-0061, USA
Abstract A one-shot simultaneous game-theoretic model is applied in a duopoly market to investigate how airport landing fees could influence airlines’ decisions on aircraft size and service frequency. It is found that higher landing fees will force airlines to use larger aircraft and less frequency, with higher load factor for the same number of passengers. It is also found that airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft, which consequently reduces airport congestion. r 2006 Elsevier Ltd. All rights reserved. Keywords: Landing fee; Aircraft size; Airport congestion; Airline competition
1. Introduction Delays caused congestion are a major problem at many airports. The traditional method of dealing with the problem focused on airport capacity expansion, but this is expensive and often only generates more traffic. Installing more advanced air traffic control systems can also enhance capacity, but this tends to be marginal compared with costs involved. Therefore, more attention has been paid to applying administrative and economic methods to the reduction of airport congestion without large investments. Concepts of slot (i.e. right of departure or arrival during a specific period at an airport) and congestion pricing (i.e. using price to ration capacity and divert traffic from peak periods to off-peak periods) are forms of administrative and economic controls. To this end, Geisinger (1989) proposes an administrative method to allocate airport runway slots among airlines and Morrison (1982) examines a simple twopart pricing model for uncongested airports. Brander and Cook (1986) find that the airport will be more efficiently operated and social costs will be reduced under congestion management, and argue that the slot auction approach— each slot goes to the highest bidder—would solve the slot Tel.: +1 4089243206; fax: +1 4089243198.
E-mail address: [email protected]. 0969-6997/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2006.07.008
shortage problem. In practice, the principal part of the landing fee in all major international airports is based on aircraft weight, and no airport in the US has adopted the time-varying landing fee policy (de Neufville and Odoni 2003). London Heathrow has in the past adopted ‘punitive peak-hour tariffs’ to encourage airlines to transfer operations from Heathrow to Gatwick and to move operations from the peak period. Given the particular situation at Heathrow and Gatwick this approach did not prove very successful (Ashford et al., 1995). Some of the more recent work has focused on applying pricing regulation and landing fee policies at airports to optimize social benefits.1 Most of these theoretical studies develop airport pricing policies from the airport’s perspective and consider the airport as a public entity that maximizes social benefits. In reality, airlines, the users of airports, play a very important role in airport pricing policy, since the structure of landing fees influences airlines’ operational and management decisions. Lack of consideration of airlines’ perspectives on such issues as practical scheduling constraints and influence on their competitive 1 Forsyth (1997) incorporates principles of efficient pricing into a pricecap regulatory framework, and Martin-Cejas (1997) proposes Ramsey pricing models for Spanish Airports. Starkie (2001), Zhang and Zhang (1997) and Oum et al. (2004) argue that the dual-till or two-till (considering both the runways and retailing) regulation is better than the single-till price-cap regulation for airport management.
ARTICLE IN PRESS W. Wei / Journal of Air Transport Management 12 (2006) 288–292
situations makes airport congestion management policy difficult to implement. Allen (1994) finds that congestion pricing policy may alter aircraft mix which favors larger aircraft and large airlines. Pels et al. (1997) explore the implications of airport pricing as possible influence on the choice of hub location for airlines. Niemeier (2002) advocates that regulatory reform should be combined with reforms to intensify competition such as slot auctioning among airlines. New York’s LaGuardia Airport (LGA) has been a flagship airport in applying administrative and economic measures to restrict traffic in the US. Since 1968, LGA has applied the high-density rule (HDR) to limit hourly slots to reduce airport congestion and delay. With some minor adjustment, this policy has been implemented in practice at LGA for more than 30 years. In April 2000, the congress passed the Wendell H. Ford Aviation Investment and Reform Act for the 21st Century (AIR-21), which requires that the slot restrictions at LGA should be eliminated after January 1, 2007 and the exemption of slots should be granted immediately to some special flights such as those provided by regional jets with less than 72 seats. Very shortly after this new policy was taken into action, FAA believed that the elimination of slots would cause severe delay problem in LGA and the whole national airspace system, and therefore withdrew the slot exemption policy and redistributed the available slots through a lottery system on December 4, 2000 (Hansen and Zhang, 2005). But today, the US congress still requires that the current slot-based demand management policy adopted at LGA should end in January of 2007. Therefore, a set of new rules and ideas have been proposed to develop the next generation of policies for pricing and slot allocation at LGA. But the critical challenge in designing new pricing and slot allocation rules, such as ‘‘slot auction,’’ is the lack of a mechanism or model for predicting airlines’ behavior in response to various landing fee polices and this behavior’s consequences on airport congestion and delay. To fill in this gap, this paper uses a set of analytical models to study how landing fee policies may influence airlines’ choice of aircraft size and service frequency in a competitive environment. Setting aside political factors that might influence airport pricing policy, we study airport pricing policy from the operational and economic perspectives of airlines. Since airport throughput depends on both aircraft size and service frequency provided by airlines, if airlines choose, or are economically forced by the landing fee policy, to use larger aircraft, then an airport can serve more passengers without any physical expansion of airport capacity, and the congestions and delay at airport can be reduced. The analysis here differs from previous studies in several aspects: we investigate the relation between airport pricing and airline management under the deregulated civil aviation umbrella, and study how landing fees may influence airlines’ decision on both aircraft size and service frequency, which has a significant impact on airport
289
congestion and delay; we take into account competition among airlines, especially their choices of aircraft size and service frequency as competitive strategies. Since most of the US domestic markets are served by two or three major airlines, a game-theoretic model is applied to predict airlines’ behavior in response to changes of landing fees in duopoly markets; and this study is based on previous empirical studies of airlines’ cost function and market share model, both of which are derived by using the real data of the airline industry in the US. 2. Research methodology We investigate if different landing fees per flight are charged to airlines, how the airlines may adjust their service frequency and aircraft size in a duopoly market, and whether it is possible that airlines may choose to use larger aircraft and less service frequency so that airport congestion and delay could be alleviated. Our research is confined to airlines’ strategic decisions at a market level, which is different from airlines’ decisions for daily operations in the network level.2 Airlines are assumed to be profit maximizers—they make their own best operation decisions to achieve the maximum profit. We consider competition as an important factor, and build our model in a market setting with two airlines competing with each other. Our analysis framework is based on a game-theoretic competition model, which has two basis: the cost function and the market share model, together capturing the differences in cost and in market share for airlines using different aircraft size and service frequency when different landing fees are charged. The impact of landing fees on airlines’ decision of aircraft size and service frequency is determined by both the cost function and the market share model. We directly apply the cost function and the market share model derived from previous studies of the cost economics of aircraft size (Wei and Hansen, 2003) and of market share modeling (Wei and Hansen, 2005) for airlines that use different aircraft size and service frequency in a competitive environment. 2.1. Cost function and market share model A de-mean translog model is used by Wei and Hansen (2003) to specify the airline cost function, which relates airlines’ direct operation cost per flight to aircraft size, stage length, unit fuel cost and unit labor cost. The model is calibrated using the data from the first quarter of 1987 to the fourth quarter of 1998 for the 10 largest US airlines in 2 For daily operations, most airlines make decisions on aircraft size and service frequency for each segment based on the computer models of ‘‘fleet assignment’’ and ‘‘capacity planning’’. The core of ‘‘fleet assignment’’ is an optimization model for maximizing airlines’ profit constrained by aircraft availability and scheduling feasibility. The core of ‘‘capacity planning’’ is a forecasting model for airlines to evaluate the effect of their market share and revenue resulting from certain aircraft type, service frequency, and type of service (non-stop vs. connection) in each market.
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the US domestic market. Based on the estimated parameters, Wei and Hansen (2003) claim that, at the mean values of the data, there are economies of aircraft size, and that the elasticity of direct operating cost with respect to aircraft size increases with aircraft size. They also claim that, as stage length increases, cost elasticity decreases, and there are stronger scale economies in aircraft operating cost at longer distances. For any given stage length, they find that there is consequently an optimal (least cost) aircraft size, that increases with stage length. According to the data source (Form 41) used by Wei and Hansen (2003), airlines’ total operation costs are classified into two categories: direct operation cost and indirect operation cost. Landing fees are included in the category of ‘‘indirect operation cost’’, which is exogenous to direct operation cost. When airlines report ‘‘indirect operation cost’’ data to FAA, they do not differentiate the amount of ‘‘landing fees’’ from other aircraft service expense such as ‘‘line service expense’’ and ‘‘control expense.’’ Therefore, we do not know explicitly the amount of landings fees included in airlines’ indirect operation cost. But we can still find the impact of additional landing fees on airlines’ total cost and choice of aircraft size, without knowing the exact amount of landing fees currently charged to airlines at each specific airport. Based on the cost function in Wei and Hansen (2003), the least-cost aircraft size can be found under the current landing fee policy and under policies that charge airlines additional landing fees. Airlines need to consider not only the cost but also revenue to achieve maximum profit. Therefore, to find the optimal aircraft size, we need to analyze not only how operation cost changes with aircraft size but also how revenue, demand and market share change when different aircraft size and service frequency are provided in the market. We directly apply the nested logit model derived in Wei and Hansen (2005), which captures the roles of aircraft size, service frequency, and fare in airlines’ market share in non-stop duopoly markets. In this model, time series quarter data, in the database products of Onboard and O&D Plus, from the first quarter of 1989 to the fourth quarter of 1998 for six of ten largest US airlines are used to estimate the model coefficients. Wei and Hansen (2005) find that there is an S-curve effect of service frequency on airlines’ market share, and that airlines can obtain higher returns in market share from increasing service frequency than from increasing aircraft size. Therefore, they conclude that ‘‘airlines have no economic incentives to use aircraft larger than the least-cost aircraft, since for the same capacity provided in the market, increase of frequency can attract more passengers than increase of aircraft size’’. According to the market share model in Wei and Hansen (2005), one airline’s market share in the duopoly market depends on the airline’s own aircraft size, service frequency and ticket price and those of its competitor. If airport charges different landing fees, airlines may choose to use different aircraft size and service frequency due to properties revealed in the cost function of Wei and Hansen (2003),
and then airlines’ revenue resulted from using different combinations of aircraft size and service frequency can be quantitatively analyzed based on the market share model. Since one carrier’s market share and revenue depend not only on its own choice of aircraft size and service frequency but also on the choices made by its competitor in the market, the competition factor must be considered to study the influence of landing fees on airlines’ service decisions. We apply a one-shot simultaneous game-theoretic model for two airlines competing in a non-cooperative non-zero sum duopoly market to study whether different airport landing fees could influence airlines’ strategic decisions on aircraft size and service frequency, and how the changes could influence airlines’ profit, as well as congestion and delay at airport.
2.2. Game-theoretical competition model Since most US domestic markets are dominated by two or three major airlines, we concentrate on airlines’ competition in duopoly markets. But, the framework and the analytic model for two airlines can be easily extended for three airlines. We consider competition in local markets and assume that local passengers are served by direct nonstop flights. The game-theoretic analysis framework would be the same for cases in which local passengers could be served by connecting flights or cases in which there are connecting passengers in direct flights, but to explore indepth the analytical and empirical results for these cases, we need to have a more advanced and complex market share model for our analysis, which is not available in literature at present. In our game theoretic model, there are two players in the game: airlines 1 and 2. Each player has two decision variables: aircraft size and service frequency, and the player’s objective is to maximize its own profit. As in Wei (2000), we assume that the fare variable is an exogenous variable in the game, and is not a strategic decision variable in our study. In practice, airlines’ pricing rules and revenue management process are very complex, and are hard to be represented by a single aggregate fare variable as in the model specified in Wei and Hansen (2005). If we had sufficient pricing data and there were a more sophisticated market share model that could capture the ‘‘real’’ pricing process, we would incorporate a fare variable in our formulated game, which is actually not difficult to implement. As in Wei (2000), it is assumed that each airline will choose only one aircraft size and one service frequency, and therefore uncertainty in airlines’ decisions is not considered here. We formulate all the games for one period, and assume ‘‘complete information’’ for airlines to make decisions based on its own and its competitor’s information. We focus on pure strategy of the game and try to find Nash equilibrium (NE) for the game, which is defined as a set of strategies chosen by each player in the
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game, where no player has the incentive to change their own strategy given the other players’ strategy. The one-shot simultaneous game model is used in which two airlines in the market choose aircraft size and service frequency at the same time; both airlines know all the available choices for each other as well as profit resulted from each choice; and each airline makes an optimal choice to achieve the maximum profit for itself. Each airline’s optimal choice of aircraft size and frequency depends not only on its own cost function and market share function, but also on the choice of its competitor. There are two simultaneous optimization problems facing the airlines. As in Wei (2000), S1, F1, S2 and F2 represent the size and frequency used by airline 1 and airline 2; S 1 ; F 1 ; S2 and F 2 denote the optimal choices for corresponding variables of S1, F1, S2 and F2; Profit1ðS 1 ; F 1 ; S 2 ; F 2 Þ and Profit 2ðS 2 ; F 2 ; S 1 ; F 1 Þ represent the profit functions for airline 1 and airline 2 when airline 1 chooses S1 and F1, and airline 2 chooses S2 and F2; arg max ProfitðÞ denotes the arguments that make function ProfitðÞ achieve maximum. The airlines’ decision problem, under the one-shot simultaneous game, are formulated through two simultaneous optimization models: 8 profit1ðS 1 ; F 1 ; S2 ; F 2 Þ; < Maximize S 1 ;F 1 (1) : Maximize profit2ðS 2 ; F 2 ; S1 ; F 1 Þ; S 2 ;F 2
with the solutions: ðS1 ; F 1 Þ
¼ argmaxðS1 ;F 1 Þ Profit1ðS 1 ; F 1 ; S2 ; F 2 Þ,
(2)
ðS2 ; F 2 Þ ¼ argmaxðS2 ;F 2 Þ Profit2ðS 2 ; F 2 ; S1 ; F 1 Þ.
(3)
Since a general strategy for the airlines can be represented as [ðS 1 ; F 1 Þ, ðS 2 ; F 2 Þ], in which airline 1 chooses aircraft size and service frequency ðS 1 ; F 1 Þ, and airline 2 chooses ðS2 ; F 2 Þ, the NE strategy is [ðS 1 ; F 1 Þ, ðS2 ; F 2 Þ], in which airline 1’s optimal choice of aircraft size and frequency is ðS1 ; F 1 Þ, given airline 2’s optimal choice of ðS 2 ; F 2 Þ, and vice versa. 3. Case study Since the cost function and the market share model applied here are derived based on real data in the US domestic markets, an idealized US domestic market is defined based on the data of these markets. 1. The hypothetical market has a 1000-mile stage length (flight distance). Population and income data for the origin and destination that are needed for the demand model are based on the metropolitan areas of Albuquerque of New Mexico (ABQ) and Phoenix-Mesa of Arizona in 1998 (PHX). The ABQ–PHX market is one of those markets that are used to calibrate the market share and demand models in Wei and Hansen (2005). The populations were 680,439 and 2,933,542, and the average personal income was $23,819 and $25,302 for ABQ and PHX in 1998.
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2. There are two identical airlines operating in the market. Their operating characteristics and cost coefficients are assumed to be the same as those for an average airline in Wei and Hansen (2003). For example, airlines’ unit fuel cost and unit pilot cost are $0.46/gallon and $354/block hour. 3. Ticket fares charged by the two airlines are the same, fixed at $100 for one way. 4. The total demand in this market, 60,000 passengers per quarter, is assumed to be inelastic with airlines’ service decisions. 5. Each airline will choose one of 18 available sizes of aircraft: from 60 to 400 seats, increasing in step of 20 seats. 6. Each airline will choose one of 16 service frequencies per day: from 1 to 31, increasing in step of 2. 7. The flights in this market only serve local passengers. For the base case, it is assumed that airlines are only charged with the basic landing fees as what was included in the ‘‘indirect operation cost’’ in Wei and Hansen (2003), although we do not know the exact amount. We apply the one-shot simultaneous game model to find out airlines’ choices of aircraft size and service frequency in this base case without any additional landing fee. Since there are 18 choices of aircraft size and 16 choices of service frequency by the two airlines there are 82944 possible strategies available in the game. To find a NE strategy [ðs1 ; f 1 Þ, ðs2 ; f 2 Þ], a combination of ðs1 ; f 1 Þ and ðs2 ; f 2 Þ is needed from all the combinations that will solve the optimization problem (1), although there is no guarantee that we can find one. The solution is [ðs1 ¼ 160; f 1 ¼ 7Þ, ðs2 ¼ 160; f 2 ¼ 7Þ], i.e., both airlines will choose aircraft of 160 seats and operate seven times per day. Based on this solution, the cost, revenue, profit, and load factor for each airline can be calculated (Table 1). We now consider the scenarios that the airport charges airlines additional landing fees, so that airlines may use larger aircraft and reduce daily service frequency. The same cost model, market share model and the one-shot simultaneous game model are applied. We find that if airlines are charged $1000/flight extra landing fees, then both airlines will use 200-seat aircraft and operate five times per day; and if airlines are charged with $3000/flight extra landing fees, Table 1 Airlines’ operational indices and financial performance associated with different landing fees Additional charge ($/flight) Aircraft size (seats) Service frequency (daily) Load factor (%) Demand (no. of local passengers in thousands, quarterly) Cost ($ in millions, quarterly) Revenue ($ in millions, quarterly) Profit ($ in millions, quarterly)
0 160 7 58.2 60 2.76 6 3.24
1000 200 5 65.2 60 2.94 6 3.06
3000 260 3 83.6 60 3.32 6 2.68
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then both airlines will use 260-seat aircraft and operate three times per day. The load factors are 65.2% and 83.6%. The cost, revenue and profit for each airline under these two scenarios are summarized in Table 1. Comparing these results with those when airlines are not charged an additional landing fee, we notice that additional airport charges change the game equilibrium, and airlines’ choices of aircraft size and service frequencies are different if airlines were charged different landing fees. This is not surprising considering the properties of the cost function and market share model applied. Airlines will have different optimal choices of aircraft size and service frequency when the operation costs are different due to additional landing fees charged. Secondly, airlines will use larger aircraft and less frequency if charged higher landing fees. Being charged $1000 extra landing fees, airlines will use larger aircraft and less service frequency than without an additional landing fee; and being charged $3000 extra landing fees, airlines will use larger aircraft and less frequency than being charged $1000 in extra landing fees. Due to the cost economies of aircraft size determined by the cost model, higher landing fees will force airlines to use larger aircraft and less frequency for the same number of passengers in service. Also, if higher landing fee policy is employed, airlines will provide less capacity in the market for the same number of passengers, therefore, airlines’ load factor will be increased. Thirdly, since airport capacity depends on the size of aircraft in operations, using larger aircraft and less frequency to serve the same number of passengers will significantly reduce airport congestion and delay. Therefore, higher landing fees will provide incentives for airlines to use larger aircraft and less frequency, and thus reduce the number of aircraft operations and reduce airport congestion and delay at the airport. Fourthly, we also find that, very interestingly, airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft and consequently reducing airport congestion. From Table 1, one sees that airlines’ cost will go up and profit down if they are charged with higher landing fees. But if part of the higher landing fees collected by the airport are given back to the airlines, the airline will not lose any profit compared with the base case. For example, if 40% of $1000 additional landing fees are returned to the airlines, or 69% of $3000 additional landing fees are returned to the airlines, then the airlines being charged with additional landing fees will make the same profit as the base case. 4. Summary A one-shot simultaneous game-theoretic model for two airlines competing in a non-cooperative duopoly market is applied to study how the changes of airport landing fees could influence airlines’ decisions on aircraft size and service frequency, and how the changes could influence airlines’ profit, as well as airport congestion and delay. It is found
that airlines’ optimal aircraft size and service frequency are affected by landing fees, and higher landing fees will force airlines to use larger aircraft and less frequency, with higher load factor for the same number of passengers in service. It is also found that airlines will be better off if some of the extra landing fees are returned to airlines as a bonus for airlines using larger aircraft and consequently contributing to airport congestion alleviation.
Acknowledgment The author started this project with suggestions from Professor Mark Hansen, and benefits from discussions with him.
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