Project: Application of Linear Programming in the Airline Industry
Fleet Assignment Problem
Models and Methods of Optimization, Fall 1999
Overview of Project
Each student will utilize the LP model described in
"Applying Integer Linear Programming to the Fleet Assignment Problem"
to determine the most cost effective fleet assignment for a given
student will then write a report discussing the results.
The project will be graded primarily on
the final project report, due on Monday, November 29, 1999. Details of the
requirements of the final project report and grading criteria are described
"Applying Integer Linear Programming to the Fleet Assignment Problem,"
appears in Interfaces Vol. 19, No. 4,
July-August 1989 (pp. 20-28). A copy of the article is on reserve at
Hunt Library (behind the circulation desk on the 1st floor). Hunt Library
also has a copy of the journal in the Bounded Journal section of the library
on the 3rd floor.
The article abstract:
formulated and solved the fleet assignment problem as an integer
linear programming model, permitting assignment of two or more fleets
to a flight schedule simultaneously. The objective function can take a
variety of forms including profit maximization, cost minimization,
and the optimal utilization of a particular fleet type. Several
departments at American Airlines use the model to assist in fleet
planning and schedule development. It will become one of the 10 key
decision modules for the next generation scheduling system currently being
developed by American Airlines Decision Technologies.
Note: Aside from the Optional Consultation with Instructor, any discussion
of individual projects with the instructor shall be done during the
instructor's office hours.
- Read the assigned article, "Applying Integer Programming to the
Fleet Assignment Problem."
- The Problem: The student should set up a linear program to
determine the most cost-effective fleet assignment for
the Vanguard Airline schedule (found at the
Vanguard homepage) over a 2
day time period.
The student should assume that there are 3 fleets available,
Fleet X, Y and Z. The student should use constants for the costs
and number of available planes of each fleet. Since we will not be
solving the problem explicitly, we will not need actual values for the
- Drafting the LP: The student shall derive an integer linear program
to determine the most cost effective fleet assignment. The student
will not have to write out each individual constraint
explicitly (see Solution Section Requirements below).
- Tuesday, November 9, 1999 and Thursday, November 11, 1999
Optional Consultation with Instructor:
The student shall
set up a 10 minute meeting with the instructor to discuss his/her
solutions to the problem. Sign up for a timeslot on the sheet outside
of 7213 Wean Hall. The student should have rough drafts of the
Solution Strategy and Solution sections of the report done before the
- Friday, Novemeber 19, 1999: Optional Rough draft of Analysis Section of report is due.
Comments will be made on the rough draft. No late rough drafts will
- Monday, November 29, 1999: Final Project Report is due.
Final Project Report Requirements
The final project report is due at the beginning of lecture on
Monday, November 29, 1999.
The typed reports should consist of the following sections:
- Problem Statement:
This section of the paper should describe the problem at hand.
The student should include solution strategies that may have been
employed in the past and reasons why a new strategy might be warranted.
- Solution Strategy:
The student should outline the solution strategy employed.
If variables are
used, explanations of what the variables represent should be given. (This
information should be provided once variables are introduced, either in
this section or the next). The student should give examples of
each of the different types of constraints used, but the student is not
required to list every single constraint individually.
Due to the number of variables involved, the student is not required to
solve the LP. The student should, instead, discuss how he/she might attempt
solving the LP. The student should make an attempt to see if he/she could
reduce the number of constraints or variables without making extra assumptions.
- Analysis: This section of the report will
act as a conclusion. The student should discuss the problem. He/She should
include the following:
- Advantages/Disadvantages to the solution strategy
- A list assumptions that were made in the formulation
and solution to the
problem and a discussion of
how reasonable the assumptions were, how one might
eliminate some of the assumptions, etc.
- Possible extensions of the problem.
- Impact of the solution on the airline company.
- Examples of other industries which have similar problems that could
be solved with variations of this LP.
Project Grading Criteria
Each student is responsible for turning in a final project report which
shall be solely the work of him/herself. No collaboration with anyone
other than the instructor or one of the TAs is allowed.
Any violation of this shall be dealt with according to university regulations.
The project grade will be calculated from the final project
report, worth 100 points, described below. For each day the project is
late, 10 points will be deducted from the project
- (15 pts) Problem Statement: These points will be awarded
for a concise statement of the problem, organized presentation of
data and discussion of the points detailed in the Problem Statement
- (15 pts) Solution Strategy: The student should outline
the solution strategy employed and give some justification why this strategy
might be more desirable than the other strategies listed in the Problem
Statement. If variables are ised, explanations of what the variables
represent should be given. (This information should be provided once
variables are introduced, either in this section or the next).
- (10 pts) Solution: These points will be based on clear
organization and discussion of the items described in the Solution
- (50 pts) Analysis: These points will be awarded for
a well-organized and thoughtful discussion of the
project, including (but not restricted to) the items listed in the
analysis section requirements above.
- (10 pts) Presentation: These points will be deducted for
spelling and grammatical errors in the report.