Valuing flight/slot pairs - Harvard University
An Imperfect Valuation Model for
Airport Landing Slots
Final Paper for Computer Science 286r – Spring 2004
Professor David Parkes
Submitted on: May 19, 2004
Submitted by:
Elaine Ou (elaine@eecs)
Jeff Shneidman (jeffsh@eecs)
Allan Sumiyama (asumiyama@hbs)
Abstract
Recent investigation has revealed that airplane takeoff and landing activity exceeds the safety standards at least once a day at TODO%a large percentage of the airports in the United States. In order to address this current resource over-utilization, and to better allocate resources to airlines in the future, several researchers have proposed using auctions and exchanges [1, 4, 6, 9??] to redistribute airport landing and departure slot resources. However, very little is known about how an airline (or administrative player) would like to interact with such an exchange. Realistic valuation models and valuation expressions do not exist, and would be proprietary information even if they had been devised by airlines. This lack of bidder input makes exchange testing more difficult, since exchange properties may depend on the semantics and valuation of a bid.
In this work, we propose one conceivable valuation methodology and expression language, and provide a problem generator based on these ideas. To create as realistic a system as possible, we imagined ourselves into the role of an airline manager tasked with participating in a particular slot auction of our own devising. While our system is currently being used to test an iterative combinatorial exchange, our contribution should be viewed as a “first step” in realistically modeling the players in a combinatorial slot exchange.
1. Introduction
According to the Federal Aviation Administration's annual industry forecasts, passenger traffic aboard US airlines is growing at an estimated rate of 4% per year. However, due to the difficulty of the government investing adequately and on a timely basis in airport expansion, airports that are currently busy need to make use of their runway capacities as efficiently as possible.
While it is debatable whether or not it is the responsibility of the government to regulate airport departure and landing slots, there are currently only four airports in the US whose landing and departure slots are pre-allocated. These are the "High-Density Rule" airports: Kennedy (New York), LaGuardia (New York), O'Hare (Chicago), and Reagan (Washington DC). Actually, this has changed; google for FAIR-21; I went and read about this some time ago at the DOT web site I think. I believe that these restrictions have been eliminated at 2 of these airports (wasn’t that whole Donohue lecture about how bad LGA was because of eliminated controls?) and that HDR airports go away entirely in 2007? I don’t think FAIR-21 has been amended. Add FAIR-21 to reference list. All other airports in the US allow aircraft operations on a first-come, first-served basis. The airports at which landing slots are pre-allocated were not chosen with regards to traffic congestion, however, and the High-Density Rule will be eliminated in 2007.
(Note, though, that HDR has nothing to do with congestion, as ATL is a prime example.) That is, you may want to say that: Government intervention at these four airports is based on old data; the recently released from slot control airport, XYZ (pick one of the four above)
At some of the nation's busier airports, airlines are facing difficulties because of a shortage of adequate slots to cope with demand at peak hours. This has led to airlines' needs being unsatisfied and has put increasing pressure on slots at congested airports and on an efficient slot allocation system.
The traditional, IATA (International Air Transport Authority)-based, system of slot allocation acknowledges an incumbent airline's "grandfather right" to a particular slot time at an airport where that slot was used in the previous equivalent season. These grandfather rights continue until an airline ceases to use a slot or surrenders it. Slots that are not “grandfathered” are allocated by a scheduling committee in accordance with IATA guidelines.
The secondary trading of airport slots is not officially regulated but does exist. An open market that provides for secondary trading of slots would help to encourage growth opportunities for incumbents while providing an opportunity for new entrants to gain access if they are prepared to pay an adequate price.
The IATA has nothing to do with U.S. Air Slots, right? In this case, move to literature review.
The traditional, IATA (International Air Transport Authority)-based, system of slot allocation acknowledges an incumbent airline's "grandfather right" to a particular slot time at an airport where that slot was used in the previous equivalent season. These grandfather rights continue until an airline ceases to use a slot or surrenders it. Slots that are not “grandfathered” are allocated by a scheduling committee in accordance with IATA guidelines.
The secondary trading of airport slots is not officially regulated but does exist. An open market that provides for secondary trading of slots would help to encourage growth opportunities for incumbents while providing an opportunity for new entrants to gain access if they are prepared to pay an adequate price.
Is the Commission on Air Transport a U.S. thing? (I wish I had Internet right now!) If not, move below with the IATA discussion. I’m guessing yes since I don’t think the Commission on Air Transport isn’t really dealing with slots right now?
The Commission on Air Transport has expressed concern that it may be wrong for airlines to receive payment for slots for which they had not been required to pay. However, in practice, airlines that sell slots are effectively giving up their own revenue opportunities.
A possible solution that would address the problem of air traffic congestion at airports would be to remove ownership of all, or a large percentage of, all landing slots from the airlines currently scheduled to use them. Then, the remaining slots could be allocated as decided in a combinatorial exchange.
The exchange of slots in a market-type setting could add flexibility to the current slot allocation system and reduce air traffic congestion during peak hours at airports. An exchange mechanism can redistribute scheduled air traffic by allocating slots based on participating airlines’ value and “willingness to pay” for particular slots. However, there are a number of issues to consider when predicting how actual airlines might participate in such an exchange.
2. Problem Definition
In order to assess the feasibility of an airport slot exchange mechanism, we must be able to generate models of how actual airlines might participate in such an exchange. There are a number of factors that must be determined in doing so, such as how the exchange should be structured - what, exactly, are the goods in such an exchange? How many landing slots should be made available, and how should they be split up?
This project is an attempt to develop a valuation model that incorporates real-world characteristics, and compare it to other, existing models, as well as real data showing airport traffic patterns throughout a 24-hour period. The goal is to have a model that can reasonably accurately estimate what value an airline might apply to a particular landing slot at an airport at a given time; or, rather, what price an airline might be willing to pay for such a landing slot were it a good in an auction. Some factors that need to be taken into account in creating this model include: the revenue an airline can generate from a flight at a certain time; the cost to the airline of a flight; the range of the flight; and the number of passengers aboard a flight. By factoring in as many variables as possible, we can generate a fairly accurate model that could estimate how an exchange of airport landing slots might occur.
3. Literature Review
See Section 7 Down Below for more notes on this. You could move this section to Section 7 after doing the discussion that is required in Section 7.
The literature on airport slot auctions and exchanges considers two major uses of the auction/exchange mechanism. One application is in allocating slots dynamically on a real-time basis as proposed by various Ground Delay Programs [1] and the other application is in allocating slots on a long-term, strategic basis [4, 6, 9]. The dynamic allocation application utilizes a marginal cost method in valuing slots [1]. In the marginal cost method, the value of a slot is estimated by computing the additional cost (due to delays) incurred by adding an extra flight to a slot [2]. This method is particularly suited for valuing slot values in the dynamic allocation problem in which the efficient allocation depends on the properties, such as the number of passengers, of the flights in queue at a particular moment in time. As such, this approach is not very useful in valuing slots on a long-term basis.
The method used in valuing slots for long-term allocation problems is based on contribution (or profit) of the use of the particular slot to an airline [6, 7]. In this method, each airline values a slot differently from its competitors and an exchange mechanism will allocate the slot to the airlines that value the slot the highest. The existing literature on this method makes simplifying assumptions in modeling how airlines value the slots. For example, in [7], it is assumed that an airline’s demand for a slot is independent of demand for other slots. We can easily think of situations where adjacent slots are substitute for one another, and demand for each slot is dependent on whether the airline acquires usage rights for one slot or the other. (I know this is some comparison, but I want the columns from Allan’s slide! See section 7.For a discussion of a more detailed comparison of the models, please refer to section 6 “Comparison with Other Work”)
Pasted from up above; if you agree with the move text decision, need wrapper around this IATA discussion with a reference to the right paper. (This is the British air system paper, right? This should be seen as a model for slot stuff, but we didn’t really do anything with this paper.)
The traditional, IATA (International Air Transport Authority)-based, system of slot allocation acknowledges an incumbent airline's "grandfather right" to a particular slot time at an airport where that slot was used in the previous equivalent season. These grandfather rights continue until an airline ceases to use a slot or surrenders it. Slots that are not “grandfathered” are allocated by a scheduling committee in accordance with IATA guidelines.
The secondary trading of airport slots is not officially regulated but does exist. An open market that provides for secondary trading of slots would help to encourage growth opportunities for incumbents while providing an opportunity for new entrants to gain access if they are prepared to pay an adequate price.
Our project will build on the existing work on profit-based valuation schemes by proposing a novel bidding language structure to express the valuation tree and generating valuations based on more realistic assumptionsmodels.
4. Bidding Language and Valuation Model
1 Bidding Language
In a combinatorial exchange, bidders place bids on combinations of goods and it is important that bidders be able to express their preferences using a bidding language. A bidding language needs to strike a balance between expressiveness and simplicity [8].
We propose that an airline should use the XOR- (AND, OR) – XOR bidding language. where In this language, the first XOR is at the business plan level (entire package of bids for the exchange), the (AND, OR) is at the flight level (scheduled times) and the XOR on the right is at the slot level (alternatives for a scheduled time). The AND in the (AND, OR) allows us to express dependencies, such as sets of flights/slots that must be acquired together. The OR in the (AND, OR) allows us to express combinations of flights/slots that the airline would like to acquire. It also keeps the size of the bid from blowing up exponentially because we do not have to enumerate all of the possible combinations. The final XOR is over the possible slots for a particular flight.
Example:
Consider the following (simple) hypothetical case:
• Airline with 5 planes available at Atlanta (ATL) airport
• Airline only bids for departure slots
• Airline wants to offer on-the-hour morning commuter service to La Guardia (LGA)
• The “ideal” scheduled departure times are 7:00, 8:00, 9:00 for the commuter service to LGA
• Maximum tolerable deviation from ideal departure time is +/- 15 minutes (1 slot) for the commuter service flights
• It is critical for the airline to acquire the appropriate slots for all the commuter service flights (in other words, unless they can offer the 3 hourly flights, their “morning commuter service” business is not viable)
• Airline also wants to offer some service to the West Coast (either to San Francisco or Los Angeles, or both), but the airline can tolerate not acquiring the necessary slots
• Airline has more tolerance for deviations from the “ideal” departure times for the flights to the West Coast
|Slot ID |Slot Window |Flight 1 |Flight 2 |Flight 3 |Flight 4 |Flight 5 |
| | |ATL-LGA |ATL-LGA |ATL-LGA |ATL-SFO |ATL-LAX |
|0630 |6:30-6:45 | | | | | |
|0645 |6:45-7:00 |100 | | | | |
|0700 |7:00-7:15 |100 | | | | |
|0715 |7:15-7:30 | | | | | |
|0730 |7:30-7:45 | | | |30 | |
|0745 |7:45-8:00 | |100 | |40 | |
|0800 |8:00-8:15 | |100 | |50 | |
|0815 |8:15-8:30 | | | |40 | |
|0830 |8:30-8:45 | | | |30 |40 |
|0845 |8:45-9:00 | | |100 | |50 |
|0900 |9:00-9:15 | | |100 | |60 |
|0915 |9:15-9:30 | | | | |50 |
|0930 |9:30-9:45 | | | | |40 |
In terms of this bidding language, the three flights for the commuter service are AND’ed because the airline must acquire slots for each of the flight. The West Coast flights are OR’ed because these are flights/slots that the airline would like to acquire independent of other flights and the failure to acquire slots is not critical to the business plan.
The structure of the bid (and the associated values) will look like the following:
{Business Plan 1 (“Morning Commuter Plan”)
Flight 1: {(0645,100) XOR (0700,100)}
(ATL-LGA)
AND
Flight 2: {(0645,100) XOR (0700,100)}
(ATL-LGA)
AND
Flight 3: {(0645,100) XOR (0700,100)}
(ATL-LGA)
OR
Flight 4: {(0645,100) XOR (0700,100)}
(ATL-SFO)
OR
Flight 5: {(0645,100) XOR (0700,100)}
(ATL-LAX)
XOR
Business Plan 2 (“Mid-day Economy Plan”)
…..…..
XOR
Business Plan 3 (“Evening Commuter Plan”)
…..….. }
4.2 Valuation Model
In our valuation model, the basic unit of valuation is the flight/slot pair. Our model computes the value of a slot given that a certain flight is going to use the slot. So, if Flight 001 departs at 7:00am, the 7:00am slot will be related to the value of flying Flight 001 at 7:00am. On the other hand, a 7:00am slot may be valued differently if the slot is used by Flight 002.
We define the revenue of a flight/slot pair as the sum of ticket sale prices the airline can expect from operating a certain flight using a particular slot.
We assume that an airline will place a premium on maintaining their existing schedule.
Although we can define the value of a slot simply as the profit from that flight, i.e., the difference between the revenue and the cost associated with a particular flight using the slot, we will not do so for the following reasons. There are various factors and considerations that cause airlines to place values on flight/slot pairs that deviate from the profit. Some of these factors are
• Airline’s preference for maintaining its existing schedule
• Cost of operating the flight
• Substitutability of adjacent slots (i.e., a 9:00 slot and a 9:15 slot are substitutes)
• Complementarities with nearby slots for a flight arriving and departing within X minutes (Elaine’s point in her e-mail of 4/16). I.e., flight arriving at ATL using a 9:00 am slot will ideally want to turn around and depart using a 10:00am slot (if X is set at 60 minutes)
• Temporal complementarities of slots constituting a scheduled service of multiple flights (i.e., 8am to LGA, 9am to LGA, 10am to LGA, so on)
• Strategic considerations: i.e.,
o To compete with rival airlines, airline AAA cannot afford to not offer a daily flight from ATL to LAX (or a series of flights)
• Type (classification) of airline
To take the various adjustments into account, we define value (V) which is a linear transformation of the revenue minus the cost:
Value (V) = (a * revenue + b) - Cost
W can attempt to estimate the parameters a and b based on the various factors we can come up with that are applicable to the airline domain. One of the advantages of this formulation is that it allows us to roll all kinds of effects (even those that we can barely estimate) into just two parameters. Also, we believe this formulation will make it easier to make refinements to our valuation model down the road as we learn more about airline economics. One disadvantage would be that this formulation might be considered too arbitrary.
Estimation of Revenue:
The revenue for single flight is
Revenue = sum of all ticket prices for a particular flight.
Since the airline coupon data does not allow for identification of flight #’s associated with the coupon, we will not be able to come up with revenues per flight from that data set. We can, however, come up with revenues associated with a particular Origin-Destination (O/D) pair. If there are multiple flights for the same O/D in a single day, we can possibly estimate the distribution of revenues across those flights by taking into account
• passenger traffic distribution of a typical day (i.e, more passenger at peak hours, etc)
• samples of market rates for airline fares for different departure/arrival times.
If the above estimation becomes too unwieldy, we can estimate revenue using the same method we will use for cost [5, Ch.10]:
Revenue = (operating revenue yield per ASM)*(# of available seats)*(miles flown)
• ASM = Available Seat Mile
• Avg. operating revenue yield per ASM is an industry-wide measure of actual revenue per ASM that is publicly available from airline annual reports.
Estimation of Cost:
We assume that the average cost of operating a single flight (with a given destination and aircraft type) is
Cost = (miles flown)*(avg. operating expense per ASM)*(# of available seats)
• ASM = Available Seat Mile
• Average operating expense per ASM is an industry-wide measure publicly available from airline annual reports
(Note: this results in a linear cost function, which does not accurately reflect the fact that short-haul flights are relatively more costly than long-haul in terms of per mile costs (presumably because the proportion of fixed costs are higher in short-haul flights). Also, this cost function does not capture differences due to aircraft types precisely. However, we can argue that this cost function is a reasonable first-order approximation because (i) it is increasing with distance (capturing the fact that longer flights cost more than shorter flights) and (ii) it is increasing with number of available seats which we can quite reasonably interpret as a proxy for aircraft type.)
Example:
• Delta Flt #001, ATL – LGA
• Miles flown = 1,000 miles
• Available seats = 200
• Delta’s operating expense per ASM = $ 0.10
Cost = (miles flown)*(operating expense per ASM)*(# of available seats)
= (1000 miles)*($0.10/seat-mile)*(200 seats)
= $20,000
Classification of airlines (“airline types”)
The U.S. government classifies airlines in to three categories based on revenues:
• major
• national
• regional
We can possibly add another classification: “low-cost” (which represents airlines with more streamlined operations and cost structures and non-union employees, such as Southwest)
(For the definition of the above categories, see Airline Handbook Chapter 3: Structure of the Industry ).
We can vary the parameters in our value model depending on the type of airlines. We need to think more about how the three classifications differ and how our parameters might vary due to the differences (for a discussion of airline types, please refer to the next section).
Generating the Valuations
We will illustrate the methodology of coming up with valuations.
• An airline has 30 flights operating at a certain airport (this means it has 15 flights arriving and 15 flights departing)
• The airline is an “low-cost” regional player with very streamlined operations.
• Airline needs to acquire 30 slots
• Bowing to political pressure, FAA rules that an incumbent can keep 33% of their existing slots. “Keep” means that the airline can assign a very large value (large enough to be INFINITE) to those slots. The airline needs to provide realistic values to the remaining 66% of the slots.
• The operating cost per ASM (CASM) of the airline is picked from a CASM distribution for economy airlines. For simplicity, let’s assume the distribution is uniform.
o For economy airlines, the distribution is U[$0.070, $0.090] (we can fine tune this using accurate industry figures)
o For other airlines, the distribution in U[$0.10, $0.12] (same as above)
• The operating revenue yield per ASM (RASM) of the airline is picked from a RASM distribution. For simplicity, assume again that the distribution is uniform.
o U[$0.070, $0.010]
o 2002 sample figures: 9.35 cents (UA), 8.02 cents (Southwest)
• The existing schedule (both arrivals and departures) for the airline is as follows:
|Arrivals |Departures |
|Flt# |Origin |Time |Slot |Seats |Spcl |
|Dominant |Hub airline who occupies a large |High |High |> 50% |0 or 1 |
| |fraction of slots |RASM = U[.11, |CASM = U[.10, | | |
| | |.13] |.12] | | |
|Low-cost |Airline who has relatively low |Low |Low |< 50% |0 or 1 |
| |ticket prices and low operating cost|RASM = U[.08, |CASM = U[.06, | | |
| | |.09] |.08] | | |
|Regular |Airline that is neither dominant nor|Medium |Medium |< 50% |Any between [3, 10] |
| |low-cost |RASM = U[.09, |CASM = U[.08, | | |
| | |.11] |.10] | | |
RASM: revenue per available seat-mile [$], CASM: cost per available seat-mile [$]
Dominant carrier:
• number_dominant: 0 or 1 (1 means there is a dominant carrier at the airport)
• dominant_share: a percentage of market share between [50%, 75%]
• number_slots_dominant =
number_dominant*dominant_share*total_slots_per_day
Low-cost carriers (existence and number of slots held)
• number_lowcost: 0 or 1
• lowcost_share: a percentage of market share less than 50% selected so that they all add up to 100%
• number_slots_lowcost = lowcost_share*total_slots_per_day
Regular carriers (number of slots held by regular carrier j, j = 1 to number_regular)
• number_regular: integer between [3,10] (we are simply setting these numbers at some reasonable level for our combinatorial exchange to handle)
• number_slots_regular_j : select percentages for each regular carrier such that all the percentages (including dominant and low-cost types) add up to 100%.
Some basic cases (and there is lot more combinations)
a) dominant exists (percentage = 50%), low-cost exists, 8 regulars with equal number of slots
b) no dominant, no low-cost, 10 regulars with equal number of slots
c) no dominant, no low-cost, 10 regulars, each with different number of slots
Types of aircraft
• Small - 23% of total slots, available seats = (70+20)/2 = 50
• Medium - 75% of total slots, available seats = (210+97)/2 = 150
• Large – 2% of total slots, available seats = (400+210)/2 = 300
Distribution by aircraft type:
|Type of aircraft |Percentage of total |Average # of available |Percentage of available|Distribution of flown miles (in miles) |
| |slots |seats |seats | |
|Small |23% |50 |9.0% |Short: U[200,1000] |
|Medium |75% |150 |87.9% |Medium: U[500, 2000] |
|Large |2% |300 |3.1% |Long: U[1000, 3000] |
The above figures are adapted from [5], which provides the following figures for Atlanta airport:
• Small (< 70 seats) 21.7% of all landing/takeoff at ATL, mainly short flights
• Medium (between 97 and 210 seats) 75.1% of all landing/takeoff at ATL, wide range of flight distances
• Large (> 210 seats) 1.7% of all landing/takeoff at ATL, mostly long flights
Note that the percentages do not add up to 100%. This is because there are cargo flights that occupy 1.5%. Although we do not know how representative ATL is among all airports, for the purpose of this study, we use the percentages in [5] as a approximate measure of our aircraft type distribution.
Steps in generating the valuation:
Step 1. Set the parameters of this experiment (these are fixed throughout the experiment)
|Parameter |Value |Comment |
|airport_start_time |6:00 |Negligible traffic throughout the |
| | |night |
|airport_close_time |23:00 |Negligible traffic throughout the |
| | |night |
|slot_window |0.25 hr/slot |Same as Donohue |
|runway_capacity |1.6 flights/minute |ATL (Donohue) |
|max_capacity_overload_factor |1.6 |ATL (Donohue) |
|number_runway |1 |For simplicity |
|number_dominant |1 |ATL |
|dominant_share |50% |Anything large |
|number_lowcost |1 |To make it interesting |
|lowcost_share |10% |Non-trivial share (could be higher)|
|number_regular |8 |Total of 10 carriers should be |
| | |enough (any additional carriers |
| | |probably will not provide more |
| | |insight) |
|(market share for each |{5%,5%,5%,5%, |For simplicity. |
|regular carrier) |5%,5%,5%,5%} | |
|large_plane_share |2% |ATL (Donohue) |
|large_plane_seats (on average) |300 avail.seats |Inferred from Donohue |
|medium_plane_share |75% |ATL (Donohue) |
|medium_plane_seats (on average) |150 avail. seats |Inferred from Donohue |
|small_plane_share |23% |ATL (Donohue) |
|small_plane_seats (on average) |50 avail.seats |Inferred from Donohue |
Step 2. Generate a snapshot of the market using the parameters set in Step 1 (this step will determine the initial allocation of slots. Valuation will be determined in Step 3).
Step 2.1 Generate the parameters for each airline
Here, Monopoly Airlines is the dominant carrier and Great Deal Airlines is the low-cost carrier.
|Airline_name |airline_ID |share |revenue_per_ASM |cost_per_ASM |
|Just a random name |Number |Set in |Random number w/uniform dist. |Random number w/uniform |
| | |Step 1 |which depends on carrier type. |dist. which depends on |
| | | |Once the initial value for this |carrier type. Once the |
| | | |variable is chosen (thru a |initial value for this |
| | | |random number generator) it is |variable is chosen (thru|
| | | |fixed throughout the experiment.|a random number |
| | | | |generator) it is fixed |
| | | | |throughout the |
| | | | |experiment. |
|Monopoly Airlines |1 |50.0% |$0.127 |$0.115 |
|Great Deal Airlines |2 |10.0% |$0.084 |$0.076 |
|Cambridge Air |3 |5.0% |$0.095 |$0.084 |
|Somerville Airways |4 |5.0% |$0.099 |$0.086 |
|Boston Airlines |5 |5.0% |$0.102 |$0.098 |
|Belmont Air |6 |5.0% |$0.099 |$0.098 |
|Lexington Airlines |7 |5.0% |$0.105 |$0.098 |
|Framingham Air |8 |5.0% |$0.099 |$0.098 |
|Burlington Airways |9 |5.0% |$0.105 |$0.081 |
|Woburn Air |10 |5.0% |$0.108 |$0.090 |
Step 2.2. Generate initial allocation of slots
This allocation will represent an airline’s ideal schedule (which presumably has been determined by each airline through an extensive network optimization exercise).
Our procedure is as follows:
• In Step 1, we have defined as an airport parameter the distribution of scheduled air traffic. Given a slot utilization factor (= slots used/total available slots, which is approx. 30% at Atlanta) and where the peaks and off-peak slots are, we should be able to come up with an air traffic distribution which looks like the following (shown only partially):
|Slot_ID |Slot |Flights |Peak |
| | | |1-peak |
| | | |0 –not |
|1 |06:00 |5 |0 |
|2 |06:15 |5 |0 |
|3 |06:30 |5 |0 |
|4 |06:45 |5 |0 |
|5 |07:00 |5 |0 |
|6 |07:15 |5 |0 |
|7 |07:30 |5 |0 |
|8 |07:45 |40 |1 |
|9 |08:00 |40 |1 |
|10 |08:15 |5 |0 |
|11 |08:30 |5 |0 |
|12 |08:45 |5 |0 |
|13 |09:00 |5 |0 |
|14 |09:15 |5 |0 |
|15 |09:30 |5 |0 |
|…. and so on until last slot. |
• We have also defined the market share (which is same as the share of utilized slots) for each airline.
• We can randomly (based on the market share of each airline) assign an airline to a utilized slot. For example, at the 8:00am slot (which is a peak time slot and has 40 utilized slots), the dominant carrier (with 50% share) will be assigned on average 20 slots from the 40 slots, the low-cost carrier (with 10% share) will be assigned on average 4 slots, and so on for each airline.
• Doing the above for all utilized slots, we should get the initial allocation of slots as shown below (again, only shown partially for purpose of illustration)
|airline_ID |slot |slot_ID |aircraft_type |miles_flown |avail_seats |base_revenue |
|Number |Slot |Number |(Small, medium or |Randomly chosen |Average number |Cost/ASM * miles_flown|
|(assigned |starting | |large) Chosen |from a uniform |of available |* avail_seats. This |
|randomly |time | |randomly from the |distribution of |seats, |will give the average |
|according to | | |distribution of |miles flown, |conditional on | |
|procedure | | |aircraft types |conditional on |aircraft type. | |
|described | | |defined in Step 1.|aircraft type |Large = 300 | |
|above) | | |Once the aircraft |(each aircraft |seats, Medium = | |
| | | |type is chosen, it|type has own |150, Small = 50.| |
| | | |will remain fixed |distribution of | | |
| | | |throughout the |miles). Again, | | |
| | | |experiment |once chosen, | | |
| | | | |fixed throughout| | |
|1 |6:00 |1 |medium |1104 |150 |$19,093.68 |
|1 |6:00 |1 |medium |988 |150 |$17,087.46 |
|1 |6:00 |1 |medium |868 |150 |$15,012.06 |
|1 |6:00 |1 |small |888 |50 |$5,119.32 |
|1 |6:45 |4 |medium |1890 |150 |$32,687.55 |
|1 |6:45 |4 |small |252 |50 |$1,452.78 |
|1 |6:45 |4 |small |996 |50 |$5,741.94 |
|1 |7:00 |5 |medium |1937 |150 |$33,500.42 |
|1 |7:00 |5 |medium |1656 |150 |$28,640.52 |
|1 |7:00 |5 |medium |1297 |150 |$22,431.62 |
|1 |7:30 |7 |small |342 |50 |$1,971.63 |
Step 3. Compute valuation for each slot
Now, given the initial allocation and the parameters for each scheduled flights, we can proceed with computing the valuation of each flight/slot pair.
• Compute the cost: the cost model assumes that the cost increases linearly with miles flown. It is given by Cost = (Cost per ASM for the airline) * (miles_flown) * (available seats)
• Adjust the base revenue by taking into account peak times. It is based on the assumption that peak time slots are valued more highly than non-peak times because of (i) higher passenger yield and (ii) competitive considerations. For this experiment, the adjustment factor is set at 2, which means peak revenue is valued double of non-peak revenue.
• Compute the value (= adjusted revenue – cost) for each flight/slot pair: we will define this function such that a currently utilized slot will always have some positive value. It means that if the difference of adjusted revenue and cost is less than zero, it is set at some positive value (in my sample data, this value is $10). There are two reasons for this: (1) free disposal condition precludes negative value and (2) if a slot is used there must be some intrinsic value to it.
o So this will be max (adjusted rev. – cost, $10)
Example:
|airline_ |slot |aircraft_ |miles_ |Avail_seats |base_ |cost |base_rev |peak-adjusted|
|ID | |type |flown | |revenue | |- cost |revenue |
| | | |If this gives|70% of ideal | |100% |If this gives|70% of ideal |
| | | |slot 0, slot |slot value | | |slot 69, slot|slot value |
| | | |0 does not | | | |69 does not | |
| | | |exist so we | | | |exist so we | |
| | | |need to | | | |need to | |
| | | |ignore it. | | | |ignore it. | |
|1 |6:00 |1 |0 |7 |1 |10 |2 |7 |
|1 |6:00 |1 |0 |7 |1 |10 |2 |7 |
|1 |6:00 |1 |0 |7 |1 |10 |2 |7 |
|1 |6:00 |1 |0 |7 |1 |10 |2 |7 |
|1 |6:45 |4 |3 |7 |4 |10 |5 |7 |
|1 |6:45 |4 |3 |7 |4 |10 |5 |7 |
|1 |6:45 |4 |3 |7 |4 |10 |5 |7 |
|1 |7:00 |5 |4 |7 |5 |10 |6 |7 |
|1 |7:00 |5 |4 |7 |5 |10 |6 |7 |
|1 |7:00 |5 |4 |7 |5 |10 |6 |7 |
|1 |7:30 |7 |6 |7 |7 |10 |8 |7 |
|1 |7:30 |7 |6 |7 |7 |10 |8 |7 |
|1 |7:45 |8 |7 |1027.614 |8 |1468.02 |9 |1027.614 |
|1 |7:45 |8 |7 |1127.189 |8 |1610.27 |9 |1127.189 |
|1 |7:45 |8 |7 |2429.63 |8 |3470.9 |9 |2429.63 |
|1 |7:45 |8 |7 |3843.595 |8 |5490.85 |9 |3843.595 |
|1 |7:45 |8 |7 |9750.384 |8 |13929.12 |9 |9750.384 |
|1 |7:45 |8 |7 |9750.384 |8 |13929.12 |9 |9750.384 |
|1 |7:45 |8 |7 |10837.74 |8 |15482.49 |9 |10837.74 |
|1 |7:45 |8 |7 |11220.11 |8 |16028.73 |9 |11220.11 |
|1 |7:45 |8 |7 |13155.85 |8 |18794.07 |9 |13155.85 |
|1 |7:45 |8 |7 |16967.58 |8 |24239.4 |9 |16967.58 |
|1 |7:45 |8 |7 |16979.53 |8 |24256.47 |9 |16979.53 |
|1 |7:45 |8 |7 |17194.61 |8 |24563.73 |9 |17194.61 |
5. Implementation - algorithm/pseudo-code
Our model generates a set of desired landing slots for each airline participating in the simulated exchange. First, the cost and revenue per seat-mile characteristics of each airline are generated by selecting a random number from a predefined range:
for(i=0;i ................
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