Fleet Assignment Problem

Option II

Models and Methods of Optimization, Fall 1999

**Overview of Project**

Each student will utilize the LP model described in the article "Applying Integer Linear Programming to the Fleet Assignment Problem" to determine the most cost effective fleet assignment for a given flight schedule. The 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 below.

The article,
"Applying Integer Linear Programming to the Fleet Assignment Problem,"
by
Jeph Abara
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:

We 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.

**Project Timeline**

- 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 costs.
- 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 consultation.**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 be accepted.**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.**Solution:**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 score.

- (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 Requirements above. - (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 Section Requirements. - (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.

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