Transcript Optimisation Approaches for Robust Airline Crew Scheduling

UNIT CREWING FOR ROBUST
AIRLINE CREW SCHEDULING
Bassy Tam
Bassy Tam
Professor Matthias Ehrgott
Professor David Ryan
Dr. Golbon Zakeri
Optimisation Approaches for Robust Airline Crew Scheduling
IRREGULAR OPERATIONS AND
ROBUST SCHEDULING
A cost minimal solution usually has high
resource utilisation
 Crew or aircraft spend minimal amount of time
on the ground between arrival and departure of
flights
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I.e. minimise any idle time incurred
Once disruption occurs
Little slack between flights to compensate for delays
 A single initial delay might propagate to later flights
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Airlines are interested in robust schedules
Optimisation Approaches for Robust Airline Crew Scheduling
ROBUST SCHEDULE PLANNING
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Robust schedule
Optimal planned cost is not necessary
 Aim for low operational cost
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Robustness of a schedule
Not well defined
 Two broad categories
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Improve flexibility of the schedule
 To allow easy recovery of schedule by switching aircraft
and/or crew
 Depends on the recovery procedure
 Minimise impacts from disruption
 To reduce delay propagation
 Schedule is operationally robust
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Optimisation Approaches for Robust Airline Crew Scheduling
ROBUST SCHEDULE PLANNING
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Robust scheduling can be considered in almost all
stages of the airline scheduling process
Four approaches for crew pairing
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Expected crew cost by simulation
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Bi-criteria
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Ehrgott and Ryan (2002)
Stochastic programming
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Schaefer et al. (2001)
Yen and Birge (2006)
Move-up crew
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Shebalov and Klabjan (2006)
Optimisation Approaches for Robust Airline Crew Scheduling
COMPARISON OF
TWO ROBUSTNESS APPROACHES
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Similar robustness measure
Both look for operationally robust crew schedules
 Improve robustness by
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Reducing the number of switching aircraft connections
when ground time is short
 Lengthen ground time when switching aircraft is necessary
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Compared robustness indicators
 Simulation to compare on-time performance
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Studied some historical data to ensure the same
delay distribution is used for both approaches
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING
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It is usual to solve the crew pairing problem
separately for different crew ranks and crew
types
Different resources allocated in each crew base
 Different operational rules
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Crew schedules are unlikely to be unit crewed
 Crew members perform different activities after
operating a flight
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However, it is more robust to keep the crew
working together as a unit
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING
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Little consideration of the flight connections of
other crew ranks when constructing a crew
schedule
What is unit crewing?
An approach to construct crew schedules so that
members of a crew perform the same sequence of
flights within their duty periods as much as possible
 A unit-crewed schedule is considered to be more
operationally robust in the sense that it is less likely
to delay other flights due to waiting for a member of
the crew from a disrupted upstream flight
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Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
SEQUENTIAL SCHEDULING
Obtain a cost minimal crew schedule for one crew
rank
 Bi-criteria optimisation problem for the other
crew rank
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Minimise crew cost
 Maximise unit crewing connection
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To solve the bi-criteria optimisation problem
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Penalty method
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Weighted sum of two objectives
Elastic constraint method
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Reformulated the crew cost objective as a constraint
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
SEQUENTIAL SCHEDULING
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Penalty method
No interpretation of the sum of two objectives
 Specification of the penalty is difficult
 Relatively few Pareto optimal solutions may be found
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Elastic constraint method
More difficult to solve compared with the penalty
method
 Might not be able to obtain good solutions within
reasonable time
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Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
SEQUENTIAL SCHEDULING
Need to experience the order of crew pairing
problems to be solved
 The final set of crew schedules might not be
optimal in terms of total crew cost and number of
unit crewing connections
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Solution of the second crew rank (the bi-criteria
optimisation problem) is limited by the solution of the
first crew rank (the cost minimal problem)
 Optimality or feasibility of the second crew rank is
not considered when solving the crew pairing
problem for the first rank
 Might result in higher cost to obtain unit crewed
solution
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Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
Minimise
Minimise
subject to
T
c1 x1
 c2 x2
T
eT s1
 eT s2
 U 2 x2
 Is1
 Is 2
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x2 ,
s1 ,
s2
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A1 x1
M 1 x1
th connection
Unit
Constraints
To minimise
total
The
iCrewing
will be unit
number ifofunon-unit
crewed
x1j – u2ikx2k = 0
1ij
One constraint represents
crewing connections
one possible unit crewing U x
1 1
connection
Non-unit crewed connection x1 ,
will
a slack
or surplus
If xkjhave
contains
connection
i,
value
1 0 otherwise
ukij = 1ofand
A2 x2
M 2 x2
Optimisation Approaches for Robust Airline Crew Scheduling
e
b1
e
b2
0
{0,1}n
UNIT CREWING BY
PARALLEL SCHEDULING
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Problem is difficult to solve due to the size of the
resulting problem
Flight and crew base balancing constraints are
doubled
 Number of unit crewing constraints is 5.7 times of
the number of flight constraints (for single crew rank)
in our test data
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Branching method
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Use special branch selection method to increase
number of unit crewing connections
Limiting number of constraints
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Include a subset of unit crewing constraints into the
problem
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Branching method
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All unit crewing constraints are removed
T
Minimise
c1 x1
subject to
A1 x1
 c2 x2
T
M 1 x1
Total crew cost is always
minimised, i.e. no choice for
making trade-offs between
unit crewing objective and
cost objective
A2 x2
M 2 x2
x1 ,
x2
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Optimisation Approaches for Robust Airline Crew Scheduling
e
b1
e
b2
{0,1}n
UNIT CREWING BY
PARALLEL SCHEDULING
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Branching with elastic constraint
Following aircraft objective introduced
 Cost objective is reformulated as a constraint
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Has problem to find a quality crew schedule that
has high number of unit crewing connections
Number of unit crewing connections is not included
in the objective
 Unit crewing is only considered as long as the cost
and following aircraft objectives are optimised
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Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Two methods to define unit crewing constraints
Define unit crewing constraints before the
optimisation process
Difficulties arise from the number of possible
connections
 Size of the problem
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Define unit crewing constraints during the
optimisation process
Size of the problem increases dynamically
 Add constraints when needed
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Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Observations
Difficult to obtain an integral solution
 Connections are unit crewed in a “fractional” way
 Sum of fractional values spill over on many
connections
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A lot of constraints need to be constructed
 Makes branch and bound difficult
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Sometimes makes originally unit crewed connections
no longer unit crewed
Impose 1-branch on unit crewed connections that
are robust (following aircraft connections)
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Advantages
Avoid the sum of fractional values to spill over on too
many connections
 Limit number of possible connections in the flight
network, i.e. column generation process is faster
 Limit number of variables in the problem, i.e.
reduced cost calculation is faster
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Disadvantage
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Optimality cannot be guaranteed
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Observations
If not many unit crewed following aircraft
connections at the end of the first LP relaxation,
problems of spill over remains
 The spill over of the sum of fractional values is
caused by the unit crewing constraints
 The more unit crewing constraints, the worse the
problems
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Limit number of unit crewing constraints
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Disadvantage
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Order the priority of connections
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Decide maximum number of unit crewing constraints
allowed in the problem
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If too many unit crewing constraints allowed
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Problems of the spill over remains
If the limit on number of unit crewing constraints is
too small
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Good quality unit crewed schedules cannot be found
Optimisation Approaches for Robust Airline Crew Scheduling
UNIT CREWING BY
PARALLEL SCHEDULING
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Dantzig-Wolfe decomposition
Block diagonal structure
 Use Dantzig-Wolfe decomposition to break the
combined model into two problems
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Master problem contains the unit crewing constraints
 Sub-problems are the two crew pairing problems
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Structure of the two crew pairing problems
remain unchanged
Longest computational time
Optimisation Approaches for Robust Airline Crew Scheduling