The Fleet Assignment Problem

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The Fleet Assignment Problem and its resolution
sami.gabteni_at_carmen.se
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Have you heard about
Decomposition methods
Linear programming
Column Generation
Network flow problem
Multi-commodity network flow problem
Sub-gradient optimization
Stochastic optimization
Non-linear Programming
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The Fleet Assignment Problem
technical constraints vehicle type specific
constraints network design constraints
fleet assignments
Fleet Assignment Optimizer
A heterogeneous fleet
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One network for each vehicle type
Grönkvist99
Chronological order prevents cycles
Alternative model Time line model (see reference)
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Multi-commodity Network Flow problem
T network
U network
V network
How to get rid of the coupling constraints ?
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Resolution philosophy
Kohl et al. 98
Whenl increases (resp. decreases), y
increases (resp.decreases). Each veh. type is a
company which Maximises its benefits from
assigning its locomotives
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a scientific bidding process
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Langrangean optimization
Fisher81, Held et al.74
We build an integer solution with a primal
heuristic
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Flight Scheduling
Ben et al. 98
Flight scheduling consists in building the most
profitable Schedule Maximizing (Revenue Costs)
Revenue Side Two identical assignments to a
particular flight might not Yield the same
revenue it depends on the seat allocation For
each (veh.type, flight), we solve a yield
maximisation Problem (yield management)
Cost Side Costs are not considered with same
accuracy in this step. Fleet costs are the most
important (other costs are approximated)
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The Seating capacity allocation problem for a
given (veh.type, flight)
Smith et al.92
G
H
S
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The Spilled Revenue
Ben et al.98
Demand is a non-deterministic variable following
a Gauss Function
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A well-known optimization problem
Minimization of the forecasted Spilled
revenue for all the client-groups
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Bibliography
Grönkvist99 Aircraft Scheduling, Chalmers Uni.
Tech.2000 (not published yet)
Kohl et al. 98 Carmen Fleet, Optimization of
Locomotive Scheduling 1998 (not published)
available upon request
Held et al.74 Validation of Sub-Gradient
Optimization Mathematical Programming 6 1974 62-88
Fisher81 The Lagrangian Relaxation Method for
Solving Integer Programming Problems Managt Sc.
Vol 27, num 1, Jan 81
Fisher94 Optimal Solution of Vehicle Routing
Problems Using Minimum K-Trees Operations
Research vol 42 num 4 1994
Ben et al.98, Schedule Optimization at SNCF
Nejib Ben-Khedher et al., Interfaces vol.28
num.1, Jan 98
Smith et al.92 Yield Management at American
Airlines, Barry Smith et al. Interfaces 22
Jan-Feb 92