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A Comparison of Static and Dynamic Schemes p y for Airline

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									        p                     y
 A Comparison of Static and Dynamic Schemes
   for Airline Alliance Revenue Management

                 Robert Shumsky
          Tuck School of Business at Dartmouth
       Chris Wright and Harry Groenevelt
                      ,          y
          Simon School, University of Rochester



INFORMS Revenue Management and Pricing Conference
                June 29, 2007
Agenda

• Alliance RM overview
  Static d d     i    h
• St ti and dynamic schemes
• A model to evaluate the schemes
• Numerical comparisons
• Further work



                                    2
International Alliances
           American, B iti h Ai
           A   i                      Cathay Pacific…
                     British Airways, C th P ifi


           Air France/KLM, Delta, Northwest…


           United, Lufthansa, Singapore…

                            g (#       y p         )
International code-share flights ( daily departures)
 2003        2005      2007
17,000     33,000     39,000
                                                  3
Source: International Air Transport Association
U.S. domestic airline alliances in 2005
  For
• F 20% of d           i
            f domestic passenger coupons, the h
  operating airline was different from the ticketing
               airline
  (marketing) airline.

                                      national regional
• A majority of these were flights by national-regional
  partners (e.g., American-American Eagle, Delta-
  Chautauqua).
  Chautauqua)

• 2% of coupons were sold via code-sharing
                                code sharing
  agreements among national network airlines
  (e.g., Northwest-Continental)
  ( g,                        )
                                                   4
Source: U.S. DOT Ticket Sample/Database 1B
Marketing vs. operating: Definitions and Questions

   Seattle                 New York                      Rome
             Delta                      Alitalia


           marketing airline          p      g
                                     operating airline
    (sells ticket, collects payment)


Delta (the marketing airline) has a $1600 fare class
          Seattle New York Rome itinerary.
  for the Seattle-New York-Rome itinerary
• Should Delta open that fare class?
  – How much money does Alitalia receive?
  – Will Alitalia make its inventory available to Delta?        5
Overall alliance coordination problem


                     Negotiation
                     Nego     o                         Designing the
            Special Prorate Agreement (SPA)             SPA is a
                                                        cooperative
                                                        game.
                                                        g

prices and                               prices and
restrictions                             restrictions



customers                               customers       Given SPA,
                                                        Alliance RM
                                                        is a competitive
     Airline
     Ai li 1                    Airline
                                Ai li 2                 game
Revenue Management         Revenue Management                    6
In practice, SPA's have two functions

1. Ensure an ‘equitable’ split of revenues
    Cover
  • Co er costs of the operating airline
  • Reward partners with more negotiating power

                          g
2. Coordinate revenue management decisions
  • Share marginal cost information
  • Share revenue information

 h    functions can conflict.
These f    i           fli
                                             7
Typical (Static) Agreements under ‘Free Sale’
• Airlines sell seats in real time;
  availability communicated via reservations systems.
• Revenue to operating airline based on
   – static fraction of revenue allocated to each airline
   – mileage proration
   – other static prices, negotiated in advance.
• Agreements seem designed for Function 1
  (cost-sharing/equity).
• These static agreements can fail miserably at Function 2
  (RM coordination) – see Boyd, 1998.                   8
Dynamic revenue-sharing

Schemes based on bid-prices have been considered by
                 j
  at least one major international alliance.

Barriers to implementation:
• Incompatible revenue management and accounting
  systems.
• A lack of trust.
  Would alliance members inflate bid-price values?
                 g       y
Would ‘cheating’ really hurt?
Is it worth the effort to implement dynamic schemes?
                                                 9
A stylized model
to assess the performance of dynamic and static schemes

• Each airline uses network bid-price controls
  (Tall ri and van Ryzin, 1998)
  (Talluri      an R in

      h      i     i li                   j     h
• Each operating airline can accept or reject the
  marketing airline’s offer to buy seats for an
  itinerary
  ii

• Both airlines have perfect information about the
  other airline's inventory and demand forecasts (!)
                                                    10
Notation
for events in time period k,


      qk j = probability of a customer arrival to airline c
       cj


            to purchase itinerary j
      q = probability of no arrival
        0
        k

      Rkcj = revenue from a customer to airline c for itinerary j
                                                              y
            (if c is the marketing airline); A random variable.
    v
p ( x ) = transfer price paid to airline c for itinerary j ,
 cj
 k
                                  v
        given inventory vector x (if c is the operating airline).

                                                                  11
Airline c's value function                                                                 Arrival of a local
                                                                                           code-share
                                                                                           (non-code-share)
                                                                                           customer to c

                            ⎜ j∈N
                                    [cj
                                            (    cj    v
                                                        )       ( v       cj       v
                            ⎛ ∑ qk E Rkcj uk Rkcj , x + J kc−1 x − A j u k Rkcj , x +  (    ))]        ⎞
                                                                                                       ⎟
                            ⎜     c
                                                                                                       ⎟
                            ⎜                                                                          ⎟
                                    [cj
                                                (
                                           ~ cj v cj ~ cj v v
                                                                )     c v
                                                                               (
                            ⎜ ∑ qk E Rk ( x )u k Rk (x ), x + J k −1 x − A u k Rk (x ), x + (
                                                                                j cj ~ cj v v
                                                                                                      ))]
                                                                                                       ⎟
                            ⎜ j∈N S                                                                    ⎟
   (                )
J kc x u k c , pk−c ( x ) = ⎜
      v −             v
                            ⎜           [           (
                                                  v −cj ~ −cj v v
                                                                     )       v
                                                                                   (              (
                                                                                          ~ −cj v v
                                                                                                       ⎟,
                                    qk cj E pk (x )uk Rk ( x ), x + J kc−1 x − A j u k cj Rk (x ), x + ⎟     ))]
                            ⎜ j∑S
                                     −        cj                                      −

                               ∈N                                                                      ⎟
                            ⎜                                                                          ⎟
                            ⎜
                                        [ (
                            ⎜ ∑ qk E J k −1 x − A uk Rk , x + qk J k −1 (x )
                                      − cj     c    v
                                                            (
                                                        j − cj − cj v
                                                                         ))] 0 1    v                  ⎟
                                                                                                       ⎟
                            ⎜ j∈N −c
                            ⎜                                                                          ⎟
                                                                                                       ⎟
                            ⎝                          Arrival of a               Arrival of a         ⎠
                     v v                               local                      code-share
   c v
J 0 ( x ) = 0 ∀x ≥ 0,                                  customer to -c customer to -c
                                    {
where u k (r , x ) = arg max ru + J k −1
        cj     v
                                                (   v
                                                    x − A u and Rk (x ) = Rkcj − p k cj ( x ).
                                                         j
                                                                    )}
                                                                ~ cj v             −      v
                          u∈{0,1}                                                                       12
We examine three dynamic transfer prices
bid price: marketing airline pays the marginal value
  (bid price) of the operating airline's seats to the
                    (Boyd
  operating airline (Boyd, 1998);
bid-price proration: revenue is split proportionally,
  based on the bid prices:

       p (x) = ⎢ 1
        1jv ⎡
                                  v j
                            ΔJ x , A
                               1
                               k −1   (   )        ⎤
        k
               ⎣ ΔJ k −1   (
                           v    j
                                 )    2    v j
                                              (
                           x , A + ΔJ k −1 x , A   )
                                                   ⎥r
                                                   ⎦

partner price: the price for a seat is set dynamically
  by the operating airline to maximize its own
                                                    13
  revenue, i.e., cheating on the bid price scheme.
Technical results

For the partners' accept/reject decisions,
  there is a unique, pure-strategy markov-perfect
  equilibrium:

  Each airline rejects an offer if its net revenue is less
  than the total cost (own bid price plus any transfer
  price) of the itinerary.




                                                     14
Technical results, Partner Price
L t f k2 j (r ) and Fk2 j (r ) b th pdf and cdf f airline 2' s
Let               d            be the df d df for i li

  distribution of revenue for itinerary j in period k .

For the partner price scheme, if Fk2 j (r ) has Increasing Generalized

  Failure Rate (IGFR) then there is a unique equilibrium price.

    p           g      y                   y                y
The price charged by airline 1 for itinerary j is defined by :

       1j v        1
                      (        )
                                  2j
     pk ( x ) = ΔJ k −1 x , A + 2 j
                                     (             ) 1j v
                        v j Fk ΔJ k −1 x , A + pk ( x )
                                        2
                                            (
                                           v j
                                                                 )
                                     ( 2
                                            (
                                           v j
                                                   ) 1j v
                               f k ΔJ k −1 x , A + pk ( x )      )
      price     1s
                1's marginal       1's i         i     b l
                                   1' price premium balances
                    value                direct revenue              15
                                   & losses due to 2's response
Numerical Comparison 1: Equal Partners

               A             C

                B            D

          Airline 1          Airline 2 (10 seats)

  Possible itineraries: A B C D AB CD AD CB
• P ibl iti        i A, B, C, D, AB, CD, AD,
                  q         g
• Airlines have equal average demand and revenue
  distributions; both see 50% of code share requests.
  Number f        t     il bl      h fli ht
• N b of seats available on each flight
                                                 16
  = 3, 6, 9, …, 18, with demand scaled appropriately.
Performance of Static Split in Revenues
                                        100%
                                        99%
                      alized Control)




                                        98%
                                        97%
                                        96%
  % of First Be (Centra




                                        95%
                                        94%                                                           18
              est




                                        93%                                                           15
                                                                                                      12
                                        92%
                                                                                                       9
                                        91%
    o




                                                                                                       6
                                        90%
                                                                                                      # seats = 3
                                        89%
                                               0.1   0.2     0.3   0.4   0.5    0.6   0.7     0.8   0.9
                                                           Fraction of Revenue to Airline 1                17
Performance of Static vs. Dynamic Schemes

                     100%
                                                               Bid Price
                                                    Bid Price Proration
   % of First Best




                     99%
                                                     Static 0.5
                                                     Static, 0 5
              B




                                                     Static, 0.4
     o




                     98%             Partner Price (Bid Price Cheating)
                                     P t     Pi         P i Ch ti )


                                                     Static, 0 3
                                                     S i 0.3

                     97%
                            3    6         9        12        15          18
                                Number of Seats on Each Flight                 18
Numerical Comparison 2: International Feeder

          A
          B
          C                  F
           D
                         Airline 2
            E
          Airline 1


• Possible itineraries: A, AF, B, BF, etc.
• Each airline receives half of all code-share requests.
• Number of seats available on first (second) leg:
  = 1 (3), 2 (6), … 6 (18)                       19
Performance of Static Split in Revenues
                     100%
                                                                                       6
                     98%                                                           5
                                                                                       4
                                                                                        3
   % of First Best




                     96%
              B




                                                                                        2

                     94%
                                                                           Scale
                                                                           factor
                     92%
                                                                            =1

                     90%
                            01
                            0.1   0.2
                                  02    0.3
                                        03     0.4
                                               04     05
                                                      0.5     06
                                                              0.6    0.7
                                                                     07      0.8
                                                                             08            0.9
                                                                                           09
                                        Fraction of Revenue to Airline 1
                                                                                                 20
Performance of Static vs. Dynamic Schemes

                                                   Bid Price
                  100%
 % of Firs Best
              t


                                                               St ti 0.6
                                                               Static, 0 6
                                                               Static, 0.5
                                                                     ,
                                                               Static, 0.4
                  99%
   o     st




                  98%
                             Partner Price

                  97%
                         1        2     3     4    5     6
                                      Scale Factor                  21
Implications

• Static scheme are more robust in larger systems
  Optimal t ti    h       f       ll
• O ti l static scheme performs well
  – we have not yet identified a scenario that ‘breaks’ the
    best static scheme
  – non-optimal static schemes may be very bad
• If partners ‘cheat’, static schemes may significantly
  outperform dynamic schemes


                                                         22
Implications, Continued

• Bid price proration sometimes is superior to the bid price
  scheme,                          issues
  scheme but has implementation issues.

           p (x) = ⎢ 1
            1jv ⎡
                                      v j
                                ΔJ x , A
                                   1
                                   k −1   (       )           ⎤
            k
                   ⎣ ΔJ k −1   (
                               v    j
                                     )    2    v j
                               x , A + ΔJ k −1 x , A  (       )
                                                              ⎥r
                                                              ⎦

                     denominator sometimes 0 or even < 0
          t bl       lt    ti
• A more stable (?) alternative:
  1j
  k
     v        1
                 ( v j
                        ) [         1    v j
                                              (          v j
 p ( x ) = ΔJ k −1 x , A + α r − ΔJ k −1 x , A − ΔJ k −1 x , A
                                                    2
                                                          )        (        )]
                                                                       23
Further Work
• Relax the full information assumption:
  In each period, each airline assumes,

  partner's future bid prices = current bid prices.

  – Is there an equilibrium?
           p                   g         y
  – Does performance suffer significantly?
  – Can current bid prices be monitored? (using business
    intelligence data companies, e.g., QL2 )

• Numerical methods to evaluate larger networks
  (necessary
  (necessar to make significant modifications to
  standard approximations).                      24
References
• "Dynamic Revenue Management in Airline Alliances," with Chris
  Wright and Harry Groenevelt, working paper,
     p                          p g         y              y   _ _           p
  http://mba.tuck.dartmouth.edu/pages/faculty/robert.shumsky/RM_in_Alliances.pdf

• "The Southwest Effect, Airline Alliances and Revenue Management,"
           f                    g      g      ,     ,
  Journal of Revenue and Pricing Management, vol. 5, no. 1.

• Boyd, A. E. 1998. Airline Alliance Revenue Management. PROS
                                Report               Management
  Strategic Solutions Technical Report, PROS Revenue Management,
  3100 Main Street, Suite #900, Houston, TX 77002.

• Talluri, K. and G. van Ryzin, “An Analysis of Bid-Price Controls for
  Network Revenue Management”, Management Science, 44 (11),
                   1577-1593.
  November 1998, 1577 1593.
                                                                         25

								
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