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Airline Schedule Optimization (Fleet Assignment I) Airline Schedule Optimization (Fleet Assignment I)

Airline Schedule Optimization (Fleet Assignment I) - PowerPoint Presentation

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Airline Schedule Optimization (Fleet Assignment I) - PPT Presentation

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

network time problem space time network space problem flight fleet assignment profit greedy solution location problems schedule airline goals

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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):