Valuing flight/slot pairs by IGv7Td

VIEWS: 27 PAGES: 20

									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




                                                                                                               2
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

                                                                                                                 3
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”)                                                                                                              Formatted

         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
4.1 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



                                                                                                                4
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           Flight 1      Flight 2      Flight 3       Flight 4        Flight 5
                  Window           ATL-          ATL-          ATL-         ATL-SFO         ATL-LAX
                                   LGA           LGA           LGA
   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




                                                                                                               5
    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




                                                                                                                 6
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:



                                                                                                                  7
            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
http://www.airlines.org/publications/d.aspx?nid=963 ).

     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   Keep?     Flt#   Dest.   Time     Slot    Seats    Spcl.   Keep?
                                                               002    LGA     06:05    06:00 100        Y
                                                               004    LGA     07:05    07:00 200        Y
                                                               006    SFO     07:35    07:30 200
001        LGA      06:55    06:45   100      Y                008    LGA     08:05    08:00 100        Y


                                                                                                                  8
003   LGA       07:55    07:45   100    Y                010   LGA     09:05    09:00   100     Y
005   BOS       08:25    08:15   200                     012   BOS     09:35    09:30   200
007   LGA       09:10    09:00   200    Y                014   LAX     10:20    10:15   200
009   LGA       09:55    09:45   100    Y                016   ORD     11:05    11:00   100
011   ORD       10:55    10:45   100                     018   MIA     12:05    12:00   100
013   LGA       14:25    14:15   75                      020   SEA     15:35    15:30   75
015   SFO       16:55    16:45   100                     022   LGA     18:05    18:00   100     Y
017   SEA       17:55    17:45   100                     024   LGA     19:05    19:00   100     Y
019   ORD       18:10    18:00   50                      026   ORD     19:20    19:15   50
021   MIA       18:55    18:45   50                      028   LGA     20:05    20:00   50      Y
023   LAX       19:55    19:45   50                      030   LGA     21:05    21:00   50      Y
025   LGA       20:55    20:30   200    Y
027   LAX       21:25    21:15   200
029   LGA       21:55    21:45   100    Y


4.3 Procedure to Generate the Valuations

4.3.1 Setting the Parameters

Airport-level parameters

Airport operating hours
          airport_start_time: time the airport starts operations (hh:mm). Ex. 06:00
          airport_close_time time the airport shuts down (hh:mm). Ex. 23:00

Duration of a slot window
         slot_window: how long is one slot? (minutes). Ex. 15 minutes

Total number of slots per day
         total_slots_per_day = (airport_close_time – airport_start_time) * 60 / slot_window .
            Ex.: (23:00 – 06:00)*(60 minutes)/(15 minutes/slot) = 68 slots per day

Maximum capacity per runway per minute (ignore differences between takeoff/landing)
       runway_capacity: theoretical capacity per runway (in number of flights handled). Ex. 25
          flights/15 min/runway (for Atlanta) = 1.67 flts/min/runway
       max_capacity_overload_factor: many congested airports operate beyond their capacity and
          we can take this into account. Ex. Atlanta experiences a maximum of 40 arrivals for a
          capacity of 25 slots, maximum overload factor = 40/25 = 1.6 at peak times.

Number of runways
        number_runway: number of runways in operation at the airport

        Combining the above, we can define the maximum number of flights that can be allocated by the
exchange mechanism to each slot as follows:

         max_slot_capacity = number_runway * runway_capacity * slot_window

         So, max_slot_capacity is the maximum number of “slots” that can be allocated by the mechanism
for each slot window. (Note that this number is less than the actual number of flights using a slot during
busy hours because safety constraints are built into this number)

Number of airlines: we should set this as the sum of the number of airlines of each type, as defined below:

Airline type (3 types)



                                                                                                          9
   dominant carrier: an airline operating a hub at the airport who occupies a large fraction of slots
    (greater than 50%). Dominant carriers have high operating costs and high ticket prices. There is at
    most one dominant carrier per airport, by definition. Ex. Delta at ATL.
   low-cost carrier: an airline with significantly low operating costs and relatively low ticket price. Ex.
    Southwest.
   regular carrier: an airline who is not dominant but is not a low-cost carrier. Ex. CO and other airlines
    at ATL.

The characteristics of the three types:

Type            Description                  Revenue       Cost per      Slot               Number per
                                             per ASM       ASM           Allocation         airport
Dominant     Hub airline who occupies a      High          High          > 50%              0 or 1
             large fraction of slots         RASM =        CASM =
                                             U[.11, .13]   U[.10, .12]
Low-cost     Airline who has relatively      Low           Low           < 50%              0 or 1
             low ticket prices and low       RASM =        CASM =
             operating cost                  U[.08, .09]   U[.06, .08]
Regular      Airline that is neither         Medium        Medium        < 50%              Any between [3,
             dominant nor low-cost           RASM =        CASM =                           10]
                                             U[.09, .11]   U[.08, .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:




                                                                                                          10
Type of        Percentage of         Average # of      Percentage of        Distribution of flown miles (in
aircraft       total slots           available seats   available seats      miles)
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




                                                                                                         11
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                Random number
                                               Step 1 w/uniform dist. which        w/uniform dist.
                                                      depends on carrier type. which depends on
                                                      Once the initial value for carrier type. Once
                                                      this variable is chosen      the initial value for
                                                      (thru a random number        this variable is
                                                      generator) it is fixed       chosen (thru a
                                                      throughout the experiment. 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



                                                                                                            12
                                        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 Randomly           Average      Cost/ASM *
(assigned     starting            or large)         chosen from a number of    miles_flown *
randomly      time                Chosen            uniform       available    avail_seats. This
according                         randomly from distribution ofseats,          will give the
to                                the distribution miles flown, conditional on average
procedure                         of aircraft types conditional aircraft type.
described                         defined in Step on aircraft     Large = 300
above)                            1. Once the       type (each    seats,
                                  aircraft type is aircraft type Medium =
                                  chosen, it will has own         150, Small =
                                  remain fixed distribution of50.
                                  throughout the miles).
                                  experiment        Again, once
                                                    chosen, fixed
                                                    throughout
          1         6:00         1medium                      1104          150        $19,093.68
          1         6:00         1medium                       988          150        $17,087.46
          1         6:00         1medium                       868          150        $15,012.06
          1         6:00         1small                        888           50         $5,119.32
          1         6:45         4medium                      1890          150        $32,687.55
          1         6:45         4small                        252           50         $1,452.78
          1         6:45         4small                        996           50         $5,741.94
          1         7:00         5medium                      1937          150        $33,500.42
          1         7:00         5medium                      1656          150        $28,640.52
          1         7:00         5medium                      1297          150        $22,431.62
          1         7:30         7small                        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.




                                                                                                          13
      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:

                                                                                           peak-         max
airline_      aircraft_ miles_ Avail base_                   base_rev peak-adjusted        adjusted      (adj.rev.,
ID       slot type      flown _seats revenue         cost     - cost revenue               rev. - cost min.value)
Number                  miles        miles *         miles * “pro-    Revenue at peak      Valuation Final
                                     seats *         seats * fit”     time is doubled      before        valuation
                                     revenue         cost             to account for       adjusting
                                     per ASM         per ASM          increased yield.     for neg.
                                                                                           valuations
   1       6:00   medium     1104    150$19,093.68     19342.08 -248.4             19093.68        -248.4           10
   1       6:00   medium      988    150$17,087.46     17309.76 -222.3             17087.46        -222.3           10
   1       6:00   medium      868    150$15,012.06     15207.36 -195.3             15012.06        -195.3           10
   1       6:00   small       888     50 $5,119.32      5185.92   -66.6             5119.32         -66.6           10
   1       6:45   medium     1890    150$32,687.55      33112.8 -425.25            32687.55       -425.25           10
   1       6:45   small       252     50 $1,452.78      1471.68   -18.9             1452.78         -18.9           10
   1       6:45   small       996     50 $5,741.94      5816.64   -74.7             5741.94         -74.7           10
   1       7:00   medium     1937    150$33,500.42     33936.24-435.825           33500.415     -435.825            10
   1       7:00   medium     1656    150$28,640.52     29013.12 -372.6             28640.52        -372.6           10
   1       7:00   medium     1297    150$22,431.62     22723.44-291.825           22431.615     -291.825            10
   1       7:30   small       342     50 $1,971.63      1997.28 -25.65              1971.63        -25.65           10
   1       7:30   small       539     50 $3,107.34      3147.76 -40.425            3107.335       -40.425           10
   1       7:45   small       258     50 $1,487.37      1506.72 -19.35              2974.74      1468.02       1468.02
   1       7:45   small       283     50 $1,631.50      1652.72 -21.225             3262.99      1610.27       1610.27
   1       7:45   small       610     50 $3,516.65       3562.4 -45.75               7033.3        3470.9       3470.9
   1       7:45   small       965     50 $5,563.23       5635.6 -72.375            11126.45      5490.85       5490.85
   1       7:45   medium      816    150$14,112.72     14296.32 -183.6             28225.44     13929.12     13929.12
   1       7:45   medium      816    150$14,112.72     14296.32 -183.6             28225.44     13929.12     13929.12
   1       7:45   medium      907    150$15,686.57     15890.64-204.075            31373.13     15482.49     15482.49
   1       7:45   medium      939    150$16,240.01     16451.28-211.275            32480.01     16028.73     16028.73
   1       7:45   medium     1101    150$19,041.80     19289.52-247.725            38083.59     18794.07     18794.07


   Step 4. Determine adjacent slots and compute valuation

   We need to come up with substitutes for each airlines ideal flight/slot pairs. To do that, we assume that
   each airline values its ideal flight/slot pairs most highly, but can also tolerate shifts to the slots to some
   degree (with some adjustments to valuation, i.e., less than ideal slots will be valued lower). In the bidding
   language framework, these slots are the ones that get XOR’d at the lowest level.

   The following parameters capture this attitude of airlines towards substitute slots:

            Maximum tolerable slot deviation: how many slots from the ideal slot can the airline still feel it
             can operate the flight? Example, if this parameter is set at 2, and the ideal slot for a certain flight




                                                                                                                 14
         is an 8:00am slot, the airline can substitute 7:30am (-2), 7:45am (-1), 8:15am (+1) and 8:30am
         (+2) slots for the original 8:00am slot. In the sample data below, this parameter is set at 1 slot.
        Forward slot deviation discount: the factor by which the value of the ideal slot for a certain
         flight is decreased when the slot is shifted one slot forward. In the sample, this value is set at 30%
         (meaning the value of the adjacent forward slot is 70% of the ideal slot)
        Backward slot deviation discount: the factor by which the value of the ideal slot for a certain
         flight is decreased when the slot is shifted one slot backwards. In the sample, this value is set at
         30% (meaning the value of the adjacent backward slot is 70% of the ideal slot). It can be argued
         that a backward shift involves less decrease in value because it is not a delay, this parameter is set
         equal to the forward discount for simplicity.

Example:

                                                   Value                                                  Value
                                     ideal slot -1 (ideal slot- ideal slot     Value        ideal slot+1 (ideal
airline_ID       slot   slot_ID      slot_ID       1)            slot_ID       (ideal slot) slot_ID       slot+1)
                                     If this gives 70% of                      100%         If this gives 70% of
                                     slot 0, slot ideal slot                                slot 69, slot ideal slot
                                     0 does not value                                       69 does not value
                                     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



                                                                                                                  15
a random number from a predefined range:

         for(i=0;i<Total_Airlines;i++){
               airlines[i].revenue_per_seat-mile =
               random(airline_seat_mile_revenue_lower-limit,
                     airline_seat_mile_revenue_upper-limit);
               airlines[i].cost_per_seat-mile =
               random(airline_seat_mile_cost_lower-limit,
                     airline_seat_mile_cost_upper-limit);

         //define the airline's market share, and airline type
         ....
         }

         Airport landing slot characteristics are also defined:

      num_landing_slots = (Apt_Time_Close - Apt_Time_Open) /
Landing_Slot_Window;

         //define peak hours, and the capacity of each slot
         for(i=0;i<num_landing_slots;i++){
               landing_slots[i].capacity = airport_slot_capacity;
               ...
         }

          Bids are then generated for each airline. Desired slots are chosen randomly with a heavier
distribution towards the peak hours. A random aircraft type is assigned to each time slot bid on, and the
total range of the flight is estimated based on the type of aircraft used for the flight. The value for the bid is
equal to the difference between the total revenue and the total cost, as calculated from the cost and revenue
per seat mile for each particular airline, and determined by the number of seats available on the type of
aircraft selected.

         for(i=0;i<Total_Airlines;i++){
               b = new Bid();
               b.slot = random(landing_slots);
               b.aircraft = random(aircraft);
               b.value = (airlines[i].revenue_per_seat-mile -
                           airlines[i].cost_per_seat-mile)
                           *num_seats*num_miles;

                   //make sure value is greater than the lowest allowed bid
                   b.value = MAX(b.value, minimum_bid_value);
         }

          Our bidding mechanism presumes that airlines have a certain tolerance of a number of landing
slots deviation (num_slots_deviation) for when a plane can take off and land, as related to the first choice in
landing slot. For each primary bid generated for a landing slot, num_slots_deviation bids are also generated
as alternatives with scaled down valuations. These bids are expressed as XORs in the bidding model.


5. Analysis of values generated by the model




                                                                                                               16
     60


     50


     40


     30


     20


     10


       0
            1:00    3:00    5:00     7:00    9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00


          This chart shows the distribution of desired landing slots among a set of ten hypothetical airlines.
By examining a number of graphs of the results generated by the valuation model, it is clear that the
landing slot allocations chosen by the airlines collectively are more evenly distributed across the available
hours than the actual aircraft traffic data from ATL airport. The peaks are still evident during more
desirable hours, but will be capped at the maximum available number of landing slots available during each
time slot.
          The following graph depicts the distribution of landing slot allocations, were all airlines able to
win as many landing slots as were available. Even though the initial chart of the desired time slots shows
that the number of time slots desired during peak hours exceeds the maximum capacity of the airport, the
airlines have the choice of alternate, adjacent time slots instead of the slots right at the peak, and there are
enough adjacent slots available to accommodate the airlines’ desired landing times.




                                                                                                             17
     45

     40

     35

     30

     25

     20

     15

     10

       5

       0
            1:00 3:00 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00



6. Suggestions for Future Work and Conclusion
          We propose an expressive and simple bidding language and a valuation model for valuing takeoff
and landing slots. Our proposed bidding language, the XOR-(OR, AND)-XOR language, allows bidders to
express complements and substitutes, and also “must-get” slots. Our valuation model builds upon prior
models by basing the valuation on revenue and costs associated with a slot, while taking into account
airline types and airport traffic patterns.

         Future work could include further evaluations of our valuation model as actually implemented in a
combinatorial exchange-type setting. It would be interesting to examine the actual airport landing slot
allocations resulting from the bids generated from this model. Also, further work might involve the
comparison of results from simulated exchanges involving valuations generated from our model, as well as
models described by other sources. An analysis of slot allocation results could show how much impact the
particular valuation model used has on the bid values and resulting slot allocations in a combinatorial
exchange.

67. Comparison with Other Work
       Really need something here that compares our work in the context of other work (CATS and
Donohue) – I’d imagine Allan’s slide, which I don’t have, in words. (Or just paste in the slide and add
some words.)

         Don’t make it sound like we’re better or worse; just want a dry comparison. Note that this goes
BEYOND the literature review, because here we are comparing our approach to CATS and Donohue.
         Our model can be compared to the “Donohue” model [6] and the CATS model [7]. The models
can be compared in terms of (1) assumptions regarding slot values and (2) expressiveness of valuation
structure.

(1) Assumptions regarding slot values




                                                                                                           18
Each of the models makes assumptions about how airlines value the slots. The CATS model assumes that
the value of a slot to an airline is determined by a random utility level (which is set for each slot for each
airline). The Donohue model assumes that the value of a slot is determined by the size of the aircraft using
the particular slot. This assumption attempts to capture the observation that the size of the aircraft
determines the number of passengers an aircraft can carry, and hence it is related to the potential revenue.
Our model extends this further by assuming that airlines base their slot values on revenue and cost for the
flight using the slot (determined from aircraft size, miles flown by the flight, and unit revenue and cost for
each airline), what type of airline they are (dominant carrier, low-cost carrier or a “regular” carrier), and
whether the slot is at a peak time or not.

Each of the models assume that airlines prefer their current schedule because the current schedule is
supposed to be the result of extensive network optimization and revenue maximization by airlines and
should reflect in some way each airline’s view of its “ideal” schedule. The CATS model randomly
generates a schedule for each airline. Our model also generates schedules randomly but takes into
consideration the traffic pattern (i.e., the peak and non-peak times and traffic). The Donohue model uses
real schedule data (from Atlanta airport, summer of 2002).

(2) Expressiveness of valuation structure
A valuation structure needs to express an airline’s preference (and the values) for a set of slots that it
wishes to acquire. Airlines can have complex preferences, including the desire for substitutes (back up
slots when preferred slots are not acquired) and complements (set of slots that airline prefer to be acquired
together). All models account for substitute slots. The Donohue model does not account for
complementary slots. The CATS model accounts for complementary slots across airports, in which a
choice of slot at one airport affects the slot choice at a connected airport. Our model accounts for
complementary slots in the same airport, but not at connected airports.




7. Suggestions for Future Work and Conclusion
          We propose an expressive and simple bidding language and a valuation model for valuing takeoff
and landing slots. Our proposed bidding language, the XOR-(OR, AND)-XOR language, allows bidders to
express complements and substitutes, and also “must-get” slots. Our valuation model builds upon prior
models by basing the valuation on revenue and costs associated with a slot, while taking into account
airline types and airport traffic patterns.

         Future work could include further evaluations of our valuation model as actually implemented in a
combinatorial exchange-type setting. It would be interesting to examine the actual airport landing slot
allocations resulting from the bids generated from this model. Also, further work might involve the
comparison of results from simulated exchanges involving valuations generated from our model, as well as
models described by other sources. An analysis of slot allocation results could show how much impact the
particular valuation model used has on the bid values and resulting slot allocations in a combinatorial
exchange.

78. References
[1] M.Ball, G.Donohue, K.Hoffman. Auctions for the Safe, Efficient and Equitable Allocation of Airspace
System Resources. In P.Crampton et al., editor, Combinatorial Auctions, Ch.22, to be published.

[2] A.Carlin, R.Park. Marginal Cost Pricing of Airport Runway Capacity. American Economic Review,
60:310-318.

[3] DotEcon Ltd. Auctioning Airport Slots. A Report for HM Treasury and the Department of the
Environment, Transport and the Regions. January 2001.



                                                                                                            19
[4] D.Grether, R.Isaac, C.Plott. The Scarce Allocation of Scarce Resources: Experimental Economics and
the Problem of Allocating Airport Slots. Underground Classics in Economics. Westview Press, 1989.

[5] S.Holloway. Straight and Level: Practical Airline Economics. Ashgate Publishing, 2003.

[6] L.Le, G.Donohue, C.Chen. Using Auction-Based Slot Allocation for Traffic Demand Management at
Hartsfield Atlanta International Airport: A Case Study. Presented at the Transportation Research Board
Annual Meeting, January 2004.

[7] K.Leyton-Brown, M.Pearson, Y.Shoham. Towards a Universal Test Suite for Combinatorial Auction
Algorithms. In ACM Conference on Electronic Commerce, 2000.

[8] N.Nisan. Bidding and Allocation in Combinatorial Auctions. In ACM Conference on Electronic
Commerce, 2000.

[9] S.Rassenti, V.Smith, R.Bulfin. A Combinatorial Auction Mechanism for Airport Time Slot Allocation.
Journal of Economics, 13:402-417, 1982.




                                                                                                         20

								
To top