Airline Schedule Optimization
(Fleet Assignment I)
Saba Neyshabouri
Agenda
• Airline scheduling process
• Fleet Assignment problem
• Time-Space network concept
Airline Schedule
• Single most important indicator of airline’s business strategy.
– Markets to be served
– Level of service
• There are many restrictions that makes the planning very
difficult:
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Gates and slots
Operational restrictions
Airport Restrictions
Location of the crew and maintenance plans
Airline’s Goals
• Airlines are operating in a competitive market.
• The ultimate goal of airlines is maximizing the profit.
• There can be some other goals that will lead to profit such as:
– Operational goals
– Marketing goals
– Strategic goals
• Airlines are trying to find the best (in terms of profit) schedules that are
consistent with their other goals.
Airlines and Decision making
• Decision making process in airline industry is a very
complicated process due to:
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Numerous airport location with different restrictions
Different aircraft types with different operational characteristics
Crew scheduling and regulations
Large number of O/D routes and markets
Complicating Factors in Decision making
• In modeling and solving optimization problems in airline
industry, 2 major complicating factor are known:
– The huge size of the problem
– Inherent uncertainty of the system
Breaking Down the Problems
• In order to handle airline’s operational problems, it has been
broken down to several hierarchical problems:
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The schedule design problem
The fleet assignment problem
The maintenance routing problem
The crew scheduling problem
Fleet Assignment Problem
• The objective:
– Finding a profit maximizing assignment of aircrafts to flight legs in
airline’s network.
• Complicating factors:
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Satisfying passenger demand
Fleet composition
Fleet balance (flow balance)
Other side constraints
The Schedule Design Problem
• The goal is to design the airline’s flights schedule specifically:
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Flight legs to be operated by airline
Scheduled departure times
Estimated scheduled arrivals
Frequency plan and the days that on which flight leg is operated
Sample Flight Schedule
• This example for flight schedule connects only 3 markets and has 10
flights.
Example
• Flight network
• Fleet composition
Example
• Given this example the goal is to find a profit-maximizing assignment of
fleet types to flight legs in a way such that:
– Not more than available number of aircrafts are used
– Balance of aircrafts at each location is maintained
• The objective function tries to maximize the profit therefore the profit of
assigning a fleet type to a flight leg should be calculated:
Profit Calculation
• After doing the calculation for each possible assignment, the
resulting profit for each assignment of fleet type to flight leg is
summarized in the following table:
Greedy Solution
• Greedy methods: heuristic method to find a solution to a
complicated problem which reduces the time of computation
however it is not guaranteed to be optimal or even feasible.
• The main idea of a greedy algorithm is to be greedy in each
step of decision making!
– Being greedy is like not considering long-term effects of decisions.
– Being greedy in some cases might not even provide any feasible solution.
Greedy Solution to Example
• Considering the most profit generating assignments, the
greedy solution will be:
• This solution is not feasible!
Greedy Solution to Example
• This solution is not feasible!
• The aircraft balance is not achieved.
• Using a network of distances (static network) makes it difficult to
determine the number of necessary aircrafts to fly for each day of
operations
Time-Space Networks
• In many problems in optimization, time is playing an
important role in the model.
• However having time as a changing parameter in the model,
usually increases the complexity of the problem in hand.
• Example of the problems that deal with time related
constraints:
– Job shop scheduling- Minimizing tardiness
– Vehicle routing problem with time windows
– Flow shop scheduling problems with job availability constraints
Time-Space Network
• Decisions that are needed to be made at different times
require adding variables that keeps track of time.
• Time is a continuous variable!
• Adding a continuous variable to an IP problem makes the
problem even more complicated to solve.
• There has to be an smart way to deal with time in our models.
Time-Space Network Concept
• Graph G=(N,E) is made of set of nodes (N) and set edges (E)
– N: usually represents the locations
– E: usually represents the arcs (connections/roads) between two
locations
– N={ORD,BOS,LGA}
– E={CL50x,CL55x,CL30x,CL33x}
Time-Space Network
• As it can be seen in the graph, there is no indication of the
times of flights:
• However in managing the flights, keeping track of time is
important since one aircraft can fly multiple legs.
Sample Time-Space Network
• In general, in time-space networks, each node represents a
location in a specific time (of the day/month/year).
• Arcs are moving between two locations considering the time
it takes for that movement.
ORD
LGA
BOS
8:00
9:00
10:00
11:00
12:00
13:00
Time-Space Network
• In our example:
ORD
LGA
BOS
8:00
9:00
10:00
11:00
12:00
13:00
• Not all the arcs exists.
• The size of the network is much bigger than the static network.
Time-Space Networks: Pros & Cons
• Time-space networks are used so the optimization problem
does not become a mixed-integer programming (MIP) which
are generally more difficult to handle.
• Using time-space networks, may cause the problem to
transform into one of the well-known network problems
which can be handled efficiently.
• Using time space network will cause the size of the problem
to grow very fast
– N= Number of locations * Number of time windows (or significant
times for each node)
– E= Every possible movements between 2 locations throughout the day.
Time-Space Network for our Example
• In our example: a time-space flight network is an expansion of
the static flight network in which each node represents both a
location and a point in time.
• In this network, two different arcs are possible:
– A flight arc: representing a flight leg with departure location and time
represented by the arc’s origin node, and arrival location and arrival
plus turn time represented by the arc’s destination node.
– A ground arc: representing aircraft on the ground during the period
spanned by the times associated with the arc’s end nodes.
Time-Space Network for our Example
• Our static network will change to another network that will
capture the temporal behavior of the system:
Flight arc
Ground arc
Optimal Fleet Assignment
• In our network, the optimal fleet assignment is shown on the
following network (Flow Balance):
Optimal Fleet Assignment
• In our network, the optimal fleet assignment is shown on the
following network (Same location for aircrafts requirement):