Inter-modal Substitution (IMS) in Airline
Collaborative Decision Making
Yu Zhang
UC Berkeley
NEXTOR Seminar
Jan. 20, 2006
FAA, Washington D.C.
1
Road Map
• Introduction
– Delay In National Airspace System (NAS)
– Idea of Inter-modal Substitution (IMS)
• Objectives
• Inter-modal Traffic Assignment Model
• Jointly Optimization of Air and Surface
Transportation
• Future Work
2
Introduction — Delay in NAS
• Adverse weather and other transient events
• Serious problem at hub airports
– Passenger misconnections
– Delay propagation
• Substantial number of short-haul flights
3
Introduction — Procedure of CDM
ATCSCC, Facilities and
AOCs Evaluate Demand
vs. Capacity
AOC Smart
Cancellation
Problem
Proposed GDP Advisory
AOC Response
(Cancellations)
Yes
Is the GDP
still required?
Issue GDP
(RBS)
AOC Response
(Substitution and
Cancellations)
Compression
No
End
Exit loop when
program expires
or is cancelled
Slot Credit
Substitution
Based on Metron 2004
4
Idea
Substitute short-haul flights
with surface transport when
capacity temporarily drops at
hub airports
Inter-modal Substitution (IMS)
5
Objectives
• Access the potential benefits of implementing
this inter-modal substitution (IMS) system.
• Develop methodology for making optimal
inter-modal substitution and flight cancellation
decision.
• Explore the compatibility into Collaborative
Decision Making (CDM)
6
Inter-modal Traffic Assignment Model —
Network
Bottleneck: hub airport
with capacity constraints
7
Problem Definition
• In the case of transient capacity
drop, choose appropriate
transportation modes in order to
minimize (maximize) airline’s
objective
Inter-modal Traffic Assignment Model
8
Continuous Delay Approximation
∑
{
f ∈ Φ∩|Ξ f <tk
}
x f = Dk
⎧ D − C I TI
⎫
+ TI − t k ⎬
wk = max ⎨0, k
CV
⎩
⎭
Cumulative
Number of
Flights
tlb
t,l
l
a ⎧ Dk
⎫
Dk − CI TI
t
,
w
wk =lmin⎨k − tk ,
+ TI − tk ⎬
⎩ CI
TI
CV
⎭
Time of day
Inter-modal Traffic Assignment Model
9
Constraints
S.t.
⎫
⎧D
D − CI TI
wk = min⎨ k − tk , k
+ TI − tk ⎬ ∀tk ≤ TI
CV
⎭
⎩ CI
⎫
⎧ Dk − CI TI
wk = max⎨0,
+ TI − tk ⎬ ∀tk > TI
CV
⎭
⎩
∑ x f = Dk
{
f ∈ Φ∩|Ξ f <tk
}
CI
Reduced capacity
CV
Full capacity
TI
Length of reduced capacity
tk
k th discrete time period
Dk
Cumulative number of
flights at time period k
xf
Decision Variables, equal to
1 if flight f is not cancelled, 0
otherwise
Inter-modal Traffic Assignment Model
10
Objective Function
[
]
K
Minimize∑ x t + β × (1− x f )t paxf + ∑
f ∈Φ
a
f f
b
f
{
∑
Decision Variables, equal to 1 if flight f is not
cancelled, 0 otherwise
t af
Flying time for flight f
t bf
Surface transportation time for flight f
pax f
}
k =0 f ∈ f |Ξ f ∈[t( k −1) ,tk ]
xf
wk
δ × wk paxf
Queuing delay for discrete time period k
Passenger number on flight f
β
Weight of surface transportation time
δ
Weight of delay time
Inter-modal Traffic Assignment Model
11
Numerical Example
• Data
–
–
–
–
–
40 flights in 3 hours
Region: 110 miles to 2000 miles
Dropped capacity: 10 flights per hour
Regular capacity: 30 flights per hour
Duration of capacity dropping: 1.5 hours
• Solution Methods
– AMPL: Branch and Bound
– C: Enumeration
Inter-modal Traffic Assignment Model
12
Numerical Example Results
Cumulative Number of Arrivals
45
Original Schedule
Adjusted Schedule
40
Passenger Time
Without
IMS
35
30
Scheduled
25 Flight
time 20
Delay 15
Benefit
0.5
With
IMS
10777
70
66
1872
1003
7
4
761
0
0
Without
IMS
11045
Surface10Transport
Time 5
Total
With
IMS
Flight Time
1
11
12917
12542
2
2.5
3
Time of day (Hour)
-375 (pax.hr)
1.5
Inter-modal Traffic Assignment Model
13
Alternative Objective Functions
• Varied weights or monetary coefficients for
different time: flying time, surface
transportation time, and delay time
• Including estimated passenger delay time
with reassignment
• Considering airlines’ operating costs
• Etc.
Inter-modal Traffic Assignment Model
14
Jointly Optimization of Air and Surface
Transportation
Space
B1
f1
B2
f2
f3
Time
Spoke A
Hub Airport
Spoke B
15
Source node O
i=1
u1
Transporting
passengers
Leg1
j=1
v1
Leg2
Waiting at the
terminal
Dead-heading to
another airport or
central airport
Time
A
B
C
C
Hub
Airport
B
A
Sink node M
16
Questions Answered
• How many flights will be cancelled, and
which one should be cancelled?
• How many vehicles (charter buses) are
needed?
• How to dispatch those vehicles?
• What is the passenger delay?
• What is the flight delay?
• What is the other objective that airlines
interested in?
17
Smart Cancellation— Complete Version
Capacity Forecast
Individual Flight
Cancellation Cost
Bank Structure
Arrival and Departure
Network Cancellation
Cost
Aircraft Balance
Smart Cancellation
Bus Transportation
Time Estimation
Delay Cost Estimation
Flight and Passenger
Passenger Itinerary
Recovery
Terminal Facility
Availability
Bus Operational Cost
18
Future Work
• Extension of Inter-modal Traffic
Assignment Model
• Formulation and numerical examples of
Joint optimization of air and surface
transportation
• Capacity Uncertainty
• Integration of Different Modes
• Cooperation among Airlines
19
Thank you!
20