ENGRI 1101 Engineering Applications of OR
Fall 08 Homework 12
Homework 12 Solutions
1. (a) The labor union has the following strategies available: they can demand any amount (rounded to multiples of 10 cents) between the managements current oer ($1.10) an

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 1
Homework 1: TSP
Due date: 4:00pm on Friday, September 5, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Upson. Reading assig

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 6
The Transportation Problem
Due date: 4:00pm on Friday, October 10, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Upson. Rea

ENGRI 1101 Engineering Applications of OR
Fall 2008 Handout 1
What is Operations Research?
In its most basic form, O.R. may be viewed as a scientic approach to solving problems; it abstracts the essential elements of the problem into a model, whic

ENGRI 1101: Engineering Applications of OR, Fall 2008 Prelab 3: The Minimum Spanning Tree Problem Name: Netid: Objectives: Introduce students to the graph theoretic concept of spanning trees.
1
Show three dierent combinatorial algorithms for solv

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 4
The Maximum Flow Problem
Due date: 4:00pm on Friday, September 26, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Up

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 8
Linear Programming
Due date: 4:00pm on Monday, November 3, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Upson. Reading ass

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 1
Homework 1: TSP
Due date: 4:00pm on Friday, September 5, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Upson. Read

ENGRI 115 Engineering Applications of OR Final Solutions
Fall 2007
Name:
1. (30 points) Linear Programming Consider the following LP depending on the parameter , which will be specified below. max -x1 + x2 s.t. -3x1 + 2x2 2 -x1 + 2x2 6 x1 0,

ENGRI 115
Engineering Applications of OR
Fall 2007
The Shortest Path Problem I.
Homework 2
Due date: Thursday, September 13 in class. References: Lecture notes; Lab 2; Winston 8.1, 8.2.
The first two problems are practice problems, DO NOT hand t

ENGRI 115 Engineering Applications of OR
Fall 2007
Solutions
Prelim 1
1. (20 points) Consider the following acyclic directed graph in which the number cij on the edge (i, j) represents the length of the edge.
2 1 3 1 1 3 2 1 5 4 1 5 2
We want to

ENGRI 115
Engineering Applications of OR
Fall 2007
The Shortest Path Problem II.
Homework 3
Due date: Tuesday, September 25 in class. References: Lecture notes; Lab 3; Winston 8.2.
The first two problems are practice problems, DO NOT hand them i

ENGRI 1101 Engineering Applications of OR
Fall 08 Homework 12
Game Theory
Due date: 4:00pm on Friday, December 12, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to Upson. Reading assignment

Part #1 - The Caterers Problem (From Winston, page 390) The Carter Caterer Company must have the following number of clean napkins available at the beginning of each of the next four days: day 1, 15; day 2, 12; day 3, 18; day 4, 6. After being used, a nap

ENGRI 115
Engineering Applications of OR
Fall 2007
The Transportation Problem
Lab 8
Name:
Objectives: Introduce students to the transportation problem. Further use of AMPL. Give an application of the transportation problem to the "caterer's pr

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 2
The Shortest Path Problem
Due date: 4:00pm on Friday, September 12, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it connects to U

What Is Operations Research?
Selin Damla Ahipasaoglu ORIE, Cornell University
OR/MS: What is it?
Operations research (management science) is a collection of techniques based on mathematics and other scientific approaches that finds solutions to com

ENGRI 1101 Engineering Applications of OR
Fall 2008 Handout 6
The baseball elimination problem
We shall now explore a much more sophisticated application of the maximum ow problem. While this application is traditionally phrased in terms of baseba

ENGRI 1101 Engineering Applications of OR
Fall 2008 Handout 4
The minimum spanning tree problem
A communication network design problem Consider the following problem. The company that you work for wishes to install dedicated ber optic cable links

ENGRI 1101
Engineering Applications of OR
Fall 2008
Prelab 8
Linear Programming Formulations
Name:
Date: Thursday section: October 30 Monday section: November 3 Objectives: Practice in formulating linear programming problems Introduce the idea of linear r

ENGRI 1101 Engineering Applications of OR
Fall 2008 Handout 3
The shortest path problem
Consider the following problem. You are given a map of the city in which you live, and you wish to gure out the fastest route to travel from your home to your

ENGRI 1101 Engineering Applications of OR
Fall 2008 Handout 2
The traveling salesman problem
The traveling salesman problem is one of the most notorious optimization problems. The setting for the problem is as follows. A salesman starts at his hom

ENGRI 1101
Engineering Applications of OR
Fall 2008
Prelab 1
The Traveling Salesman Problem
Name:
Objectives: Introduce students to a real world problem solved by OR practitioners Demonstrate the use of heuristics to obtain good solutions to o

ENGRI 115
Engineering Applications of OR
Fall 2007
Linear Programming Formulations
Lab 9
Name:
Objectives: Practice in formulating linear programming problems Introduce the idea of linear relaxation Demonstrate the relationship between an inte

ENGRI 115
Engineering Applications of OR
Fall 2007
The Assignment Problem
Lab 7
Name:
Objectives: Show how to find maximum weight matching in bipartite graphs using the Hungarian Algorithm. Key Ideas: weighted matching, maximum weighted matchin

ENGRI 115
Engineering Applications of OR
Fall 2007
The Simplex Algorithm
Lab 11
Name:
Objectives: Practice the simplex algorithm Demonstrate unboundedness Demonstrate the two phases of the simplex algorithm Key Ideas: Objective function, cons

ENGRI 115
Engineering Applications of OR
Fall 2007
Maximum Matchings in Bipartite Graphs
Lab 6
Name:
Objectives: Show how to find maximum cardinality matching in bipartite graphs using maximum flows. Demonstrate the Augmenting Path Algorithm fo

ENGRI 115
Engineering Applications of OR
Fall 2007
The Diet Problem
Lab 10
Name:
Objectives: Give the students practice in formulating linear programming problems Introduce students to the idea of linear relaxation Demonstrate the relationship

ENGRI 115
Engineering Applications of OR
Fall 2007
The Critical Path Method
Lab 3
Name:
Objectives: Introduce the Critical Path Method for project scheduling as used in industry. Demonstrate the concept of sensitivity analysis. Practice formul

ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 3
The Minimum Spanning Tree Problem
Due date: 4:00pm on Friday, September 19, 2008 in the ENGRI 1101 box at the west end of the corridor on the second oor of Rhodes Hall, where it conne