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Year over Year Schedule Match Up using LP by broverya86

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									Year over Year Schedule
  Match Up using LP
 Judy Pastor, Continental Airlines
       AGIFORS YM 2001
       Bangkok, Thailand
              Schedule Changes
• One thing is constant in an airline
   – CHANGE (of Schedule)
      •   Departure/arrival times
      •   Frequency
      •   Equipment – Jet/Express
      •   Connecting bank structure
      •   Flight number changes to reflect new throughs
      •   Seasonal flying
• Good forecasts are necessary for RM
• Appropriate flight history is crucial for good
  demand forecasts
              RM Systems
• RM Systems must be able to construct flight
  history from past schedules for future flight
  forecasts
• Heuristics (good guesses) have been
  implemented in RM systems with varying
  degrees of success
• Most based on time banding – some
  primitive methods based on Departure Hour
             Time Banding
• Example – AAABBB – 1 Flight/Day
  – Future schedule shows Flight 123 in market
    AAABBB departing at 0935 on Mondays
  – Past schedule has Flight 999 in market
    AAABBB departing at 0830 on Mondays
  – If the TB parameter for the heuristic is two
    hours, then Flight 999 is in same time band as
    Flight 123
  – If the TB parameter is one hour, then Flight 999
    is in a new time band
            Time Banding
• Heuristics seem to break down when overall
  structure of a market changes
• In new markets, frequencies may increase if
  successful entry or decrease if not
• In low frequency markets especially,
  departure times may shift dramatically
  – 0600 and 1900 departures to 1100 and 1900
    (change may be made to accommodate
    connections)
             Time Banding
• Time Bands can also “drift” over time
• Static Time Band parameters can also be
  squeezed out over many schedule changes
• More robust way to doing the match up is
  needed
• One solution:
  – use the OR practitioners favorite tool:
     • The Linear Program (LP)
 The Transportation Problem
• Well known problem in OR
• Traditional TP concerned with
  – distribution of goods from several sources
    (supply points) to several destinations (demand
    points)
  – above done at minimum total cost
• All goods must be distributed and all
  demands must be satisfied
• “Dummy Nodes” for possible imbalances
              Abstraction
• Use the TP to solve the distribution problem
  of flights from one schedule to flights in
  another schedule
• Objective function is to minimize total
  absolute time difference between flights in
  schedule 1 (supply points) to flights in
  schedule 2 (demand points)
• Dummy nodes used to treat changes in
  frequency from one schedule to another
          Model Formulation
• Parameters
  – aaabbb     market for flights
  –m           # flights in aaabbb for Schedule 1
  –n           # flights in aaabbb for Schedule 2
• Data
  – cmn        absdif(depttime) between flight m
               and flight n
  –M           big penalty number to encourage
               flight matching
          Model Formulation
• Decision Variables
  – Xmn    =1, flight m from Schedule 1 matches
           with flight n from Schedule 2
  – Ym     =1 flight m from Schedule 1 is
           unmatched
  – Yn     =1 flight n from Schedule 2 is
           unmatched
        Model Formulation
• Objective Function
  – Minimize SUM(m)SUM(n) (cmn * Xmn) +
    SUM(m) (M * Ym) + SUM(n) (M * Yn )
• Minimize the absolute difference between
  matched flights and penalties for unmatched
  flights
        Model Formulation
• Constraints
  – Each flight in both schedules must be either
    matched or unmatched
  – Each flight can be matched to at most one other
    flight
  – Correct frequencies in Schedules 1 and 2 must
    be preserved
  – Decision Variables X and Y must be binary (0
    or 1)
           Model Solution
• Currently implemented to be solved as an
  LP
• Could be done more efficiently as a
  transportation problem but requires some
  programming
• Entire schedule (all markets) done as one
  big LP though it really consists of many
  stand alone sub-models
                      Some Results
OandD    Flt   Dept Flt     Dept
====== ==== ==== ==== ====
DFWIAH 700      600   700   600
DFWIAH 1953     700   702   700
DFWIAH 708 1005 706 900
DFWIAH 710 1125       710 1120
DFWIAH    34 1340     712 1247
DFWIAH 716 1525 716 1540
DFWIAH 718 1704       718 1745
DFWIAH 720 1840
                      Some Results
OandD Flt     Dept Flt      Dept
====== ==== ==== ==== ====
EWRSFO 151 740        147    730
EWRSFO 155 915        161    920
EWRSFO 153 1100       149 1045
EWRSFO                114 1410
EWRSFO      37 1540   157 1600
EWRSFO 157 1715       119 1800
EWRSFO 159 1955       159 1945
                   Some Results
OandD Flt   Dept Flt    Dept
====== ==== ==== ==== ====
IAHCLL 3462 755
IAHCLL 3098 1045 3518    935
IAHCLL 3524 1310
IAHCLL 3466 1530 3466 1440
IAHCLL 3460 1900 3351 1815
                       Some Results
OandD    Flt    Dept Flt     Dept
====== ==== ==== ==== ====
IAHDEN    378    700   378    805
IAHDEN    587    923   291    927
IAHDEN    755 1200 1511 1109
IAHDEN 1051 1422       799 1320
IAHDEN     35 1530 1707 1430
IAHDEN    626 1725 1855 1750
IAHDEN 1441 2026 1728 2012
       Future Enhancements
• Change from AbsDif function in Obj to
  AbsDif**2
• Match up of multiple schedules
• Addition of OA schedules – past and
  present
• Connecting opportunity match up
• Fuzzy logic/Sensitivity Analysis to
  determine historical quality of information

								
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