Saba Neyshabouri Agenda Airline scheduling process Fleet Assignment problem TimeSpace network concept Airline Schedule Single most important indicator of airlines business strategy Markets to be served ID: 734068
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Slide1
Airline Schedule Optimization (Fleet Assignment I)
Saba NeyshabouriSlide2
Agenda
Airline scheduling processFleet Assignment problemTime-Space network conceptSlide3
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:
Gates and slots
Operational restrictions
Airport Restrictions
Location of the crew and maintenance plansSlide4
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.Slide5
Airlines and Decision making
Decision making process in airline industry is a very complicated process due to:
Numerous airport location with different restrictions
Different aircraft types with different operational characteristics
Crew scheduling and regulations
Large number of O/D routes and marketsSlide6
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 systemSlide7
Breaking Down the Problems
In order to handle airline’s operational problems, it has been broken down to several hierarchical problems:
The schedule design problem
The fleet assignment problem
The maintenance routing problem
The crew scheduling problemSlide8
Fleet Assignment Problem
The objective:Finding a profit maximizing assignment of aircrafts to flight legs in airline’s network.
Complicating factors:
Satisfying passenger demand
Fleet composition
Fleet balance (flow balance)
Other side constraintsSlide9
The Schedule Design Problem
The goal is to design the airline’s flights schedule specifically:Flight legs to be operated by airline
Scheduled departure times
Estimated scheduled arrivals
Frequency plan and the days that on which flight leg is operatedSlide10
Sample Flight Schedule
This example for flight schedule connects only 3 markets and has 10 flights.Slide11
Example
Flight network
Fleet compositionSlide12
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:Slide13
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:Slide14
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.Slide15
Greedy Solution to Example
Considering the most profit generating assignments, the greedy solution will be:
This solution is
not feasible!Slide16
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 operationsSlide17
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 constraintsSlide18
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.Slide19
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}Slide20
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.Slide21
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.
BOS
LGA
ORD
8:00
9
:00
10:00
11:00
12:00
13:00Slide22
Time-Space Network
In our example:
Not all the arcs exists.
The size of the network is much bigger than the static network.
BOS
LGA
ORD
8:00
9
:00
10:00
11:00
12:00
13:00Slide23
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.Slide24
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.Slide25
Time-Space Network for our Example
Our static network will change to another network that will capture the temporal behavior of the system:
Ground arc
Flight arcSlide26
Optimal Fleet Assignment
In our network, the optimal fleet assignment is shown on the following network (Flow Balance):Slide27
Optimal Fleet Assignment
In our network, the optimal fleet assignment is shown on the following network (Same location for aircrafts requirement):