4
ISyE 6203
Fall, 2002
Practice Exam 2
Vande Vate
Instructions
You have until 10:55 am to complete the exam. Watch your time. If you are having difficulty with a question, you might wish to pass over it and return to it later if you have enough time at the end of the exam.
Be sure to put your name on your exam. Show your work – that will allow me to award partial credit. Make sure your answers are legible and clearly marked.
The exam is open book: you may use any notes or text material.
The exam is to be completed individually, without collaboration with anyone else.
1. (20 points) Formulate a linear mixed integer programming model to solve the following problem.
The county is trying to site a landfill within its incorporated boundaries. All of the towns within the county are opposed to having the landfill located near them. So the county’s challenge is to find a location within its borders that maximizes the distance between the landfill and the nearest town. Since the county is in Kansas and all the roads run North-South or East-West, the county proposes to use rectilinear distance. Formulate a linear mixed integer programming model to help them. Use the following parameters in the model:
The county is a rectangle with principal axes oriented North-South and East-West.
param MinLatitude; /* The minimum latitude of the county in decimal form.*/
param MaxLatitude; /* The maximum latitude of the county in decimal form.*/
param MinLongitude; /* The minimum longitude of the county in decimal form.*/
param MaxLongitude; /*The maximum longitude of the county in decimal form*/
Comment: There is no guarantee that any of these numbers is non-negative.
set TOWNS; /* The set of towns in the county */
param Latitude{TOWNS}; /* The latitude in decimal form of each town */
param Longitude{TOWNS}; /* The longitude in decimal form of each town */
Your model should include the variables:
var Lon >= MinLongitude, = MinLatitude, ................
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