Department of Industrial Engineering & Operations Research
IEOR 160: Operations Research I (Fall 2014)
Manpower planning
Certain types of facilities operate seven days each week and face the problem of allocating person power
during the week as stang requ
Homework 1 Solution
Problem 40
Define:
number of units of A produced.
number of units of B produced.
number of units of raw materials purchased.
number of units of raw materials produced.
Note that producing a unit of B requires 2 hrs of assembly 1, 2 hrs
Homework 4 Solution
Page 502-problem 3:
Define
Define
,
as the number of product produced.
to denote whether we produce any product ,
.
Then the formulation is
is a very large number.
Page 503-problem 10:
Assume
is a very large number:
where is a binary d
1
SOLUTIONS TO MP CHAPTER 5 PROBLEMS
SECTION 5.1 1. Typical isoprofit line is 3x1+c2x2=z. This has slope -3/c2. If slope of isoprofit line is <-2, then Point C is optimal. Thus if -3/c2<-2 or c2<1.5 the current basis is no longer optimal. Also if th
Department of Industrial Engineering & Operations Research
IEOR 160: Operations Research I (Fall 2014)
Homework 1 Solutions
Due: Friday, Sept 12th
Question 1. We are helping Sheldon plan his upcoming meals. To simplify the problem, we assume
that there ar
Department of Industrial Engineering & Operations Research
IEOR160 Operations Research I
Final Exam
Fall 2005
Name:
Grade:
1. (15 points) For an inequality constrained optimization problem with concave objective function f , suppose none of the constraint
Department of Industrial Engineering & Operations Research
IEOR 160: Operations Research I (Fall 2014)
Homework 1
Due: Friday, Sept 10th
Question 1. We are helping Sheldon plan his upcoming meals. To simplify the problem, we assume
that there are three fo
IEOR 160 - Practice Final
Fall 2008
Problem 1 Three cities are located at the vertices of an equilateral triangle. (That is, the distance between any two cities is the same as the distance between any two other cities.) An airport is to be built at a loca
Department of Industrial Engineering & Operations Research
IEOR 160 (Fall 2014)
1
The general network ow problem
A common scenario of a network-ow problem arising in industrial logistics concerns the distribution of a
single homogenous product from plants
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
1
1.1
Linear programming modeling examples
Bakery problem
You are the owner of Cal Bakery, that can bake: cookies, breads or cakes. You have limited reso
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Integer Linear Programming
An integer linear program is a linear program with the added restriction that the decision variables must have integer values.
Introduction to Integer Programming
Integer programming models
1
IEOR160 2014
A 2-Variable Integer program
maximize
3x + 4y
subject to
5x + 8y 24
x, y 0 and integer
What is the optimal solution?
2
IEOR160 2014
The Feasible Region
4
5
Question: What is the
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Critical Path Method (CPM)
Notice: This is using Activity On Node, AON, and not Activity On Arc, AOA, as in textbook.
1
Department of Industrial Engineering & Operations Research
IEOR 160: Operations Research I (Fall 2014)
Homework 9
Due: Friday, Nov 7th
For each of the four questions, sketch the associated network and label the nodes and arcs with the appropriate
quantiti
Department of Industrial Engineering & Operations Research
IEOR 160: Operations Research I (Fall 2014)
IEOR160 Course Review
(Not necessarily comprehensive!)
1. Optimization Model Formulation (Homework 1-5)
Formulating LP and IP models
Logical constrain
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
1
1.1
Linear programming modeling examples
Bakery problem
You are the owner of Cal Bakery, that can bake: cookies, breads or cakes. You have limited reso
Using Cutting Planes
y
Optimum
(integer)
solution
P
x
Example. Minimize x + 10y
subject to x, y are in P
x, y integer
IEOR160-2014
Optimum
fractional
(i.e. infeasible)
solution
1
Using Cutting Planes
Idea: add
constraints that
eliminate fractional
solutio
Representing Non-linear functions
Suppose we are to buy laptops and
desktop computers, subject to
some demand requirements.
Suppose that the cost of
computers is as follows:
$2,000 each if you buy 1 to 10
$1,800 for each computer from 11 to 25
$1,700 for
Other Search Techniques
Instead of taking derivatives (which may be
computationally intensive), use two function
evaluations to determine updated interval. Can use
Golden section (as in book), or here, Fibonacci search
Fibonacci Search
Step 1. Begin with
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Inventory/Production Problem as Transportation Problem
Sailco Corporation must determine how many sailboats should be produced during each of the next fo
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Consider the CPM analysis of the Designer Gene Project given below.
The workforce requirements for the Designer Gene Project are given in the table below
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Leasing of warehouse space problem
A rm has discovered that its own warehouses will not be sucient to meet its space requirements
over the next ve months
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Minimum Spanning Tree
The minimum spanning tree problem was rst proposed by the Czech mathematician Otakar Boruvka. This idea originated from the problem
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
1
Another example of the general network ow problem
1.1
Problem description
A company manufacturing chairs has four plants located around the country. Th
IEOR 160: Operations Research I (Spring 2015)
Midterm, March 2nd, 2015
Professor Dorit Hochbaum
Name:
SID :
Answer each question in the spaces provided. If you feel you need more space to show your work,
use the back of the previous page. Please present y
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2014)
Class time & location
Lecture: MW 10-11A, 3108 ETCHEVERRY
Discussion: F 10-11A or F 11-12P, 3107 ETCHEVERRY
Instructor
Professor Dorit S. Hochbaum
E-mail
Department of Industrial Engineering & Operations Research
IEOR 160 Operations Research I (Fall 2012)
Class time & location
Lecture: MW 2-3P, 150 GSPP (Goldman School of Public Policy)
Discussion:F 8-9A, 3113 Etcheverry or F 11-12P, 3107 Etcheverry
Instru