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AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
An Analysis of Resource Rationing Methods for
Collaborative Decision Making
Michael Ball and Thomas VossenR.H. Smith School of Business & Institute for Systems Research
University of Maryland&
Robert HoffmanMetron Aviation
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Ground Delay Programs
delayed departures
delayed departures
delayed departures
delayed arrivals/no airborne holding
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
GDPs under CDM
Resource Allocation Process:• FAA: initial “fair” slot allocation
[Ration-by-schedule]• Airlines: flight-slot assignments/reassignments
[Cancellations and substitutions]• FAA: periodic reallocation to maximize slot utilization
[Compression]Note:- reduced capacity is partitioned into sequence of arrival slots- ground delays are derived from delays in arrival time
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Allocating Slots under CDMRation-By-Schedule:
Step 1: Order flights by theiroriginal scheduled time of arrival
Step 2: Select the first flight that has not been assigned an arrival slot.– assign the selected flight to the earliest unassigned slot– repeat step 2.
The resulting allocation is independent of current status of flights and is not affected by status information given by airlines!!
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Slot Reallocation under CDMNeed for Inter-airline slot exchange:
slots made available through flight cancellations and delays
Compression Algorithm
InitialAAL1:1200 S1200AAL2:1201 S1202 CNXUAL1:1202 S1204USA1:1203 S1206UAL2:1204 S1208COA1:1205 S1210USA2:1206 S1212AAL3:1207 S1214
FinalAAL1:1200 S1200AAL2:1201 S1202UAL1:1202 S1204USA1:1203 S1206UAL2:1204 S1208COA1:1205 S1210USA2:1206 S1212AAL3:1207 S1214
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTORGeneralizations and Extensions of CDM Procedures
• View RBS as Process for Achieving Equitable Allocation of Time Slots – extend to insure better equity during dynamic GDP operation
• Extension of RBS to Enroute Airspace: Priority based on accrued delay
• Interpret Compression as slot trading process: extend from 1-for-1 trades to 2-for-2 trades
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR#1. GDPs as Balanced Just-in-Time Scheduling Problem
flts nb
Xb
na
time
• Airlines = products, flights = product quantities• Minimize deviation between “ideal” rate and actual production
“ideal”production rate
Cumulative production
Possible deviation measures
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
GDP Situationflts
na
Xa
“Release times” defined by scheduled arrivals
slots
Questions:• What are appropriate “production rates” ?• How to minimize deviations ?• Managing program dynamics
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTORWhat is an appropriate production
rate/ideal allocation??
Answer: RBS!!It can be shown that RBS lexicographically minimizes the maximum
delay assigned to each flight. General Principles of equity applied to a set of claimants; equity defined
relative to pair-wise comparisons: in an equitable solution it should not be possible to improve the
allocation to a claimant at performance level p without moving another claimant to a performance level of p or worse.
For the mini-max (RBS) solution:if flight f has been assigned t* units of delay, it is impossible to
reduce the delay assigned to f without increasing the delay assigned to another flight a value of t* or higher.
It can be shown that RBS satisfies some very fundamental axioms for consistent, fair allocation process (there are other alternatives that we are now investigating)
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTORModels and Algorithms for Minimizing Deviation
from Ideal Allocation
• General class of problems: minimize deviation between actual slot allocation and ideal slot allocationVariants based on:– Objective function (deviation measures)– Constraints on feasible allocations
• Minimize cumulative/maximum deviation: – complex network flow model (based on JIT scheduling models)
can solve most variants• Minimize sum of deviations between jth slot allocated to
airline a and ideal location for airline a’s jth slot:– Assignment model– Greedy algorithm for several cases
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
GDPs and Flight Exemptions• GDPs are applied to an “included set” of flights• Two significant classes of flights destined for the
airport during the GDP time period are exempted:– Flights in the air– Flights originating at airports greater than a certain
distance away from the GDP airport
• Question: Do exemptions induce a systematic bias in the relative treatment of airlines during a GDP??
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Deviation RBS (standard) vs RBS (+exemptions), Boston
-40-30-20-10010203040
1/6/01
1/13/0
1
1/20/0
1
1/27/0
1
2/3/01
2/10/0
1
2/17/0
1
2/24/0
1
3/3/01
3/10/0
1
3/17/0
1
3/24/0
1
3/31/0
1
4/7/01
4/14/0
1
4/21/0
1
GDPs
Min
utes
/Flig
ht
TWA CJC COA UAL UCA DAL USA AAL
Analysis of Flight Exemptions (Logan Airport)
Flight exemptions introduce systematic biases:• USA (11m/flt), UCA (18m/flt) “lose” under exemptions
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Reducing Exemption Bias
Objective :• Use deviation model to mitigate exemption bias
– i.e. “inverse” compressionApproach:• RBS applied to all flights whose arrival times fall within
GDP time window ideal allocation• Set of exempted flights are defined as before (there are good
reasons they are exempted)• Time slots given to exempted flights “count against”
allocation• Delays allocated to non-exempted flights so as to minimize
overall deviation from ideal allocation
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Flight Exemptions
• Minimize deviations using optimization model that incorporates exemptions
• reduces systematic biases, e.g. USA from 11m/flt to 2m/flt, UCA from 18m/flt to 5m/flt
-40
-30
-20
-10
0
10
20
30
40
1/6/01
1/13/0
1
1/20/0
1
1/27/0
1
2/3/01
2/10/0
1
2/17/0
1
2/24/0
1
3/3/01
3/10/0
1
3/17/0
1
3/24/0
1
3/31/0
1
4/7/01
4/14/0
1
4/21/0
1
TWA CJC COA UAL UCA DAL USA AAL
-40
-30
-20
-10
0
10
20
30
40
1/6/01
1/13/0
1
1/20/0
1
1/27/0
1
2/3/01
2/10/0
1
2/17/0
1
2/24/0
1
3/3/01
3/10/0
1
3/17/0
1
3/24/0
1
3/31/0
1
4/7/01
4/14/0
1
4/21/0
1
TWA CJC COA UAL UCA DAL USA AAL
Deviation RBS ideal-RBS actual Deviation RBS ideal-Opt. model
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
DiscussionApproach yields system where:• airlines are assigned priority lists
– based on sched. arr. times, constant during GDP• dynamic changes (capacity, airline data) initiate (re)rationing
– ration according to airline priorities (compression)• priority scheme cannot (completely) be maintained with
flight exemptions– deviation model shows potential to reduce exemption bias
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR#2. Extension of RBS to Enroute Airspace:
Priority Based on Accrued Delay
Priority given to flight with largest accrued delay;accrued delay (downstream) defined as difference between ETA and scheduled arrival time.
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Scenario
Flow Constrained Area (FCA)
Targeted Region (NY area)
???
Scenario: flights in air and on the ground; need to reroute flights around flow constrained area:Which flights are rerouted?? Which flights are delayed on ground??
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Impact on Allocated Delay
Motivation for Priority Based on Accrued Delay:
• Generalization of RBS – equivalent relative to equity principles
• Implicitly coordinates multiple initiatives since previously delayed flights are given priority.
1st come/1st served
Priority Based on Accrued Delay
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Implementation Alternatives
F-BasedStep 1: For each unassigned flight,
calculate its total accrued delay assuming it is assigned to the earliest available slot for which it is eligible.
Step 2: Choose the flight with the maximum accrued delay that has not been assigned to a slot.– assign the selected flight to the
earliest unassigned slot for which it is eligible
– if there are remaining unassigned flights, go to step 1; otherwise stop
S-BasedStep 1: Choose the earliest available slot,
s.Step 2:Find the set of flights, F, that can be assigned
to s.For each flight in F, calculate the total
accrued delay assuming the flight is assigned to s.
Choose the flight in F with the maximum calculated accrued delay and assign it to s.
If there are remaining unassigned flights go to step 1; otherwise stop.
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTORF-Based vs S-Based: The Leap Frog Principle
F-Based:• Utilization = 100%• Avg. delay = 30 min• Avg. of top 20% = 103
min• Std. Dev. = 43 min.
S-Based:• Utilization = 100%• Avg. total delay = 30
min• Avg. of top 20% = 50
min• Std. Dev = 14 min.
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
#3. Compression vs Trading
RBS allocates slots to airlines during a GDPCompression provides a mechanism whereby
an airline gives up a slot it cannot use and get one (from another airline) that it can use …
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTORAn Alternate View of Compression:
Inter-Airline Bartering
Mediator:FAA
AALAAL
DALDAL
UALUAL
NWANWASWASWA
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Mediated Slot Exchange
• Offer:– slot_O: slot willing to give up– slot_A1,…, slot_An: slots willing to accept in
return• Each airline submits a set of offers• Mediator determines set of offers to accept
and for each accepted offer, the returned slot
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Default Offers
earliest timeof arrival
slot_O
slot_A1
slot_An
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOROffer Associated with Canceled or Delayed Flights
time slot fromcanceled flight
occupiedtime slot
occupiedtime slot
earliest time ofarrival for earliest available flight
slot_O
slot_An
slot_A1
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
1-for-1 trades to 2-for-2 trades• Compression ⇔ 1-for-1 trading system, i.e. offers involve
giving up one slot and getting one in return (many offers processed simultaneously)
• What about k-for-k or k-for-n offers, e.g. 2-for-2:
Trade??
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Initial Results• Compression Benefits
– performance improvement if compression executed after flts with excessive delay (>2hrs) are canceled
Compression Improvement
0
5
10
15
20
25
30
35
40
bos01-0
6-01
bos01-1
5-01
bos01-1
9-01
bos01-3
0-01
bos02-0
8-01
bos02-1
4-01
bos02-2
1-01
bos02-2
6-01
bos03-1
0-01
bos03-1
3-01
bos03-2
1-01
bos03-2
3-01
bos03-3
0-01
bos04-0
8-01
bos04-1
8-01
GDP
% im
prov
emen
t
Global Max.Compression
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Initial Results• 2-for-2 Trading Model:
– proposed offers: all at-least, at-most pairs that improve on-time performance
Trading Improvement
0
5
10
15
20
25
30
35
40
bos01-06-01bos01-15-01bos01-19-01bos01-30-01bos02-08-01bos02-14-01bos02-21-01bos02-26-01bos03-10-01bos03-13-01bos03-21-01bos03-23-01bos03-30-01bos04-08-01bos04-18-01
GDP
%Im
prov
emen
t
Global MaxTrading Model
ComputationalEfficiency:• 13sec avg.• 67% solved by
LP relaxation
AVIATION OPERATIONS RESEARCH
NATIONAL CENTER OF EXCELLENCE FOR
NEXTOR
Generic View of CDM GDP Procedures
• Equitable allocation among airlines• Intra-airline maximization of economic
efficiency• Inter-airline resource exchange