IEOR E4405.001IEOR E4405.001

Airline CrewAirline Crew

SchedulingScheduling

Presented by:Presented by:

Fatima KhalidFatima Khalid

Scope

Goal of airline industry: Maximization of Profits.

Requirement for reaching the goal: Planning at strategic, tactical and operational levels.

Airline planning involves processes such as timetable, fleet assignment, crew pairing and crew assignment.

Note: Focus of presentation: Crew pairing and Crew assignment.

Research based on following papers

A Stochastic Programming Approach to the Airline Crew Scheduling Problem

Joyce W.Yen

An Optimization Approach to Solving the Airline Crew Pairing Problem

Amy Cohn and Shervin AhmadBeygi

Characteristics of Crew Scheduling Problem

Comprises of two components

Crew-Pairing Problem: Assigning crew pairings (crew comprising: pilot, co-pilot and flight attendants) to flights such that all flights are covered.

Crew Assignment: Crews are assigned to given pairings. Most airlines use a kind of bidding system to assign pairings to crews.

Background on Aircraft Economics

Two costs components:

Aircraft

Variable Costs(Operating costs, i.e fuel)

Fixed Costs(Monthly Payments)

Cost Components

IP Formulation – Crew Pairing:

Min Σp cp xp

st Σp δfp xp = 1 for all f xp E {0, 1} for all p

Terminology:Xp -> is the binary variable taking the value 1 if pairing p is

included in the solution else the solution is 0.

δfp -> is a binary variable with value 1 if flight is included in the pairing else 0.

Cp -> cost of pairing p.

Solution to the problem formulated

First Approach: Branch and Bound (as explained in class)

The Algorithm tries to find the optimal solution of the problem, that is root problem.

In case the optimal solution could not be found, the feasible region is then subdivided into sub regions and the algorithm is then applied to each respective sub-region, resulting in sub problems.

If an optimum solution is found to a sub problem it is feasible solution to the root problem but not necessarily globally optimal.

The optimal solution to the sub problem can be used to prune the tree.

Solution to the problem formulated

Second Approach: Carmin Algorithm This algorithm uses reduced costs and dual values

to find the integer solutions. The IP is formulated as unconstrained non-linear

problem The reduced cost is found by finding solutions to the

equation ri = c i + yi where yi = (ri- + ri+) / 2

Analysis

The advantage of using branch and bound over Carmin’s method is the confirmation of optimality that branch and bound solution has.

In addition, model doesn’t change with duals However, drawback is the lack in efficiency in

finding the solution.