IE 400: Homework 1 Solution
Due March 15, 17.30 PM
1) Let us define the decision variables:
X1= number of acres of land planted with wheat
X2= number of acres of land planted with corn
X3= number of acres of land planted with barley
X4= number of acres of
IE 400: Homework 2
Due April 2, 17.30 PM
1) Consider the following LP:
Min z= 4 X1 + 2 X2
s.t.
3 X1 + X2 2 7
-X1 - X2 -21
X1 + 2X 2 3 0
X10
X2 unrestricted
a) Solve the above LP by using the graphical method.
b) Solve the above LP by using Big M Method, a
2/16/2012
IE 400: Principles of
Engineering Management
Lecture Notes: 1
1
What is Operations Research (OR)?
OR is a decision making tool based on
mathematical modeling and analysis to aid in
determining how best to design and operate a
system usually unde
14.10.2011
THE SIMPLEX ALGORITHM
Lecture Notes 3
So far, we have studied how to solve two-variable
LP problems graphically.
However, most real life problems have more than
two variables!
Therefore, we need to have another method to
solve LPs with more tha
23.10.2011
THE SIMPLEX ALGORITHM II
Lecture notes: 4
1
The Simplex Algorithm:
To begin the simplex algorithm, convert the LP into
a standard form,
Convert the objective function z=c1x1+c2x2+ cnxn
to the row-0 format:
z-c1x1-c2x2- cnxn=0
2
1
23.10.2011
The
IE 400 PRINCIPLES OF ENGINEERING MANAGEMENT: HW 1
Due Date: Friday, Oct 2, 2015
Note: Pay attention to stating your decision variables precisely in your models with the correct units.
Q1. Three refineries with maximum daily capacities of 6 million, 5 mill
IE 400 PRINCIPLES OF ENGINEERING MANAGEMENT: HW 2
Due Date: Tuesday, Oct 20, 2015 at the beginning of class
Note: There is a total of 4 questions. Good luck.
Question 1. Convert the following mathematical program into an LP.
minimize (max cfw_2x-4, |x|)
s
IE 400 PRINCIPLES OF ENGINEERING MANAGEMENT
HW 1 Solution Set
Q1. (a) This is a cost minimization problem. There is a network of pipelines through which the
gas is going to be transported with the minimum cost while still meeting a set of constraints. We
IE 400-01-02: Principles of Engineering Management Lecture 1 Problem Solutions
Diet Problem solution is on the lecture presentations.
Transportation Problem
Let xij be the electricity ow from PP i to Factory j for i cfw_1, 2 and j cfw_1, 2, 3. The model c
Question 2. Bel Aire Pillow Company
This Week
Next Week
New employment (1)
Fired (4)
Line workers (2)
Line workers (5)
Supervisors (3)
Supervisors (6)
Consider the above relationship graph. Numbers in each box is an identifier. Let xij refer to the number
public class AssignmentProblem cfw_
private static final int UNMATCHED = -1;
private
private
private
private
private
private
int N;
double[][] weight;
double[] px;
double[] py;
int[] xy;
int[] yx;
/
/
/
/
/
/
number of rows and columns
the N-by-N cost mat
11/4/2011
IE 400: INTEGER PROGRAMMING
Lecture Note: 5
1
Integer Programming:
So far, we have considered problems under the following
assumptions:
i.
ii.
iii.
Proportionality & Additivity
Divisibility
Certainty
While many problems satisfy these assumptions
27.02.2012
IE 400 Principles of Engineering Management
The Simplex Algorithm-I:
Lecture Notes 4
So far, we have studied how to solve two-variable
LP problems graphically.
However, most real life problems have more than
two variables!
Therefore, we need
07.03.2012
IE 400 Principles of Engineering Management
The Simplex Algorithm-II:
Lecture Notes 5
The Simplex Algorithm:
To begin the simplex algorithm, convert the LP into
a standard form,
Convert the objective function z=c1x1+c2x2+ cnxn
to the row-0 fo
IE 400: Homework 1
Due March 15, 17.30 PM
1) A farmer has 60 acres of land and he is planning to plant the fields with grain. The available
options are wheat, corn, barley and oat. Each acre of land planted with wheat yields 1 ,500
TL revenue, each with c
IE 400: HW 3
Due By April 26 2012, Thursday
1) Use the Branch-and-Bound method to find the optimal solution to the following IP:
a) Min z = 4X1 + 5X2 - 2X3
s.t.
X1 + 4 X2 + X3 5
3X1 + 2X2 - 2X3 7
X1, X2 0; X1, X2 integer
X3cfw_0,1
(Hint: Without solving P
IE 400: HW 3
Due By April 26 2012, Thursday
1) Use the Branch-and-Bound method to find the optimal solution to the following IP:
a) Min z = 4X1 + 5X2 - 2X3
s.t.
X1 + 4X2 + X3 5
3 X1 + 2 X2 - 2 X3 7
X1, X2 0; X1, X2 integer
X3cfw_0,1
(Hint: Without solving
09.04.2012
IE 400 Principles of Engineering Management
Integer Programming:
Lecture Notes 6
Integer Programming:
So far, we have considered problems under the following
assumptions:
i.
ii.
iii.
Proportionality & Additivity
Divisibility
Certainty
While man
2/21/2012
IE 400: Principles of
Engineering Management
Lecture Notes: 1&2
1
What is Operations Research (OR)?
OR is a decision making tool based on
mathematical modeling and analysis to aid in
determining how best to design and operate a
system usually un
public class AP cfw_
public static void assignment(int n, int cost[][], int sol[])
cfw_
int h, i, j, k, tmpcol, tmprow, m, optcost, n1, temp;
int tmpsetcol=0, tmpsetrow=0, r=0, l=0;
int unexplorecol[] = new int[n + 1];
int labelcol[] = new int[n + 1];
int