ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 8
The Transportation Problem
Name:
Objectives:
Introduce students to the transportation problem.
Further use of AMPL.
Give an application of the transportation problem to the caterers problem.
K

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 4
The Maximum Flow Problem
Due date: Thursday, February 19, by noon in the OR homework drop box.
References: Lecture notes; Lab 4; Winston 8.3.
The rst three problems are practice problems, DO NOT h

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 5
Maximum Matching in Bipartite Graphs
Due date: Friday, March 6 by noon in the homework drop box.
References: Lecture notes; Lab 6.
The rst two problems are practice problems, DO NOT hand them in.

ENGRI 115, Spring 2008
Homework 5 solutions
Problem 3
It is easy to observe that 3 machines: a crane, a piledriver and a cement mixer can be operated by 2
workers only, A and F . Consequently, all machines cannot be operated at the same time, and thus, a

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 6
The Assignment and Transportation Problems
Due date: Friday, April 3 by noon in the homework drop box.
References: Lecture notes; Labs 7 and 8; Winston 7.1.
The rst three problems are practice pro

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 7
Linear Programming Formulation Problems
Due date: Fri., April 17 by noon in the drop box on the second oor of Rhodes Hall.
References: Lecture notes; Lab 9; Winston 3.1-3.5, 3.8, 3.9.
The rst four

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 8
Linear Programming The Simplex Algorithm
Due date: Mon., May 4 by 3:00pm in the drop box on the second oor of Rhodes Hall.
References: Lecture notes; Lab 11; Winston 4.1-4.8, 4.13
The rst three pr

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 3
The Shortest Path Problem II.
Due date: Thursday, February 12, by noon in the OR homework drop box.
References: Lecture notes; Lab 3; Winston 8.2, 18.2.
The rst two problems are practice problems,

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 2
The Shortest Path Problem I.
Due date: Thursday, February 5, by noon in the OR homework drop box.
References: Lecture notes; Lab 2; Winston 8.1, 8.2.
The rst two problems are practice problems, DO

ENGRI 1101
Engineering Applications of OR
Spring 2009
HW 1
The Minimum Spanning Tree Problem
Due date: Thursday, January 29, by 4:00pm in the OR homework drop box for ENGRI 1101.
References: Lecture notes; Lab 1; Winston 8.6
The rst two problems are pract

1101 HW 6 solution
Please, let me know on mg342@cornell.edu if you find any mistake. Thanks!
Problem 4:
Starting equality subgraph:
8
a
1
0
8
b
2
0
8
c
3
0
8
d
4
0
4
e
5
0
Weight of the node cover = 36
Weight of current matching = 0
Lets start building an

ENGRI 1101, Spring 2009
1
Homework 1 solutions
Problems 1 and 2
Feel free to stop by if you have any questions.
Problem 3
(a)Yes, indicated spanning tree remains optimal. After changing the cost on edge cfw_1, 5 from 2 to
3, edge cfw_1, 2 is still the che

Summation Notation:
The following two expressions are equivalent:
n
ci xi = c1 x1 + c2 x2 + c3 x3 + . + cn xn .
i=1
The indexing of the summation just says that we start with the term ci xi where
i is 1 and we add up to the term ci xi where i is n.
So, fo

ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 11
The Simplex Algorithm
Name:
Objectives:
Practice the simplex algorithm
Demonstrate unboundedness
Demonstrate the two phases of the simplex algorithm
Key Ideas:
Objective function, constraint

ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 10
The Diet Problem
Name:
Objectives:
Give the students practice in formulating linear programming problems
Introduce students to the idea of linear relaxation
Demonstrate the relationship betwe

ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 9
Linear Programming Formulations
Name:
Objectives:
Practice in formulating linear programming problems
Introduce the idea of linear relaxation
Demonstrate the relationship between an integer pr

ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 7
The Assignment Problem
Name:
Objectives:
Show how to nd maximum weight matching in bipartite graphs using the Hungarian Algorithm.
Key Ideas:
weighted matching, maximum weighted matching
maxim

ENGRI 1101
Engineering Applications of OR
Spring 2009
Lab 6
Maximum Matching in Bipartite Graphs
Name:
Objectives:
Show how to nd maximum cardinality matching in bipartite graphs using maximum ows.
Demonstrate the Augmenting Path Algorithm for nding a m