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Airline route network expansion: Modelling the benefits of slot purchases
Journal of Air Transport Management 23 (2012) 25e30
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Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Airline route network expansion: Modelling the benefits of slot purchases Danica Babic, Milica Kalic* University of Belgrade, Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, Belgrade 11000, Serbia
a b s t r a c t Keywords: Airport slots auctions Airline schedules Airline profit Airline network expansions
This paper describes a decision-making model for estimating the value of airport slots for airlines. Assuming that an airline wants to improve its flight schedule by adding new slots to its portfolio the model would enable it to investigate if such a purchase of slots in the secondary market would be profitable. The model outputs are the new flight schedule, the years necessary to recoup the initial outlay in buying the new slots, and the number of potential connections that the airline could realize if the new slots are introduced. The solutions are feasible from the aspect of aircraft availability for new flights, the realized profit for an airline, and finally, an acceptable pay-off period for the purchased slots. The model is tested on real data from a mid-sized European airline. 2012 Elsevier Ltd. All rights reserved.
1. Introduction Airport slot allocation is based on the International Air Transport Association (IATA) system and allocations are made twice a year, at the IATA Scheduling Conference. Slots in Europe, subject to the Regulations 95/93 “on common rules for the allocation of slots at Community airports” (European Commission, 1993). Its purpose is to provide consistency within EU air transport policy, to maintain effective competition at EU airports and to ensure compatibility between intra-EU arrangements and worldwide procedures for allocating slots. The IATA system of slot allocation and the EC slot regulation have been criticized by experts because of their rigid rules and inefficiency. Also, scarce airport capacity is an important market entry barrier and as such protects incumbents from competition (De Wit and Burghouwt, 2008). The critics support the idea of introducing market mechanisms, such as secondary slot trading and slot auctions that would be based on airline’s willingness to pay for slots (Mott MacDonald, 2006). The most important argument for the introduction of market mechanisms is that allocating airport slots to airlines that are most willing to pay for them will bring important social benefits. This would also help an airline in achieving network optimization, by buying those slots that fit best into its flight schedule and passenger demand. In contrast, the lack of desired slots may lead to airline revenue loss, due to the inability to meet passengers’ demand. Furthermore, for airlines with huband-spoke (HS) networks, secondary slot trading/slot auctions would be an alternative way for gaining new slots and possibility for concentration of more flights into waves at their hubs. The aim * Corresponding author. E-mail address: [email protected] (M. Kalic). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2012.03.002
of such structures is to optimise the number and quality of connections offered and, also, to enable an airline to exploit economy of scope and density (Burghouwt and Wit, 2005). Although, HS network is not the only type of network that could provide a successful business model for an airline, it is certainly the dominant form in many parts of the world, (Button, 2002). Taking into the consideration the presence of secondary slot market on both continents, in Europe and in the US, the subject of this research was only this type of market. If an airline wants to improve its flight schedule by adding new slots in its portfolio (the slots purchased at secondary market), the role of the model would be to enable an airline to investigate if the given purchase is lucrative. The additional flights are chosen according to potential revenue, aircraft availability, operating costs and the period of return on the investment. The model outputs are the new flight schedule, the number of years necessary to recoup the initial outlay for purchasing the new slots and the number of potential connections that the airline could add if it were to introduce the new slots. 2. Secondary slot market In 2008 the European Commission accepted secondary slot trading at European airports as a legal way for the airlines to buy slots. Previously, European airlines traded their slots on the “grey market” for airports in Great Britain. The slot prices in this market were set ad hoc through many direct negotiations between the airlines.1 Some airlines were not comfortable about this approach, 1 Most of the airlines today belong to one of the global alliances and the modes of governance in alliances vary greatly from case to case. The strong modes of interfirm governance tend to be associated with a more long-term strategic dimension to the collaborative relationship, which further could affect the decisions of member airline in term of influencing bid price (Hanlon, 2007).
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D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
doubtful about its lawfulness and not confident about the status of the purchased slots. The secondary slot market in Europe therefore is still limited and slot prices are not being set according to the market rules. Although there is no general rule for setting slot prices, there are certain factors that have important influence on them: time of the day, perimeter rules, use restrictions, number of slots held, airline regulations, transport demand etc, (Gillen, 2006). There is little information about the financial aspects of the trades at secondary markets at airports in Europe and US, but some prices paid for the slots at those airports are known. For example, at Heathrow airport the price for a slot is between £4 and V6 million, and at Washington National airport is around $1 million (Gillen, 2006). The differences in the slot prices at those two markets is the result a lack of legal market in Europe and the considerably smaller number of transactions in this market compared with the US, where the secondary slot market has existed since 1986. 3. Problem definition, model and heuristic algorithm Our model enables an airline to calculate if buying a new slots on the secondary market is profitable or not. The aim of the model is to create a new flight schedule consisting of all the flights already operated by the airline as well as the flights assigned to the new slots, where the airline revenue needs to be maximized and all assumptions and operational constraints must be satisfied. The following notation is used: F: set of all flights from flight schedule F0 : set of flights that consists of the destinations served by an airline on the given day, (F0 ˛F) F00 : set of flights that consists of the destinations not served by the airline, F00 (F00 ;F) D: profit of the flight schedule RD: profit difference between the new flight schedule and the existing (original) schedule c1(i): business fare c2F(i): economy full fare c2D(i): economy discount fare p1(i): business class passengers on flight i, i˛F p2(i): economy class passengers on flight i, i˛F p2F(i): passengers that paid full fare in the economy class on flight i, i˛F p2D(i): passengers that paid discount fare in the economy class on flight i, i˛F p*1(i): estimated business class passengers on flight i, i˛F0 p*2(i): estimated economy class passengers on flight i, i˛F0 p*2F(i): estimated passengers that paid full fare in the economy class on flight i, i˛F0 p*2D(i): estimated passengers that paid discount fare in the economy class on flight i, i˛F0 ci: average ticket price on flight i, i˛F00 paxi: estimated passengers on flight i, i˛F0 P(Qi): the probability that a maximum of Q passengers will pay full fare in economy class on flight i, i˛F BHDOC(i,j): block-hour direct operating cost of flight i with aircraft j, i˛F0, j˛A IOC(i,j): indirect operational costs of flight i with aircraft j, i˛F0, j˛A AP: set of airports o(i): origin airport d(i): destination airport DT(i): departure time AT(i): arrival time T: time of the new slot
Dt: passenger attraction period, (determined by a user) P(Wi): probability that maximum W passengers will buy business class tickets on flight i, i˛F0 hi(T): passenger demand per unit of time on flight i, i˛F0 Ri: estimated revenue per flight i, i˛F0 Ri0 : estimated revenue per flight i, i˛F00 hi0 (T): passenger demand per unit of time on flight i, i˛F00 A: set of aircraft TYPE: set of aircraft types ta(l,k): turnaround time of aircraft l at airport k, l˛TYPE, k˛AP t(i,j): flight time of flight i by aircraft j, i˛F00, j˛A ATj(z): arrival time of flight z by aircraft j, z˛F, j˛A DTj(w) departure time of flight w by aircraft j, w˛F, j˛A cap(atype (j)): capacity of aircraft type j, j˛A, atype(j)˛TYPE opn(k), opn(m): start of working hours at airports k and m, k, m˛AP cls(k), cls(m): end of working hours at airports k and m, k, m˛AP r: discount rate RDt00 estimated profit in the tth year of using the new slot RSD: airline’s willingness to pay for a slot today on the assumption that this will be paid off in the future N: years Nw: weeks in a season’s flight schedule; the summer season has 31 weeks and the winter season 21. R: internal rate of return C: slot price The flights assigned to new slots are either chosen from the set of flights F0 that consists of the destinations served by an airline or F00 that consists of the destinations not served by the airline (depends if the airline wants to use the new slot for increasing flight frequency or for network expansion). The model calculates a profit of the flight schedule. The profit difference between the new flight schedule (D1) and the existing schedule without new slots (D0) can be considered as the gain or loss (RD) of adding new slots:
RD ¼ D1 D0
(1)
The profit of a flight schedule (D) in this paper represents the difference between revenue from sold passenger tickets and operational costs, Eq. (2). Due to the fact that covering all the fares that an airline offers on the market is very complex, it is assumed that there are only three fares on each flight i that belongs to set of flight (F): c1(i), c2F(i) and c2D(i). The number of passengers in economy class that paid full fare (p2F(i)) and discount fare (p2D(i)) is determined by Eqs. (3) and (4). Due to International Civil Aviation Organisation standards, airline costs are classified as direct operational costs (DOCs) and indirect operational costs (IOCs). DOC include all costs attributable to the type of aircraft operated and are converted into BHDOC(i,j) for each flight i and aircraft type j, j˛A. IOCs are difficult to measure, we assumed that they depend on DOCs and the type of flight (Gvozdenovic, 1995) and expressed by Eqs. (5) and (6).
D ¼
X ½ðc1 ðiÞ$p1 ðiÞ þ c2F ðiÞp2F ðiÞ þ c2D ðiÞ$p2D ðiÞÞ i˛F
XX ½ðBHDOCði; jÞ þ IOCði; jÞÞ
ð2Þ
i˛F j˛A
p2F ðiÞ ¼ p2 ðiÞ*PðQi Þ
(3)
p2D ðiÞ ¼ p2 ðiÞ*ð1 PðQi ÞÞ
(4)
IOCði; jÞ ¼ catðjÞ;
(5)
i˛F; j˛A
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
8 < 0:5$BHDOCði; jÞ; catðjÞ ¼ 0:8$BHDOCði; jÞ; : 1:0$BHDOCði; jÞ;
regional ; continental intercontinental
and
i˛F; j˛A
Tþ Z Dt
(6) The additional assumptions and operational constraints are: the new slot is introduced to an existing seasonal flight schedule; new flights to do not cause changes in flights in the original schedule; in the Dt the existence of the same flight in the daily flight schedule as selected the one for the new slot is not allowed; the airline fleet consists of different types of aircraft and each aircraft type is characterized by certain capacity and operational costs; the aircraft of the same type have equal capacity; the aircraft turnaround time depends on the aircraft type and the airport where the turnaround occurs; flights with no passengers are not allowed in the new flight schedule; there are no spare aircraft in the fleet; flights must occur during airport working hours; and the network expands without competition. A heuristic algorithm for creating a new flight schedule is used, where the airline revenue is maximized and all assumptions and operational constraints must be satisfied. The algorithm consists of three steps: flight selection, aircraft type selection and estimation of the pay off period for investment, Fig. 1. In the case of increasing flight frequency, flight i is selected from the set of flights F0 (F0 ˛F) that consists of all departure/arrival flights already operated by an airline on the same day as the slot day. The estimated revenue per flight from F0 is determined following Eq. (7). The number of passengers on each flight is established in Eq. (8). Assuming that T is the departure/arrival time of the flight i, then passengers that want to start or finish their trip in T Dt, T þ Dt will decide to choose this flight i, Eq. 9, (Teodorovic, 1988). There are three tariffs on each flight and the number of passengers by each tariff is determined by Eqs. (10)e(13). Potential flight i for the new slot is selected according to the maximum estimated revenue per flight (Ri) that the airline can realize if flight i is introduced into the flight schedule. Airline revenue is estimated according to the estimated demand for the flight i (paxi) and the time of departure/arrival slot (T) (Pavlovic and Kalic, 2011):
maxRi ¼ c1 ðiÞ$p*1 ðiÞ þ c2F ðiÞ$p*2F ðiÞ þ c2D ðiÞ$p*2D ðiÞ
(7)
where:
p*1 ðiÞ þ p*2F ðiÞ þ p*2D ðiÞ ¼ paxi
(8)
paxi ¼
hi ðTÞvT
(9)
TDt
p*1 ðiÞ ¼ PðWi Þ$paxi
(10)
p*2 ðiÞ ¼ p*2F ðiÞ þ p*2D ðiÞ
(11)
p*2F ðiÞ ¼ p*2 ðiÞ$PðQi Þ
(12)
p*2D ðiÞ ¼ p*2 ðiÞ$ð1 PðQi ÞÞ
(13)
Due to constraint (c), the selected flight must satisfy the following conditions:
i* ¼ maxðRi Þ;
i˛F 0
(14)
o i* ¼ oðjÞ;
i* ˛F 0 ; j˛F
(15)
d i* ¼ dðjÞ;
i* ˛F 0 ; j˛F
(16)
and
DTðjÞ þ Dt DT i* or DT i* DTðjÞ Dt; i* ˛F 0 ; j˛F
List of the estimated revenue per flight in descending order
Adding a new route
Flight and aircraft selection, new flight schedule
Calculation of the profit difference between new and original schedule
Number of potential connections
(17)
Eq. (14) denotes that it is the flight with the maximum revenue from F0, while Eqs. (15)e(17) denote that in Dt the existence of the same flight in a daily flight schedule as selected one for new slot is not allowed. If these conditions are not satisfied by the selected flight i, then the next flight with the maximum Ri is selected. If an airline wants to use the new slot for network expansion, flight i is selected from F00, which consists of all departure/arrival flights that must be between the airline’s hub airport and a new destination, not previously served by the airline. The estimated revenue per flight i, i˛F00 is determined according to the estimated daily passenger demand per flight (Eq. (19)) and the estimated average ticket price (Eq. (18)). Potential flight i for the new slot is selected according to the maximum Ri0 that the airline could achieve if flight i is introduced into the flight schedule (Pavlovic and Kalic, 2010).
Original flight schedule, new slot, passenger demand, passenger attraction period
Increasing frequency on the route
27
Estimated payoff period for investment
Fig. 1. Conceptual model.
28
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
maxR0i ¼ ci $paxi
i˛F 00
(18)
where Tþ Z Dt
paxi ¼
(Eq. (25)). If the compatibility condition between flights i and j is denoted by F(i,j), where F(i,j) is defined by
Fði; jÞ ¼ TRUE if h0i ðTÞvT
i˛F
00
(19)
In the second step the available corresponding aircraft type are found: 1. The capacity of aircraft j must be equal or greater than the estimated number of passengers on flight i, i˛F0, j˛A To avoid that aircraft with too high capacity could be selected, the additional constraint is introduced that the capacity of aircraft j must be equal or lower than the estimated number of passengers on flight i increased by 25%, (Eq. 20). This constraint is defined according to the practice of some airlines to change between short-, medium- and long-haul aircraft once the average load factor on a flight reaches 75%; the upper boundary can thus be changed according to user preferences.
(20)
2. The airport where aircraft j is located and the origin airport of the flight i must be the same at the moment of departure of flight i, i˛F0, j˛A. 3. Aircraft j must be available during a time period that is a sum of the periods necessary for preparing aircraft j for flight i at airport k, for executing flight i by aircraft j from airport k to airport m, the turnaround time at airport m, for the return flight i by aircraft j from airport m to airport k, and the turnaround time for the next flight at airport k, i˛F˛, j˛A, k˛AP, m˛AP, (Eq. 21):
ATj ðzÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ DTj ðwÞ
(21)
4. The selected flight i for the new slot must be executed during airport working hours,
opnðkÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ clsðkÞ opnðmÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ clsðmÞ
(24)
MIN departure time of flight j arrival time of flight i MAX;
TDt
1:25paxi capðatypeðjÞÞ paxi
destination of flight i ¼ origin of flight j and
(22) (23)
If at least one condition is not satisfied, then the next flight with the maximum Ri/Ri0 is selected. If there are several aircraft that satisfy the defined conditions above, the aircraft with lower DOCs is selected. If there are still more aircraft, the aircraft already engaged that day has priority (to increase utilization). Further, if there are more such aircraft, the one first found is selected because the crew constraint is not considered. The next step is the estimation of the profit ((Eq. 1)) that could be realized if the new flight schedule is accepted. If RD is negative, then the next flight with the maximum Ri/Ri0 would be selected. RD can be negative, if the operational costs of the assigned aircraft are higher than the estimated revenue of the selected flight i. A connection is a sequence of flights such that for every pair of consecutive flights in the sequence a certain compatibility conditions are satisfied for the pair. The conditions entail (Mashford and Marksjo, 2001); the destination of the first flight must equal the origin of the second flight (Eq. (24)); The departure time of the outgoing flight must be later than the arrival time of the incoming flight; The departure time of the outgoing flight must be no later than the arrival time of the incoming flight plus a certain margin
Fði; jÞ ¼ FALSE otherwise;
(25) for i˛F0
and j˛F or i˛F and j˛F0
depends if the new flight is incoming or outgoing. Where; 0 < MIN < MAX and MIN and MAX are numbers determined by the user. MIN is the shortest time needed for passengers to disembark from one aircraft and to board another. MAX is the longest period that one would want a passenger to wait while still being considered part of a single connection. The number of potential connections is determined as a set of all flights i where F(i,j) ¼ TRUE. Purchasing a new slot on the secondary market is like any other investment involving an initial investment costs to be off-set by revenues revenue flows in the future that take decreasing values because of such things as the need to make interest payments and possible inflation. This is why the process of discounting is applied to determine the present value of future revenues; Eq. (26). The estimated profit realized in the tth year of using the new slot is given by Eq. (27):
RSD ¼
n X
RDt
t t ¼ 1 ð1 þ rÞ
RDt ¼ RD $Nw
(26)
(27)
Four values of the discount rate are used: 8%, 12%, 16% and 20%. Following Eq. (27) the value of RSD is an airline’s willingness-to-pay for a certain slot today assuming the amount will be paid off over a defined period. When RSD equals the slot price C the pay off period for new slot is determined. Eq. (28) is used to calculate the internal rate of return (r) equates the present value of the revenues with that of cost for n years: n X
RDt
t t ¼ 1 ð1 þ rÞ
C ¼ 0
(28)
The process returns to step one and the next flight with the maximum revenue per flight is selected. The model takes into consideration the influence of change in annuam profit (RD) to allow for the cyclical nature of the industry. Five scenarios are tested:
Scenario 1 e the realized profit (RDt) decreases 10% per annum. Scenario 2 e the realized profit (RDt) decreases 5% per annum. Scenario 3 e the realized profit (RDt) is constant. Scenario 4 e the realized profit (RDt) increases 5% per annum. Scenario 5 e the realized profit (RDt) increases 10% per annum.
4. Data The model is tested using data from a mid-sized European airline2 operating a HS network, with a variety of aircraft types and serving diverse routes. It relates to flight schedules in June 2006. The airline organizes flights into five major banks. The data includes
2 Because of confidentiality the name of the airline, hub airport and registration number of an aircraft are not provided.
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
information on flights during the period, aircraft in the fleet, passengers on flights, fares and aircraft operational costs. Daily passenger flows on each flight is based on historical data from the previous three months.
29
a
Discount rate 8%
Twenty per cent of seats in economy class are sold at full are and 80% at a discount. Each aircraft is available during the period. P(Qi) and P(Wi) are obtained from 30 days of the historical demand for flights in 2006. It is assumed that the minimum slot price, C, of initially buying a slot is V1 million with the maximum slot price is defined as the maximum that the airline is willing to pay.
1
2
3
4
b
5. Analysis We consider a slot purchased on the secondary market for the airline’s hub for departure at 08:10am on 1 June. The original flight schedule is determined by the slot date. The data used for estimating the repayment period the initial outlay for purchasing the new slot are seen in Table 1. Dt, based on 08:10am is four hours and covers the period between the end of the first and the beginning of the third departure banks. The flight, i with the maximum Ri is that from the hub to Frankfurt airport (FRA). An Airbus 321 satisfies all the conditions relating to capacity and availability, having between 118 and 154 seats, positioned at the hub airport at 07:25am and having no flights assigned between 07:25am and 11:56am. The benefit for the airline would be V21274.50 per week and V659509.50 per year. The present value of profits for various periods are presented in Fig. 2, and reflect the airline’s willingness to pay for those slots today on the assumption that this amount will be paid off in the given period. Prolonging the pay off period increases the airline’s willingness to pay, but at a decreasing rate, except when annual profit increases by 10% and discount rate is 8% (Fig. 2(a)). The investment cost is equal to the price of two slots (V2 million), because operating at Frankfurt Airport requires the airline to have both take-off and landing capacity. At a discount rate of 8% and profit increase of 10%, the airline’s willingness-to-pay V2 million for two slots would be reached in the 4th year after the purchase, Fig. 2(a). The maximum price that the airline is willing to pay for these slots during 10 years is about V6.6 million. Lowering the annual profit, the period for returning the investment would increase and the maximum price that the airline would be willing to pay for these slots would decrease. When increasing the discount rate, this change is more rapid, Fig. 2(b)e(d). The present value of profit has low sensitivity regarding the different values of the discount rate. If the discount rate is increased from 8% to 12% the present value of profit will decrease by no more than 18%, for all scenarios. However, the present value of profit is sensitive regarding different profit trends:
Table 1 Results.
5
6
7
8
9
10
7
8
9
10
7
8
9
10
7
8
9
10
Number of years Discount rate 12%
1
2
3
4
5
6
Number of years
c
Discount rate 16%
1
2
3
4
5
6
Number of years
d
Discount rate 20%
1
2
3
4
5
6
Number of years
Variable
Value
Passenger attraction period, Dt Maximum estimated revenue per flight, RHUB-FRA Estimated number of passengers, paxHUB-FRA Revenue for the flight in the opposite direction, RFRA-HUB Estimated passengers, paxFRA-HUB Realized profit of the original flight schedule, D0 Realized profit of the new flight schedule, D1 Profit difference between the new flight schedule and the original schedule, RD The potential connections if the new slot is introduced
120 min V22987.00 99 V22767.50 118 V1107184.25 V1128458.75 V21274.50 30
Fig. 2. The present value of profit at a discount rate of (a) 8%, (b) 12%, (c) 16%, and (d) 20% for the scenarios.
if profit increases 10% annually, their present value is 50% greater than when the profit flow is constant. When profits are negative, an annual decrease of 10% results in an up to 30% decrease in their present value compared to a constant profit flow. In all scenarios the pay-off period is 5 years, and this is used with a minimum discount rate of 8% in Eq. (28) to give rates of return are:
30
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
11.85% for Scenario 1, 15.63% for 2, 19.37% for 3, 23.07% for and 26.73% for 5. 6. Conclusion A model and algorithm are developed to enable an airline to perform some quick and inexpensive analysis as to the profitability of buying new slots. The benefit of using this model could be viewed in terms of increasing its profitability and service quality (new destination, increased flight frequency, improved schedule connectivity). The solutions are feasible according to aircraft availability for the new flights, the realized profit for an airline and, the acceptable pay-off period for the slots. The model can be applied to all airline route structures, but is tested here with respect to a hub-and-spoke carrier. It can be used to assess the impact of the annual profit change for discount rate on the airline’s willingness to pay for slots on secondary market. Acknowledgement This research has been supported by the Ministry of Science and Technological Development, Republic of Serbia, as a part of projects TR15023 (2008-2010) and TR36033 (2011-2014).
References Burghouwt, G., Wit, J., 2005. Temporal configurations of European airline networks. Journal of Air Transport Management 11, 185e198. Button, K.J., 2002. Debunking some common myths about airport hubs. Journal of Air Transport Management 8, 177e188. Council of the European Communities, 1993. Council Regulation (EEC) No 95/93 on common rules for the allocation of slots at Community airports, Brussels. De Wit, J., Burghouwt, G., 2008. Slot allocation and use at hub airports, perspectives for secondary trading. European Journal of Transport and Infrastructure Research 8, 147e164. Gillen, D., 2006. Slot Trading in North America. EUACA Seminar on Secondary Trading Amsterdam Airport, Schiphol June 28. Gvozdenovic, S., 1995. Aircraft, Part 1. University of Belgrade, FTTE, Belgrade (in Serbian). Hanlon, P., 2007. Global Airlines: Competition in a Transnational Industry, third ed. Butterworth-Heinemann, Oxford. Mashford, J.S., Marksjo, B.S., 2001. Airline base schedule optimisation by flight network annealing. Annals of Operations Research 108, 293e313. Netherlands. Mott MacDonald, European Commission, 2006. Study on the Impact of the Introduction of Secondary Trading at Community Airports, vol. I. Report, Brussels. Pavlovic, D., Kalic, M., 2010. Airline profit and airport slots: route network expansion. 12th World Conference on Transport Research (WCTR). Lisbon, Portugal. No 2376. Pavlovic, D., Kalic, M., 2011. Modelling the estimation of the airline profit in case of purchasing new slots for increasing flight frequency. In: Proceedings of the Conference 14th EWGT Meeting & 26th Mini-EURO & 1st ESC RH, Procedia Social & Behavioral Sciences, vol. 20, pp. 1060e1068, Poznan. Teodorovic, D., 1988. Air Transportation Models. University of Belgrade, FTTE, Belgrade (in Serbian).
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Airline route network expansion: Modelling the benefits of slot purchases Danica Babic, Milica Kalic* University of Belgrade, Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, Belgrade 11000, Serbia
a b s t r a c t Keywords: Airport slots auctions Airline schedules Airline profit Airline network expansions
This paper describes a decision-making model for estimating the value of airport slots for airlines. Assuming that an airline wants to improve its flight schedule by adding new slots to its portfolio the model would enable it to investigate if such a purchase of slots in the secondary market would be profitable. The model outputs are the new flight schedule, the years necessary to recoup the initial outlay in buying the new slots, and the number of potential connections that the airline could realize if the new slots are introduced. The solutions are feasible from the aspect of aircraft availability for new flights, the realized profit for an airline, and finally, an acceptable pay-off period for the purchased slots. The model is tested on real data from a mid-sized European airline. 2012 Elsevier Ltd. All rights reserved.
1. Introduction Airport slot allocation is based on the International Air Transport Association (IATA) system and allocations are made twice a year, at the IATA Scheduling Conference. Slots in Europe, subject to the Regulations 95/93 “on common rules for the allocation of slots at Community airports” (European Commission, 1993). Its purpose is to provide consistency within EU air transport policy, to maintain effective competition at EU airports and to ensure compatibility between intra-EU arrangements and worldwide procedures for allocating slots. The IATA system of slot allocation and the EC slot regulation have been criticized by experts because of their rigid rules and inefficiency. Also, scarce airport capacity is an important market entry barrier and as such protects incumbents from competition (De Wit and Burghouwt, 2008). The critics support the idea of introducing market mechanisms, such as secondary slot trading and slot auctions that would be based on airline’s willingness to pay for slots (Mott MacDonald, 2006). The most important argument for the introduction of market mechanisms is that allocating airport slots to airlines that are most willing to pay for them will bring important social benefits. This would also help an airline in achieving network optimization, by buying those slots that fit best into its flight schedule and passenger demand. In contrast, the lack of desired slots may lead to airline revenue loss, due to the inability to meet passengers’ demand. Furthermore, for airlines with huband-spoke (HS) networks, secondary slot trading/slot auctions would be an alternative way for gaining new slots and possibility for concentration of more flights into waves at their hubs. The aim * Corresponding author. E-mail address: [email protected] (M. Kalic). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2012.03.002
of such structures is to optimise the number and quality of connections offered and, also, to enable an airline to exploit economy of scope and density (Burghouwt and Wit, 2005). Although, HS network is not the only type of network that could provide a successful business model for an airline, it is certainly the dominant form in many parts of the world, (Button, 2002). Taking into the consideration the presence of secondary slot market on both continents, in Europe and in the US, the subject of this research was only this type of market. If an airline wants to improve its flight schedule by adding new slots in its portfolio (the slots purchased at secondary market), the role of the model would be to enable an airline to investigate if the given purchase is lucrative. The additional flights are chosen according to potential revenue, aircraft availability, operating costs and the period of return on the investment. The model outputs are the new flight schedule, the number of years necessary to recoup the initial outlay for purchasing the new slots and the number of potential connections that the airline could add if it were to introduce the new slots. 2. Secondary slot market In 2008 the European Commission accepted secondary slot trading at European airports as a legal way for the airlines to buy slots. Previously, European airlines traded their slots on the “grey market” for airports in Great Britain. The slot prices in this market were set ad hoc through many direct negotiations between the airlines.1 Some airlines were not comfortable about this approach, 1 Most of the airlines today belong to one of the global alliances and the modes of governance in alliances vary greatly from case to case. The strong modes of interfirm governance tend to be associated with a more long-term strategic dimension to the collaborative relationship, which further could affect the decisions of member airline in term of influencing bid price (Hanlon, 2007).
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doubtful about its lawfulness and not confident about the status of the purchased slots. The secondary slot market in Europe therefore is still limited and slot prices are not being set according to the market rules. Although there is no general rule for setting slot prices, there are certain factors that have important influence on them: time of the day, perimeter rules, use restrictions, number of slots held, airline regulations, transport demand etc, (Gillen, 2006). There is little information about the financial aspects of the trades at secondary markets at airports in Europe and US, but some prices paid for the slots at those airports are known. For example, at Heathrow airport the price for a slot is between £4 and V6 million, and at Washington National airport is around $1 million (Gillen, 2006). The differences in the slot prices at those two markets is the result a lack of legal market in Europe and the considerably smaller number of transactions in this market compared with the US, where the secondary slot market has existed since 1986. 3. Problem definition, model and heuristic algorithm Our model enables an airline to calculate if buying a new slots on the secondary market is profitable or not. The aim of the model is to create a new flight schedule consisting of all the flights already operated by the airline as well as the flights assigned to the new slots, where the airline revenue needs to be maximized and all assumptions and operational constraints must be satisfied. The following notation is used: F: set of all flights from flight schedule F0 : set of flights that consists of the destinations served by an airline on the given day, (F0 ˛F) F00 : set of flights that consists of the destinations not served by the airline, F00 (F00 ;F) D: profit of the flight schedule RD: profit difference between the new flight schedule and the existing (original) schedule c1(i): business fare c2F(i): economy full fare c2D(i): economy discount fare p1(i): business class passengers on flight i, i˛F p2(i): economy class passengers on flight i, i˛F p2F(i): passengers that paid full fare in the economy class on flight i, i˛F p2D(i): passengers that paid discount fare in the economy class on flight i, i˛F p*1(i): estimated business class passengers on flight i, i˛F0 p*2(i): estimated economy class passengers on flight i, i˛F0 p*2F(i): estimated passengers that paid full fare in the economy class on flight i, i˛F0 p*2D(i): estimated passengers that paid discount fare in the economy class on flight i, i˛F0 ci: average ticket price on flight i, i˛F00 paxi: estimated passengers on flight i, i˛F0 P(Qi): the probability that a maximum of Q passengers will pay full fare in economy class on flight i, i˛F BHDOC(i,j): block-hour direct operating cost of flight i with aircraft j, i˛F0, j˛A IOC(i,j): indirect operational costs of flight i with aircraft j, i˛F0, j˛A AP: set of airports o(i): origin airport d(i): destination airport DT(i): departure time AT(i): arrival time T: time of the new slot
Dt: passenger attraction period, (determined by a user) P(Wi): probability that maximum W passengers will buy business class tickets on flight i, i˛F0 hi(T): passenger demand per unit of time on flight i, i˛F0 Ri: estimated revenue per flight i, i˛F0 Ri0 : estimated revenue per flight i, i˛F00 hi0 (T): passenger demand per unit of time on flight i, i˛F00 A: set of aircraft TYPE: set of aircraft types ta(l,k): turnaround time of aircraft l at airport k, l˛TYPE, k˛AP t(i,j): flight time of flight i by aircraft j, i˛F00, j˛A ATj(z): arrival time of flight z by aircraft j, z˛F, j˛A DTj(w) departure time of flight w by aircraft j, w˛F, j˛A cap(atype (j)): capacity of aircraft type j, j˛A, atype(j)˛TYPE opn(k), opn(m): start of working hours at airports k and m, k, m˛AP cls(k), cls(m): end of working hours at airports k and m, k, m˛AP r: discount rate RDt00 estimated profit in the tth year of using the new slot RSD: airline’s willingness to pay for a slot today on the assumption that this will be paid off in the future N: years Nw: weeks in a season’s flight schedule; the summer season has 31 weeks and the winter season 21. R: internal rate of return C: slot price The flights assigned to new slots are either chosen from the set of flights F0 that consists of the destinations served by an airline or F00 that consists of the destinations not served by the airline (depends if the airline wants to use the new slot for increasing flight frequency or for network expansion). The model calculates a profit of the flight schedule. The profit difference between the new flight schedule (D1) and the existing schedule without new slots (D0) can be considered as the gain or loss (RD) of adding new slots:
RD ¼ D1 D0
(1)
The profit of a flight schedule (D) in this paper represents the difference between revenue from sold passenger tickets and operational costs, Eq. (2). Due to the fact that covering all the fares that an airline offers on the market is very complex, it is assumed that there are only three fares on each flight i that belongs to set of flight (F): c1(i), c2F(i) and c2D(i). The number of passengers in economy class that paid full fare (p2F(i)) and discount fare (p2D(i)) is determined by Eqs. (3) and (4). Due to International Civil Aviation Organisation standards, airline costs are classified as direct operational costs (DOCs) and indirect operational costs (IOCs). DOC include all costs attributable to the type of aircraft operated and are converted into BHDOC(i,j) for each flight i and aircraft type j, j˛A. IOCs are difficult to measure, we assumed that they depend on DOCs and the type of flight (Gvozdenovic, 1995) and expressed by Eqs. (5) and (6).
D ¼
X ½ðc1 ðiÞ$p1 ðiÞ þ c2F ðiÞp2F ðiÞ þ c2D ðiÞ$p2D ðiÞÞ i˛F
XX ½ðBHDOCði; jÞ þ IOCði; jÞÞ
ð2Þ
i˛F j˛A
p2F ðiÞ ¼ p2 ðiÞ*PðQi Þ
(3)
p2D ðiÞ ¼ p2 ðiÞ*ð1 PðQi ÞÞ
(4)
IOCði; jÞ ¼ catðjÞ;
(5)
i˛F; j˛A
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
8 < 0:5$BHDOCði; jÞ; catðjÞ ¼ 0:8$BHDOCði; jÞ; : 1:0$BHDOCði; jÞ;
regional ; continental intercontinental
and
i˛F; j˛A
Tþ Z Dt
(6) The additional assumptions and operational constraints are: the new slot is introduced to an existing seasonal flight schedule; new flights to do not cause changes in flights in the original schedule; in the Dt the existence of the same flight in the daily flight schedule as selected the one for the new slot is not allowed; the airline fleet consists of different types of aircraft and each aircraft type is characterized by certain capacity and operational costs; the aircraft of the same type have equal capacity; the aircraft turnaround time depends on the aircraft type and the airport where the turnaround occurs; flights with no passengers are not allowed in the new flight schedule; there are no spare aircraft in the fleet; flights must occur during airport working hours; and the network expands without competition. A heuristic algorithm for creating a new flight schedule is used, where the airline revenue is maximized and all assumptions and operational constraints must be satisfied. The algorithm consists of three steps: flight selection, aircraft type selection and estimation of the pay off period for investment, Fig. 1. In the case of increasing flight frequency, flight i is selected from the set of flights F0 (F0 ˛F) that consists of all departure/arrival flights already operated by an airline on the same day as the slot day. The estimated revenue per flight from F0 is determined following Eq. (7). The number of passengers on each flight is established in Eq. (8). Assuming that T is the departure/arrival time of the flight i, then passengers that want to start or finish their trip in T Dt, T þ Dt will decide to choose this flight i, Eq. 9, (Teodorovic, 1988). There are three tariffs on each flight and the number of passengers by each tariff is determined by Eqs. (10)e(13). Potential flight i for the new slot is selected according to the maximum estimated revenue per flight (Ri) that the airline can realize if flight i is introduced into the flight schedule. Airline revenue is estimated according to the estimated demand for the flight i (paxi) and the time of departure/arrival slot (T) (Pavlovic and Kalic, 2011):
maxRi ¼ c1 ðiÞ$p*1 ðiÞ þ c2F ðiÞ$p*2F ðiÞ þ c2D ðiÞ$p*2D ðiÞ
(7)
where:
p*1 ðiÞ þ p*2F ðiÞ þ p*2D ðiÞ ¼ paxi
(8)
paxi ¼
hi ðTÞvT
(9)
TDt
p*1 ðiÞ ¼ PðWi Þ$paxi
(10)
p*2 ðiÞ ¼ p*2F ðiÞ þ p*2D ðiÞ
(11)
p*2F ðiÞ ¼ p*2 ðiÞ$PðQi Þ
(12)
p*2D ðiÞ ¼ p*2 ðiÞ$ð1 PðQi ÞÞ
(13)
Due to constraint (c), the selected flight must satisfy the following conditions:
i* ¼ maxðRi Þ;
i˛F 0
(14)
o i* ¼ oðjÞ;
i* ˛F 0 ; j˛F
(15)
d i* ¼ dðjÞ;
i* ˛F 0 ; j˛F
(16)
and
DTðjÞ þ Dt DT i* or DT i* DTðjÞ Dt; i* ˛F 0 ; j˛F
List of the estimated revenue per flight in descending order
Adding a new route
Flight and aircraft selection, new flight schedule
Calculation of the profit difference between new and original schedule
Number of potential connections
(17)
Eq. (14) denotes that it is the flight with the maximum revenue from F0, while Eqs. (15)e(17) denote that in Dt the existence of the same flight in a daily flight schedule as selected one for new slot is not allowed. If these conditions are not satisfied by the selected flight i, then the next flight with the maximum Ri is selected. If an airline wants to use the new slot for network expansion, flight i is selected from F00, which consists of all departure/arrival flights that must be between the airline’s hub airport and a new destination, not previously served by the airline. The estimated revenue per flight i, i˛F00 is determined according to the estimated daily passenger demand per flight (Eq. (19)) and the estimated average ticket price (Eq. (18)). Potential flight i for the new slot is selected according to the maximum Ri0 that the airline could achieve if flight i is introduced into the flight schedule (Pavlovic and Kalic, 2010).
Original flight schedule, new slot, passenger demand, passenger attraction period
Increasing frequency on the route
27
Estimated payoff period for investment
Fig. 1. Conceptual model.
28
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
maxR0i ¼ ci $paxi
i˛F 00
(18)
where Tþ Z Dt
paxi ¼
(Eq. (25)). If the compatibility condition between flights i and j is denoted by F(i,j), where F(i,j) is defined by
Fði; jÞ ¼ TRUE if h0i ðTÞvT
i˛F
00
(19)
In the second step the available corresponding aircraft type are found: 1. The capacity of aircraft j must be equal or greater than the estimated number of passengers on flight i, i˛F0, j˛A To avoid that aircraft with too high capacity could be selected, the additional constraint is introduced that the capacity of aircraft j must be equal or lower than the estimated number of passengers on flight i increased by 25%, (Eq. 20). This constraint is defined according to the practice of some airlines to change between short-, medium- and long-haul aircraft once the average load factor on a flight reaches 75%; the upper boundary can thus be changed according to user preferences.
(20)
2. The airport where aircraft j is located and the origin airport of the flight i must be the same at the moment of departure of flight i, i˛F0, j˛A. 3. Aircraft j must be available during a time period that is a sum of the periods necessary for preparing aircraft j for flight i at airport k, for executing flight i by aircraft j from airport k to airport m, the turnaround time at airport m, for the return flight i by aircraft j from airport m to airport k, and the turnaround time for the next flight at airport k, i˛F˛, j˛A, k˛AP, m˛AP, (Eq. 21):
ATj ðzÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ DTj ðwÞ
(21)
4. The selected flight i for the new slot must be executed during airport working hours,
opnðkÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ clsðkÞ opnðmÞ taðl; kÞ þ tði; jÞ þ taðl; mÞ þ tði; jÞ þ taðl; kÞ clsðmÞ
(24)
MIN departure time of flight j arrival time of flight i MAX;
TDt
1:25paxi capðatypeðjÞÞ paxi
destination of flight i ¼ origin of flight j and
(22) (23)
If at least one condition is not satisfied, then the next flight with the maximum Ri/Ri0 is selected. If there are several aircraft that satisfy the defined conditions above, the aircraft with lower DOCs is selected. If there are still more aircraft, the aircraft already engaged that day has priority (to increase utilization). Further, if there are more such aircraft, the one first found is selected because the crew constraint is not considered. The next step is the estimation of the profit ((Eq. 1)) that could be realized if the new flight schedule is accepted. If RD is negative, then the next flight with the maximum Ri/Ri0 would be selected. RD can be negative, if the operational costs of the assigned aircraft are higher than the estimated revenue of the selected flight i. A connection is a sequence of flights such that for every pair of consecutive flights in the sequence a certain compatibility conditions are satisfied for the pair. The conditions entail (Mashford and Marksjo, 2001); the destination of the first flight must equal the origin of the second flight (Eq. (24)); The departure time of the outgoing flight must be later than the arrival time of the incoming flight; The departure time of the outgoing flight must be no later than the arrival time of the incoming flight plus a certain margin
Fði; jÞ ¼ FALSE otherwise;
(25) for i˛F0
and j˛F or i˛F and j˛F0
depends if the new flight is incoming or outgoing. Where; 0 < MIN < MAX and MIN and MAX are numbers determined by the user. MIN is the shortest time needed for passengers to disembark from one aircraft and to board another. MAX is the longest period that one would want a passenger to wait while still being considered part of a single connection. The number of potential connections is determined as a set of all flights i where F(i,j) ¼ TRUE. Purchasing a new slot on the secondary market is like any other investment involving an initial investment costs to be off-set by revenues revenue flows in the future that take decreasing values because of such things as the need to make interest payments and possible inflation. This is why the process of discounting is applied to determine the present value of future revenues; Eq. (26). The estimated profit realized in the tth year of using the new slot is given by Eq. (27):
RSD ¼
n X
RDt
t t ¼ 1 ð1 þ rÞ
RDt ¼ RD $Nw
(26)
(27)
Four values of the discount rate are used: 8%, 12%, 16% and 20%. Following Eq. (27) the value of RSD is an airline’s willingness-to-pay for a certain slot today assuming the amount will be paid off over a defined period. When RSD equals the slot price C the pay off period for new slot is determined. Eq. (28) is used to calculate the internal rate of return (r) equates the present value of the revenues with that of cost for n years: n X
RDt
t t ¼ 1 ð1 þ rÞ
C ¼ 0
(28)
The process returns to step one and the next flight with the maximum revenue per flight is selected. The model takes into consideration the influence of change in annuam profit (RD) to allow for the cyclical nature of the industry. Five scenarios are tested:
Scenario 1 e the realized profit (RDt) decreases 10% per annum. Scenario 2 e the realized profit (RDt) decreases 5% per annum. Scenario 3 e the realized profit (RDt) is constant. Scenario 4 e the realized profit (RDt) increases 5% per annum. Scenario 5 e the realized profit (RDt) increases 10% per annum.
4. Data The model is tested using data from a mid-sized European airline2 operating a HS network, with a variety of aircraft types and serving diverse routes. It relates to flight schedules in June 2006. The airline organizes flights into five major banks. The data includes
2 Because of confidentiality the name of the airline, hub airport and registration number of an aircraft are not provided.
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
information on flights during the period, aircraft in the fleet, passengers on flights, fares and aircraft operational costs. Daily passenger flows on each flight is based on historical data from the previous three months.
29
a
Discount rate 8%
Twenty per cent of seats in economy class are sold at full are and 80% at a discount. Each aircraft is available during the period. P(Qi) and P(Wi) are obtained from 30 days of the historical demand for flights in 2006. It is assumed that the minimum slot price, C, of initially buying a slot is V1 million with the maximum slot price is defined as the maximum that the airline is willing to pay.
1
2
3
4
b
5. Analysis We consider a slot purchased on the secondary market for the airline’s hub for departure at 08:10am on 1 June. The original flight schedule is determined by the slot date. The data used for estimating the repayment period the initial outlay for purchasing the new slot are seen in Table 1. Dt, based on 08:10am is four hours and covers the period between the end of the first and the beginning of the third departure banks. The flight, i with the maximum Ri is that from the hub to Frankfurt airport (FRA). An Airbus 321 satisfies all the conditions relating to capacity and availability, having between 118 and 154 seats, positioned at the hub airport at 07:25am and having no flights assigned between 07:25am and 11:56am. The benefit for the airline would be V21274.50 per week and V659509.50 per year. The present value of profits for various periods are presented in Fig. 2, and reflect the airline’s willingness to pay for those slots today on the assumption that this amount will be paid off in the given period. Prolonging the pay off period increases the airline’s willingness to pay, but at a decreasing rate, except when annual profit increases by 10% and discount rate is 8% (Fig. 2(a)). The investment cost is equal to the price of two slots (V2 million), because operating at Frankfurt Airport requires the airline to have both take-off and landing capacity. At a discount rate of 8% and profit increase of 10%, the airline’s willingness-to-pay V2 million for two slots would be reached in the 4th year after the purchase, Fig. 2(a). The maximum price that the airline is willing to pay for these slots during 10 years is about V6.6 million. Lowering the annual profit, the period for returning the investment would increase and the maximum price that the airline would be willing to pay for these slots would decrease. When increasing the discount rate, this change is more rapid, Fig. 2(b)e(d). The present value of profit has low sensitivity regarding the different values of the discount rate. If the discount rate is increased from 8% to 12% the present value of profit will decrease by no more than 18%, for all scenarios. However, the present value of profit is sensitive regarding different profit trends:
Table 1 Results.
5
6
7
8
9
10
7
8
9
10
7
8
9
10
7
8
9
10
Number of years Discount rate 12%
1
2
3
4
5
6
Number of years
c
Discount rate 16%
1
2
3
4
5
6
Number of years
d
Discount rate 20%
1
2
3
4
5
6
Number of years
Variable
Value
Passenger attraction period, Dt Maximum estimated revenue per flight, RHUB-FRA Estimated number of passengers, paxHUB-FRA Revenue for the flight in the opposite direction, RFRA-HUB Estimated passengers, paxFRA-HUB Realized profit of the original flight schedule, D0 Realized profit of the new flight schedule, D1 Profit difference between the new flight schedule and the original schedule, RD The potential connections if the new slot is introduced
120 min V22987.00 99 V22767.50 118 V1107184.25 V1128458.75 V21274.50 30
Fig. 2. The present value of profit at a discount rate of (a) 8%, (b) 12%, (c) 16%, and (d) 20% for the scenarios.
if profit increases 10% annually, their present value is 50% greater than when the profit flow is constant. When profits are negative, an annual decrease of 10% results in an up to 30% decrease in their present value compared to a constant profit flow. In all scenarios the pay-off period is 5 years, and this is used with a minimum discount rate of 8% in Eq. (28) to give rates of return are:
30
D. Babic, M. Kalic / Journal of Air Transport Management 23 (2012) 25e30
11.85% for Scenario 1, 15.63% for 2, 19.37% for 3, 23.07% for and 26.73% for 5. 6. Conclusion A model and algorithm are developed to enable an airline to perform some quick and inexpensive analysis as to the profitability of buying new slots. The benefit of using this model could be viewed in terms of increasing its profitability and service quality (new destination, increased flight frequency, improved schedule connectivity). The solutions are feasible according to aircraft availability for the new flights, the realized profit for an airline and, the acceptable pay-off period for the slots. The model can be applied to all airline route structures, but is tested here with respect to a hub-and-spoke carrier. It can be used to assess the impact of the annual profit change for discount rate on the airline’s willingness to pay for slots on secondary market. Acknowledgement This research has been supported by the Ministry of Science and Technological Development, Republic of Serbia, as a part of projects TR15023 (2008-2010) and TR36033 (2011-2014).
References Burghouwt, G., Wit, J., 2005. Temporal configurations of European airline networks. Journal of Air Transport Management 11, 185e198. Button, K.J., 2002. Debunking some common myths about airport hubs. Journal of Air Transport Management 8, 177e188. Council of the European Communities, 1993. Council Regulation (EEC) No 95/93 on common rules for the allocation of slots at Community airports, Brussels. De Wit, J., Burghouwt, G., 2008. Slot allocation and use at hub airports, perspectives for secondary trading. European Journal of Transport and Infrastructure Research 8, 147e164. Gillen, D., 2006. Slot Trading in North America. EUACA Seminar on Secondary Trading Amsterdam Airport, Schiphol June 28. Gvozdenovic, S., 1995. Aircraft, Part 1. University of Belgrade, FTTE, Belgrade (in Serbian). Hanlon, P., 2007. Global Airlines: Competition in a Transnational Industry, third ed. Butterworth-Heinemann, Oxford. Mashford, J.S., Marksjo, B.S., 2001. Airline base schedule optimisation by flight network annealing. Annals of Operations Research 108, 293e313. Netherlands. Mott MacDonald, European Commission, 2006. Study on the Impact of the Introduction of Secondary Trading at Community Airports, vol. I. Report, Brussels. Pavlovic, D., Kalic, M., 2010. Airline profit and airport slots: route network expansion. 12th World Conference on Transport Research (WCTR). Lisbon, Portugal. No 2376. Pavlovic, D., Kalic, M., 2011. Modelling the estimation of the airline profit in case of purchasing new slots for increasing flight frequency. In: Proceedings of the Conference 14th EWGT Meeting & 26th Mini-EURO & 1st ESC RH, Procedia Social & Behavioral Sciences, vol. 20, pp. 1060e1068, Poznan. Teodorovic, D., 1988. Air Transportation Models. University of Belgrade, FTTE, Belgrade (in Serbian).