Incorporating Weather
Uncertainty in Airport Arrival
Rate Decisions
FAA-NEXTOR-INFORMS
Conference on Air Traffic Management and Control
Joyce W. Yen
Zelda B. Zabinsky
Catherine A. Serve’
University of Washington
Industrial Engineering ATM
Group
5 June 2003
Objective


Investigate the trade-off between ground
delay and air delay given uncertainties in
the weather prediction
To examine, “How do inaccuracies in
weather forecasts affect flow decisions?”
University of Washington
Industrial Engineering ATM Group
Agenda





Air Traffic Background
Stochastic Optimization Formulation
Sample Test Case
Sensitivity Analysis on Weather Forecast
Accuracy
Next Steps
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Industrial Engineering ATM Group
Flow Control Decisions


A collaborative decision is made between
Air Traffic Control (ATC), the Airline
Operational Control (AOC), and affected
centers
Decisions result in some form of ground
delay or air delay


Ground holding (delay on ground)
Miles-in-Trial (delay in air)
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Industrial Engineering ATM Group
Decision Representation

Single airport with multiple arrivals
Flights
1
2
Queue
Airport
N-1
N
Queuing Phenomenon

How to make delay decisions to minimize total
delay or cost of delay?
University of Washington
Industrial Engineering ATM Group
Agenda





Air Traffic Background
Stochastic Optimization Formulation
Sample Test Case
Sensitivity Analysis on Weather Forecast
Accuracy
Next Steps
University of Washington
Industrial Engineering ATM Group
Stochastic Optimization
Formulation - Assumptions



Due to weather uncertainty, there is a probabilistic
reduction of capacity, airport acceptance rate
(AAR)
Modeled decisions as a stochastic optimization
problem
Model Assumptions



Single airport
Flights aggregated by scheduled arrival
Previous work



Octavio Richetta and Amedeo Odoni (1993,1994)
Min E[Cost of ground delay] + E[Cost of air delay]
Dynamic formulation
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Industrial Engineering ATM Group
Stochastic Optimization
Formulation - Utility Function

New objective function included utility of flight
as function of total delay Utility of a Flight as a function of Total Delay
2
t

Utility 
2*0.59
e
Utility 
e
t in hours
100 %
2
t

10 *0.022
t in minutes
Utility of
Flight
50 %
2 hours
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Industrial Engineering ATM Group
Delay Time of Flight
Stochastic Optimization
Formulation - Utility Function




In addition to cost of ground delay and air
delay, the value of the system should include
the utility of the flights based on their total delay
This new objective would be a utilitarian point of
view; good for both ATC and AOC
Max (Utility - Cost)
Delay Costs



Air delay cost = Ground delay cost
Air delay cost = 2* Ground delay cost
Air delay cost = 5* Ground delay cost
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Industrial Engineering ATM Group
Deterministic Mathematical
Formulation
T
max
T 1 T 1
 
i 1 j i k  j
ijk
[ U (k  i )  C a (k  j )  C g ( j  i ) ]


 
 


Utilityof a flight
Air delay cost
Ground delay cost
subject to
T 1
X
j i
 Ni
ij
k
k
S k   Ωijk  M k
i 1 j i
T 1
i  1, ,T
Every plane is reschedule d.
The number of planes landing
k  1, ,T  1 is less than or equal to the
capacity.
X ij   Ωijk
i  1, ,T
i  j  T 1
Every plane lands.
X ij , S k , Ωijk  0
i  1, ,T
i  j  T 1
j  k  T 1
The number of planes reschedule d
and actually landing is positive.
k j
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Industrial Engineering ATM Group
Expansion into Stochastic
Formulation
 T T 1 T 1

pq  qijk[U (k  i)  Ca (k  j )  Cg ( j  i)]

q 1
 i 1 j i k  j

Q
max
Coupling Constraint s :
X 1ij  X 2ij    X Qij ; i  1,, T ; i  j  T  1
Network
component
for q=1
Network
component
for q=2
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Industrial Engineering ATM Group

Network
component
for q=Q
Stochastic Optimization
Formulation
 T T 1 T 1



k  i )  C a (k  j )  C g ( j  i ) ]
 pq    qijk [ U(






q 1
 i 1 j i k  j
Utility of a Flight Air DelayCost Ground DelayCost 


Q
max

Two sets of decision variables determine rescheduled
number of arrivals (RNA) for each time period
ο



First stage decisions (Xij) reschedule the arrival time of flights from
i to j
Recourse decisions ( ijk ) assign actual arrival time k (which may
differ from the original arrival time i or rescheduled arrival time j)
Probability of scenario q, (pq ) weather uncertainty
University of Washington
Industrial Engineering ATM Group
Agenda





Air Traffic Background
Stochastic Optimization Formulation
Sample Test Case
Sensitivity Analysis on Weather Forecast
Accuracy
Next Steps
University of Washington
Industrial Engineering ATM Group
Experimental Design Demand Vector
Sixteen time period model - 15 min intervals
Number of Flights Per 15 Minute Interval - Boston Logan Airport
Based On
Official Airline
Guide
50
45
40
Number of Flights

Boston Logan
Airport Arrival
Data
35
30
25
Demand for
Monday 8AM
to 12PM
20
15
10
5
0
1
2
3
4
5
6
7
8
9
15 Min Interval
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Industrial Engineering ATM Group
10
11
12
13
14
15
16
Experimental Design –
Scenario Setup


Forecast gives capacity for each time period
Five capacity cases (each with three possible
forecasts) created to represent various weather
conditions







Fair Weather
Late Storm
Intense Storm
Mid-time Storm
Unpredictable Weather
Four probability cases represent different
distributions of capacity forecasts
Twenty scenarios
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Industrial Engineering ATM Group
Experimental Design Probability Cases
Each capacity case has three possible forecasts
Probability Distributions
0.6
0.5
Probabilty

0.4
0.3
0.2
0.1
0
Forecast 1 (F1)
Forecast 2 (F2)
Probability Case 1
Probability Case 3
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Industrial Engineering ATM Group
Forecast 3 (F3)
Probability Case 2
Probability Case 4
Model Run Results –
Makeup of Total Delay
Total Delay Makeup for All Capacity Cases
& Cost Cases
Total Expected Delay
350.00
300.00
250.00
200.00
150.00
100.00
50.00
0.00
1X 2X 5X
Fair
Ave Ground
Ave Air
1X 2X 5X
1X 2X 5X
Late Storm
Intense Storm
One Unit of Delay = 15 min
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1X 2X 5X
1X 2X 5X
Mid Storm
Unpredictable
Model Run Results –
Time & Length of Delays

As cost of air delay increases see more flights
rescheduled in later time periods
Rescheduled # of Flights Per Time Period (j)
50
45
40
35
 Xij 30
i
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Time Period (j)
Cost 1X
Cost 2X
Cost 5X
demand
Averaged over all weather cases
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Industrial Engineering ATM Group
14
15
16
17
Model Run Results –
Summary of Insights

Decisions sensitive to value of total delay and
relative costs of air delay and ground delay
If only minimize cost of air and ground (and ignore
total delay), assign more ground delay and not value
opportunity to take advantage of clearing weather



When air delay cost > ground delay cost,
schedules more ground delay
Unpredictable & Late Storm scheduling longer
delays
As relative cost of air delay increases see more
flights rescheduled in later time periods
University of Washington
Industrial Engineering ATM Group
Agenda





Air Traffic Background
Stochastic Optimization Formulation
Sample Test Case
Sensitivity Analysis on Weather Forecast
Accuracy
Next Steps
University of Washington
Industrial Engineering ATM Group
Sensitivity Analysis - Objective


Currently attempting to understand effects of
weather forecast accuracy on model
Constructed three new capacity cases each
again with three possible forecasts



Late Storm
Early Storm
Intense Storm
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Industrial Engineering ATM Group
Sensitivity Analysis - Objective


Created five probability profiles to reflect
varying inaccuracies of forecasts each with
three probability cases (distributions for
forecasts)
Examining changes in scheduling decisions
as confidence in timing of storm varies
University of Washington
Industrial Engineering ATM Group
Sensitivity Analysis Experimental Setup
Late Capacity Forecasts
Early Capacity Forecasts
35
30
25
20
15
10
5
0
50
40
30
20
Demand
AAR
Created capacity cases
representing a early, late, and
intense storm

10
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
50
F1
F2
F3
demand
40
20
Intense Capacity Forecasts
10
0
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
AAR
1
Tim e Period
F1
F2
F3
Demand
35
30
25
20
15
10
5
0
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Tim e Period
F1
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Industrial Engineering ATM Group
F2
F3
demand
Demand
30
Demand
AAR
Tim e Period
35
30
25
20
15
10
5
0
Sensitivity Analysis Experimental Setup
Probability Profile 2 (40% Spread)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Probability
Probability
Probability Profile 1 (30% Spread)
F1
F2
F3
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
F1
Probabilty Case 1
Probability Case 2
Probabilty Case 1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Probabilty Case 1
F2
Probability Case 2
Probability Case 2
F3
Probability Case 3
Probability Profile 4 (70% Spread)
Probability
Probability
Probability Profile 3 (55% Spread)
F1
F2
Probability Case 3
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
F3
F1
Probability Case 3
Probabilty Case 1
F2
Probability Case 2
F3
Probability Case 3
Created 5 probability profiles each
reflecting a different % inaccuracy
in forecast
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Industrial Engineering ATM Group
Probability
Probability Profile 5 (80% Spread)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
F1
Probabilty Case 1
F2
Probability Case 2
F3
Probability Case 3
Sensitivity Analysis - Results
Total Delay Make-up
Early Capacity Profiles
30
700
25
40
20
30
15
600
10
20
10
5
0
500
Total Delay by Probability Profile - Early Storm
Demand
50
AAR
35
0
1
2
3
4
5
6
7
8
9
10
11 12 13 14
15 16
Time Period
F1
F2
F1 .5
F2 .3
F3 .2
F1 .2
F2 .5
F3 .3
F3
Demand
400
300
F1 .3
F2 .2
F3 .5
200
100
0
Ground Delay
Air Delay
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P1
Profile
1x
2x
5x
Sensitivity Analysis - Results
Total Delay Make-up
Total Delay by Probability Profile - Early Storm
Early Capacity Profiles
35
50
30
AAR
25
20
30
15
20
10
600
Demand
40
700
10
5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Time Period
500
400
F1
F2
F1 .5
F2 .3
F3 .2
F3
Demand
F1 .6
F2 .2
F3 .2
F1 .75
F2 .2
F3 .05
F1 .65
F2 .25
F3 .10
F1 .85
F2 .10
F3 .05
300
200
100
0
P1
Ground Delay
P2
Air Delay
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P3
P4
Profile
P5
Sensitivity Analysis - Results
Total Delay Make-up
Late Capacity Profiles
35
30
25
700
20
15
10
5
600
0
Total Delay by Probability Profile - Late Storm
50
AAR
30
20
Demand
40
10
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Time Period
F1
500
400
F2
F3
demand
F1 .5
F2 .3
F3 .2
F1 .6
F2 .2
F3 .2
F1 .65
F2 .25
F3 .10
F1 .75
F2 .2
F3 .05
F1 .85
F2 .10
F3 .05
300
200
100
Ground
Air Delay
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Profile
P
5
P
4
P
3
P
2
P
1
0
Sensitivity Analysis - Results
Total Delay Make-up
50
20
30
15
10
5
20
Total Delay by Probability Profile - Intense Storm
40
Demand
AAR
Intense Capacity Profiles
35
30
25
10
0
800
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Time Period
F1
F2
F3
F1 .65
F2 .25
F3 .10
demand
700
600
F1 .5
F2 .3
F3 .2
F1 .6
F2 .2
F3 .2
F1 .75
F2 .2
F3 .05
F1 .85
F2 .10
F3 .05
500
400
300
200
100
Ground Delay
Air Delay
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Industrial Engineering ATM Group
Profile
P
5
P
4
P
3
P
2
P
1
0
Sensitivity Analysis - Results
Timing Of Rescheduling
Decision variables Xij indicate when
flights are being rescheduled
Early Storm Profile 3 Cost 1x & Cost 2x
# of Rescheduled Flights
(Xj)

50
45
40
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Tim e Period
demand
F1 cost1 x
F2 cost 1x
F1 cost 2x
F2 cost 2x
F3 coxt 2x
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Industrial Engineering ATM Group
F3 cost 1x
Sensitivity Analysis Summary of Insights



When cost of air delay is same as cost
of ground delay see insensitive ground
delay decisions
More ground delay is taken as cost of
air increases
As the forecast certainty increases
better able to assign proper amount
ground delay
University of Washington
Industrial Engineering ATM Group
Next Steps


More examination of demand effects
especially when relative cost of air is
greater than 5x ground
Investigate possible application to
particular real weather scenarios, such
as morning fog effects in San
Francisco
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Industrial Engineering ATM Group
Questions
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Industrial Engineering ATM Group
Contact Information
Joyce W. Yen
joyceyen@u.washington.edu
206-543-4605
Zelda B. Zabinsky
zelda@u.washington.edu
206-543-4607
University of Washington
Industrial Engineering ATM Group