Crew Assignment

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Crew Assignment

Nidhi Sawhney Carmen Systems AB nidhi_at_carmen.se
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Outline

• Description of the Crew Assignment / Rostering
  problem
• Solution Methods Generate Optimize framework
• Modelling Issues
• Rules vs Costs
• Taming the optimizer
• Preferrential Bidding System
• Measuring the system vital statistics

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Carmen Crew Rostering
PassengerTracking
Carmen Aircraft Tracking
Carmen Fleet Assignment
Carmen Tail Assignment

Carmen Integrated Operation Control
Aircraft Routings
Anonymous fleet assignment
Carmen Roster Maintenance
Carmen Crew Pairing
Carmen Crew Rostering
Carmen Crew Tracking
Manpower
Anonymous pairings
Training need
Carmen Time Table Manager
Carmen Rave (General Modelling Language)
Carmen Crew Communicator
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The Input Problem 374 Crew 867 Pairings
Unassigned slots 1607 Objective cost 169 milj
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(No Transcript)
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After Greedy 20 mins
Unassigned slots 10 Objective cost 10.4 milj
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After Improvement Method 2 hrs
Unassigned slots 0 Objective cost 3.5 milj
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Initial Construction Method

• To get a starting point for the improvement
  heuristics.
• Solution quality is not important.
• To get the right structure in the solution.
• To get difficult trips assigned (often special
  objects such as simulator training, medical
  checks and long pairings)

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Sequential matching
Hansen
Jensen
Peterson
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a b c
Hansen 8 12 X Jensen
X 14 17 Petersen 10 11
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Variables Constraints

• yij Trip i to be assigned to crew j
• xi A pattern, a list of trips, a monthly plan
  will be chosen as a roster or not
• Constraints
• Need to cover production i.e trips
• Assign all resources i.e crew
• Respect union and airline regulations

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Variables

• xi A pattern, a list of trips, a monthly plan
• will be chosen as a roster or not
• yij Trip i to be assigned to crew j

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Mathematical Formulation

• min cx
• subject to Ax b
• x binary

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Costs Examples

• Cost of unassigned pairing
• Buffer to legal rest before flying 1 hour
• Cost per min less than buffer 30
• Cost for early start after days off 100
• Time when start is considered early 700
• Bids Penalty when below satisfaction target.
• Fairness Penalty for deviation from targets.

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Rules Examples

• Max 100 block hrs in 28 days
• Max 5 consecutive early start duties
• Max 4 consecutive night duties
• Max 6 consecutive days with duty between days off
• Min 75 block hours in 28 days

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Additional Constraints

• Training requirements
• 2 or 3 crew need to be route-instructed for a
  specified period
• Atmost 1 inexperienced crew in the cockpit
• Language requirements
• Trip or leg level
• Global Constraints
• Balancing production at the different bases
• Upper bound on the total cost of the solution

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IP Formulation
Slack column for CP A.
Roster for CP A.
Roster for FO B.
Slack column for pairing at CP pos.
1 1 . . 0 . . 0 1 0 0 . . 1
. . 0 1 . . . 1 0 . . 0 . . 1
1 0 0 . . 1 . . 0 1 . . . 0
0 . . 1 . . 0 ? 1
One assignment for CP A.
One assignment for FO B.
A
Assign the pairing once at CP pos.
Assign the pairing once at FO pos.
Max one inexperienced on pairing.
CP A. is experienced, FO B. is inexperienced.
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Searching the solution space

• Generate new options i.e rosters / columns via
• Heusristic methods
• LP duality

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Gen Opt with Time-Window
CP Smith

• Generation in general
• 1 Produce a large number of rosters.
• Check legality and cost with RAVE.
• Translate to columns and send to optimizer.

Generation with time window

• 1 Take rosters from the previous solution.
• Remove pairings inside time window.
• Generate new rosters by assigning new pairings
  inside time window.

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Trip
Trip
Trip
Trip
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Depth First Search Generation

• Assign the pairings in (time-) order.
• Back-track when the roster becomes illegal or
  time-window is full.
• The number of branches is determined by
  parameter search width.

until you cannot put in more pairings.
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The Time Window
Trip 7
Trip 5
Trip 8
Trip 4
Trip 6
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Generation With Duals

• Suppose we have generated a lot of rosters
  (columns) and solved the LP-relaxation
• Calculate the reduced cost for new rosters
• Generate more attractive rosters i.e most
  negative reduced costs
• In case of illegal roster being generated, find
  the next best (K-SP algorithm)

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The Time Window
Trip 5
Trip 4
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Generator
Cost information
RAVE
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The Time Window





Trip 5





Trip 4


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Estimated Reduced Cost
i) Calculate reduced cost of roster with
time-window empty R0 cost
of roster dual costs
ii) Calculate reduced cost of roster with one
new pairing (Rx)
iii) Reduced cost of pairing i Ri Rx R0
(Rx Ro Ri)
iv) The hope is R R0 Ri

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The Time Window
Trip 7
Trip 5
Trip 8
Trip 4
Trip 6
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Assignment Cost Components

• Production
• Stability
• Bid-satisfaction
• Social quality
• Fairness

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Fairness Cost
Penalty

• Something is distributed to all crew Duty hrs,
  days off etc.
• Each crew has an individual target value
• Penalty for deviation from target
• This is a highly non-linear cost!

Target
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Preferrrential Bidding System
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The Products
José and Paul shall fly
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The Products
José wants short pairings and has birthday on
the 24th. Paul prefers long pairings and lives
in FRA.
So lets plan differently
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How does the system handle it?

• Determine the dream roster for each crew
• Model the costs to drive the solution towards
  maximizing crew satisfaction
• Use these costs both as cost components sent to
  the IP solver and during the previous generation
  phase

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Satisfaction Target
Reward in this region.
High penalty in this region.
Satisfaction Target
Satisfaction Level
Senior
Junior
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Vital Statistics

• What does the planner have to say?
• Are the crew happy with their rosters?
• How much tuning does the system need from month
  to month?
• Is it possible to use the system at the
  operational level?
• How much money can the system guarantee to save?

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Future

• Process
• One shot optimization combine pairing and
  assignment processes
• Assign legs directly to crew
• Iterative feedback from assignment to pairing
• Allowing for changes in the time table at the
  optimization step

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Future

• Optimization
• Improving generation strategies
• Customized branching decisions in BB
• Implementing new constraints for PAQS
• Modelling
• Investigate replacing the weighted sum costs by a
  balanced or pareto-optimal cost function