Robust Schedule Planning and Recovery The Role of Operations

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```					Robust Schedule Planning and
Recovery:
The Role of Operations Research

Dr. Amy Cohn, University of Michigan

MIT Airline Industry Consortium
Executive Eductation Course
June 20 – 22, 2007

1
Key Questions
 What is “operations research”?
 How can it be used to improve the
operational performance of an airline
plan?
 What is the state-of-the-art in new
research, and what problems still need to
be solved?

2
What is operations research?
   Using mathematics to improve decision
making
 Problems  involving planning, scheduling,
sequencing, and organizing
 Looking at complex interactions between
decisions
 Making trade-offs in a systematic way

3
Example: Diet Problem
 Decisions: For each food choice, how
much should I eat?
 Rules: Limits on calories, fat, protein, folic
acid, etc.
 Goal: Minimize cost

4
What is math programming?
 A set of finite, concrete decisions
 A set of rules that these decisions have to
obey and which link them together
 A means for evaluating a solution
 Modeling
 Algorithms

5
Example: Fleet Assignment
   For each flight, what fleet type to assign?
A   set of finite, concrete, decisions
   Every flight has to have one fleet type; can’t use
more planes that you have
A set of rules that these decisions have to obey and
   Maximize expected revenue minus operating
cost
A   means for evaluating a solution

6
Why math programming?
 Given 1000 flights and 5 fleet types…
 … there are 9 x 10700 combinations!
 There are about 4 x 1080 atoms in the
universe
   Math programming provides us with the
tools to find the best combination of
decisions without actually looking at all of
them…

7
OR and Airline Planning
   OR (and math programming) have been
used for several decades to help the
airlines build better plans
 Sparked   major advances in underlying theory
   These are ideal visions of what should
happen in operations
 Assume flight departure, travel times are
known and fixed

8
Present and Future
   How are airline plans built today?
 Deterministic
 Dis-aggregated
 Focused   on planning metrics
   How should they be built in the future?
 Stochastic
 Integrated
 Focused   on operational performance metrics

9
Airline Planning Process
Schedule
Design

Fleet
Assignment

Maintenance
Routing

Crew
Scheduling
10
Fleet Assignment
 For each flight, pick a fleet type
 Satisfy:
 Cover constraints
 Balance constraints
 Count constraints

   Maximize expected revenue minus
operating cost

11
Fleet Assignment
   Key challenges:
 Estimating  revenue
 Taking into account multi-leg passenger
itineraries

12
Maintenance Routing

 For each flight assign a tail number
 Need to create cycles
 Every tail flies every flight?
 No clear objective function
 Plan changes frequently – more a
validation than a plan
13
Crew Scheduling

 For each flight assign a crew (cockpit,
cabin)
 Need to respect lots of complex FAA and
labor restrictions
 Minimize cost
 Broken down into two phases
 Crew pairing
 Crew rostering
14
Crew Scheduling

   Key challenges:
 Non-linear cost function
 Very large number (trillions) of feasible
pairings

15
Schedule Design

 Decide markets, frequency, time table
 Precedes (and drives) all other planning
decisions
 Lots of qualitative decisions
 Feasibility difficulty to establish

16
Planning Decisions…

 Lots of combinatorial options
 Complex feasibility rules and interactions
 Perfect for math programming!

17
The Good News
“Without revenue management
and schedule planning decision
tools, American Airlines would
have been profitable only one year
in the 1990’s…”
- Tom Cook

Source: T. Cook. 2000. “Creating competitive advantage using model-driven support
systems”. MIT Global Airline Industry. Study Distinguished Speaker Seminar Series,
Cambridge, MA.
18
The Good News
“Delta Air Lines flies over 2,500 domestic flight legs every day, using
about 450 aircraft from 10 different fleets...

Recent advances in mathematical programming algorithms and
computer hardware make it possible to solve optimization problems
(fleet assignment) of this scope for the first time...

Use of the Coldstart model is expected to save Delta Air Lines
\$300 million over the next three years.”

INTERFACES 24:1 Jan-Feb 1994, pp:104-120
19
The Good News
“Between 1986 and 1999, Air New Zealand staff and consultants in
collaboration with the University of Auckland have developed eight
application-specific optimization-based computer systems to solve all
aspects of the tours-of-duty planning and rostering processes for Air
New Zealand's national and international operations.

These systems have saved NZ\$15,655,000 per year while providing
crew rosters that better respect crew members' preferences.”

INTERFACES Vol. 31, No. 1, January-February 2001, pp. 30-56
20
1995             2000

1    15 minutes On Time Performance                80.6%            73.5%

2      Average flight delay (minutes)                7.0             10.5

3   Number of articles in US newspapers              22              101

4   Complaints (Per 100,000 passengers)             0.76             2.98

Sources: (1 &2) ASQP, (3) Lexis-Nexus, (4) DOT air travel consumer reports
21
   “Flight delays worst in 13 years”
 Jan   – Apr delays worse than any other year in
DOT-recorded history
 Only 72% of domestic flights of 20 largest US
airlines arrived on time
 US Airways had only 63% of flights on time
 2.8% of all domestic flights canceled

USA Today (2007), Department of Transportation
22
Where’s the disconnect?
 Fundamental conflict: Plans that are good
on paper often don’t perform well in
practice – slack is bad in planning, good in
performance
 Slack is what keeps delays from
propagating!

23
Three Important Questions
 How do we measure robustness in an
airline plan?
 How do we value robustness in an airline
plan?
 How do we incorporate robustness in an
airline plan?

24
Institutional Barriers to Robustness

   Silos – different departments, different incentives
   Feedback loop is ad hoc, not systematic
   Planning process is largely automated, recovery
is largely personal
   Need to bring together expertise across the
whole system (all individual planning stages,
operational/recovery phases)

25
Computational/Technological
Barriers to Robustness
 Need to integrate planning stages
 Need to incorporate variability/uncertainty
 Need to address ill-defined objectives
 These problems are:
 Large
 Hard
 Data-intensive

26
The Barriers Are Coming Down
   Carriers are recognizing the importance of
robust planning, working across silos, re-aligning
incentives
   Computers are getting faster
   Algorithms are gettings better
   Researchers are becoming better educated
about the nature of the problem and how to
solve it

27
Current Research -- Metrics

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007   28
Conventional Wisdom 1
   CW: “Propagated delays are more significant than the
original delays themselves.”
   True or false?
   Both!
 When delays propagate, the propagated delay can be
significantly larger than the initial root delay…
 …but lots of delays don’t propagate at all.
   Off-peak times
   Crews going off-duty
   Aircraft going off-rotation
   End-of-day effects

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007   29
Severity Across All Delay Lengths

Severity                                                                                                  Severity

100%                                                                                                      100%
10
90%                                                                                                       90%
9
80%                                                                                                       80%                                                                          7
8
percent of the flights

percent of the flights
70%                                                                                                       70%                                                                          6
7
60%                                                                          5
60%                                                                         6
4
50%                                                                         5                             50%
3
40%                                                                         4                             40%                                                                          2
30%                                                                         3                             30%                                                                          1
2                             20%                                                                          0
20%
1
10%                                                                                                       10%
0
0%                                                                                                        0%
15   30   45   60   75     90    105    120   135   150   165   180
15   30   45   60   75     90   105    120   135   150   165   180
root delay
root delay

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007                                                                30
Conventional Wisdom 2
   CW: “A single delay can “snowball” through the entire
network.”
   True or false?
   False
   Buffers keep delays from propagating extensively (i.e.
number of impacted flights is contained)
   Down periods
   Crews going off-duty
   Aircraft going off-rotation
   Crews and aircraft staying together
   Propagation trees tend to only have one branch
   Limited number of down-stream delays still have
significant cost impact
Cohn, Belobaba, Ahmadbeygi, and Guan, 2007   31
Conventional Wisdom 3
   CW: “Keeping crews and aircraft together can mitigate
the impact of disruption.”
   True or false?
   True
 Most of the “trees” we saw did not actually branch at all
 Nonetheless there can be significant propagation (e.g. 8 –
10 flights deep in the tree)
 Can keeping crews and aircraft together ever increase
propagation?

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007   32
Conventional Wisdom 4
   CW: “Delays that occur early in the day can cause
greater propagation than delays later in the day.”
   True or false?
   True (on average)

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007   33
Conventional Wisdom 4
time window 1 - severity                                                                                  time window 1 - depth                                                                                       time window 1 - magnitude

100%                                                                                                     100%                                                                                                         100%

90%                                                                                                      90%                                                                                                          90%

80%                                                                                                      80%                                                                                                          80%
7                                                                                                        7
(5,6]

percent of the flights
percent of the flights

percent of the flights
70%                                                                        6                             70%                                                                        6                                 70%
(4,5]
60%                                                                        5                             60%                                                                        5                                 60%                                                                        (3,4]
4                                                                                                        4
50%                                                                                                      50%                                                                                                          50%                                                                        (2,3]
3                                                                                                        3
40%                                                                                                      40%                                                                                                          40%                                                                        (1,2]
2                                                                                                        2
(0,1]
30%                                                                        1                             30%                                                                        1                                 30%
0
0                                                                                                        0
20%                                                                                                      20%                                                                                                          20%

10%                                                                                                      10%                                                                                                          10%

0%                                                                                                       0%                                                                                                           0%
15   30   45   60   75   90    105    120   135   150   165   180                                        15   30   45   60   75   90    105    120   135   150   165   180                                            15   30   45   60   75   90    105    120   135   150   165   180
root delay                                                                                               root delay                                                                                                   toot delay

time window 2 - severity                                                                                  time window 2 - depth                                                                                       time window 2 - magnitude

100%                                                                                                     100%                                                                                                         100%

90%                                                                                                      90%                                                                                                          90%

80%                                                                                                      80%                                                                                                          80%
7                                                                                                        7
(5,6]
percent of the flights

percent of the flights
70%                                                                        6                             70%                                                                        6                                 70%
percent of flights

(4,5]
60%                                                                        5                             60%                                                                        5                                 60%
(3,4]
4                                                                                                        4
50%                                                                                                      50%                                                                                                          50%                                                                        (2,3]
3                                                                                                        3
40%                                                                                                          40%                                                                        (1,2]
40%                                                                        2                                                                                                        2
(0,1]
30%                                                                        1                             30%                                                                        1                                 30%
0
0                                                                                                        0
20%                                                                                                      20%                                                                                                          20%

10%                                                                                                      10%                                                                                                          10%

0%                                                                                                       0%                                                                                                           0%
15   30   45   60   75   90    105    120   135   150   165   180                                        15   30   45   60   75   90    105    120   135   150   165   180                                            15   30   45   60   75   90    105    120   135   150   165   180
root delay                                                                                               root delay                                                                                                   root delay

time window 3 - severity                                                                                  time window 3 - depth                                                                                       time window 3 - magnitude

100%                                                                                                     100%                                                                                                         100%
90%                                                                                                     90%                                                                                                           90%
80%                                                                                                     80%                                                                                                           80%
6                                                                                                        6
percent of the flights

percent of the flights

percent of the flights
70%                                                                                                     70%                                                                                                           70%
5                                                                                                        5                                                                                                            (3,4]
60%                                                                       4                             60%                                                                        4                                  60%                                                                       (2,3]
50%                                                                       3                             50%                                                                        3                                  50%                                                                       (1,2]
40%                                                                       2                             40%                                                                        2                                                                                                            (0,1]
40%
1                                                                                                        1                                                                                                            0
30%                                                                                                     30%                                                                                                           30%
0                                                                                                        0
20%                                                                                                     20%                                                                                                           20%
10%                                                                                                     10%                                                                                                           10%
0%                                                                                                       0%                                                                                                            0%
15   30   45   60   75    90    105   120   135   150   165   180                                        15   30   45   60   75   90    105    120   135   150   165   180                                            15   30   45   60   75    90    105   120   135   150   165   180
root delay                                                                                               root delay                                                                                                   root delay

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007                                                                                                                                     34
Conventional Wisdom 5
     CW: “It is most important to add slack to flights early in
the day.”
     True or false?
     False

Lowest impact
Greatest impact
but greatest frequency
but lowest frequency

Cohn, Belobaba, Ahmadbeygi, and Guan, 2007            35
Current Research -- Metrics
   Many others have also looked at quantifying and
understanding sources of delay
 Rupp  2007 looks at weather, station type, and
seasonality to try to predict delay patterns
 Hsiao and Hansen 2006 built a statistical model
looking at time of day, weather, and congestion
 Tu et al 2006 look at both long-term (seasonal) and
short-term (time-of-day effects) to try to understand
delays

36
Important Insights
   There are significant sources of external delay in
any airline operation that cannot be avoided
   These delays can have significant additional
impact by propagating (through commons
crews, aircraft, passengers, etc.) to future flights
   The flight and crew schedules, routing, fleeting
greatly impacts the extent of this propagation

37
Needs for Improvement
 Interactions between resources affect
propagation – we should schedule all
resources simultaneously
 Flight departure and travel times are
variable – we should consider the potential
delays in the planning process and see
how they propagate in the plan

38
Realistic Improvement
 Unfortunately, doing all of this – all at once
– is still too hard and too slow!
 Instead, the primary focus today is on
identifying key sources of fragility in the
network and working to improve these
without making planned costs increase too
much

39
Current Research – Robustness
   Erghott and Ryan (2002) use multi-criteria
optimization for crew scheduling
 Want   to maximize robustness and minimize
cost
 Two options to improve robustness
 Keep crew and aircraft together
 Add extra slack when aircraft changes are
scheduled

40
Current Research – Robustness
   Klabjan and Shebalov (2006) use multi-
criteria optimization for crew scheduling
 Want  to maximize “move-up crews” and
minimize cost
 Instead of focusing on absorbing delay
propagation through slack, consider recovery
opportunities

41
Current Research – Robustness
 Minor re-timings of the flight schedule can
enable more robust connections without
significantly altering planned costs or level
of resources
 OR tools (and particularly math
programming) are very good at this type of
problem

42
Current Research – Robustness
   Lan, Clarke and Barnhart (2006) use flight
re-timing to improve passenger metrics
 Consider  multi-leg itineraries
 Move flights slightly earlier or later to
decrease probability of missed connections

43
Current Research – Robustness
   Cohn, Ahmadbeygi, and Belobaba (2007)
use re-timings to decrease propagation of
delays
 Simultaneously   consider cockpit crews and
aircraft
 Follow propagated delays fully, into they are
absorbed by existing slack

44
Current Research – Robustness
   Rosenberger, Johnson, and Nemhauser
(2004) focus on fleeting robustness
 Lotsof short cycles to allow easy
cancellations
 Keeps both aircraft and crew in circulation

45
Current Research – Robustness
   Johnson and Smith improve operational
robustness through fleeting limitations
 Minimize  number of fleet types assigned into
and out of spoke stations
 Provides increased opportunities for swapping
aircraft
 Simplifies maintenance operations

46
Current Research – Robustness
   Weide and Ryan (2007) focus on
improving crew robustness
 Keep crew and aircraft together whenever
possible
 Especially concerned with tight turns

47
Current Research – Robustness
   Lan, Clarke and Barnhart (2006) use
changes in aircraft routing to improve
robustness
 Better utilize the slack in the system to absorb
disruption
 Solve string-based routing problem with input
estimates of delay propagation for a given
string

48
Current Research – Recovery
   CALEB Technologies and Continental
Airlines
 How   to recover quickly from a major
disruption
 In place for 9/11/02 – estimated savings of
\$40 million in resuming operations (faster
than all other carriers)

49
Current Research – Recovery
   Stojkovic, Soumis, Desrosiers, and Solomon
(2002) use flight re-timing to recover from minor
disruptions
 Maintain  all existing crew, maintenance, and
passenger connections
 Not only allow changes in flight departure times, but
also allow activities to be expedited
 Minimize costs of extra resources and passenger
inconvenience

50
Current Research – Recovery
   Rosenberger, Johnson, and Nemhauser
(2003) also provide optimization tools to
recover from minor disruptions
 Re-routing aircraft
 Cancelling flights

51
Current Research – Recovery
   Abdelghany, Ekollu, Narasimhan,
Abdelghany (2004) consider crew
recovery after minor disruptions
 Rolling-window of repeated optimization
problems, focusing on the earliest departure
times, successively

52
Current Research – Recovery
   Barnhart and Bratu (2006) consider
recovery after minor disruptions
 Focus   is on minimizing impact on passenger
itineraries, missed connections
 Control recovery costs

53
Conclusions
 There is a clear need to improve the
robustness of airline plans
 There is tremendous incentive to improve
robustness
now make it possible

54
Conclusions
 There is no “Holy Grail”
 Keys to success:
 Re-aligning   of incentives
 Breaking down of silos
 Codification/automation of recovery policies
 Identification of key metrics and performance
indicators
 Incremental schedule modification tools

55