HW 1 Solutions
1) At a company workers work 8 hour days. In a certain month 8600 units were produced by a
work group of 20 workers. There were 21 work days in the month. (a) What is the labor
productivity ratio for this month? (b) In the next month, a red
IE 111
Fall 2015
Exam 3
NAME_Solutions_
Instructions
1.
2.
3.
4.
5.
6.
7.
You have 50 minutes to complete this test.
The test is open book, open notes.
Calculators are allowed. Cell phones are not allowed.
You must show sufficient work to receive credit.
IE 111
9:00 Section
Exam 2
Fall 2007
NAME_
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately
Partial credit will be given, but not without sufficient support
Complex
IE 111
Exam 1.1
Fall 2015
NAME_Solutions_
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately. Partial credit will
be given, but not without sufficient support. However,
IE 111 Fall 2011
Homework #5
Due Friday October 14 in class
Question 1
Let X be a Binomial random variable with n=100, p=.7
(a) Which one of the following Excel formulas will calculate Pr(X10) ?
=BINOMDIST(100,10,.7,TRUE)
=BINOMDIST(10,100,.7,TRUE)
=BINOM
NAME_Solutions_
IE 111
Monday 11/23 Exam 4
Fall 2015
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately
Partial credit will be given, but not without sufficient suppor
IE 111
Fall 2007
9:00 Section
Exam 3
NAME_
Instructions
1.
2.
3.
4.
5.
The test is open book, open notes.
You must show sufficient work to receive credit.
You do not need to interpolate in any tables you use. Just use the closest value.
All probabilities
IE 111
Exam 2a Fall 2015
NAME_Solutions_
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately. Partial credit will be given,
but not without sufficient support.
Each of
IE 111
Final Exam
Fall 2009
Solutions
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately
Partial credit will be given, but not without sufficient support
3 hours (180
IE 111 Fall 2011
Homework #3
1. Learn the concept of conditional probability by Venn diagram
a) If P(A|B) =1, must A=B? Draw a Venn diagram to explain your answer?
Answer:
From the Venn diagram, it satisfies P(A|B)=1, but AB.
b) Suppose A and B are mutual
lSE426 ~ Optimization models and applications
Fall 2014 e Quiz #2, November 11, 2014
First name
Last name
Lehigh email
You have 75 minutes. There are three problems. This quiz accounts for
10% of the nal grade. There are 40 points available.
ISE426 Optimization models and applications
Fall 2013 Quiz #1, October 8, 2013
First name
Last name
Lehigh email
You have 75 minutes. There are two problems. This quiz accounts for
10% of the nal grade. There are 40 points available. Please write cl
Homework 2
1. Consider the 1 | chain |
jobs
wj
pj
1
0
3
2
18
6
3
12
6
4
8
5
5
8
4
wj Cj problem with the following data
6
17
8
7
16
9
The jobs are subject to precedence constraints which take the form of chains:
12
345
67
Find all optimal sequences.
2. Fi
Homework 4
1. Consider MPS of 4 jobs and a processing environment of 4 machines.
jobs
p1j
p2j
p2j
p4j
1
6
2
4
8
2
4
10
8
2
3
6
4
0
6
4
8
6
2
6
a) Apply the PF heuristic to find a cyclic schedule. Choose job 1 as the initial job and compute
the MPS cycle t
Homework 1
Problems 4.3, 4.6(a), 4.8 from the book. Note that there is a typo in
problem 4.8. It should read Exercises 3.2 and 4.4 instead of Exercises
3.1 and 4.4. See scans for texts and pictures: the precedence graph used in
problems 4.3 and 4.6 is sho
Report on News Paper Delivery
Chaitanya, Avineesh, Mihir, Purvesh & Chandan
15th December 2015
Chapter 1
Introduction
We were given the coordinates of 60 customers and a depot. The objective of the problem
is to deliver the newspapers to all the 60 custom
Midterm 15
1. Consider the 1 | chain |
jobs
wj
pj
1
10
3
2
18
6
3
12
3
4
9
5
wj Cj problem with the following data
5
8
4
The jobs are subject to precedence constraints which take the form of chains:
12
345
Find all optimal sequences.
1
2. Consider the 1 |
ISE 426
Optimization models and applications
Lecture 13 October 6, 2016
I
MinMax
I
Goal programming
I
Winston & Venkataramanan, pages 191-194
Minimizing the maximum of a set of linear functions
Consider an optimization problem of the form
min maxcfw_
2x1
ISE 426
Optimization models and applications
Lecture 5 September 13, 2016
I
Production planning problem
I
Shortest path problem
I
Optimization on graphs
Reading:
WV 3.10, 7.1 and 8.2
Example: Production planning
A small firm produces plastic for the car i
ISE 426
Optimization models and applications
Lecture 22 November 17, 2016
I
Nonlinear Programming (NLP)
I
Least squares example
I
Quadratic Programming
Reading:
I
Winston&Venkataramanan, Ch. 12 up to 12.4; 12.10
Nonlinear Programming (NLP)
Consider the co
ISE 426
Optimization models and applications
Lecture 21 November 15, 2016
I
Intro to Stochastic Programming (SP)
Reading:
I
Book by Kall & Wallace (pdf Chapter 1 up to 1.6)
I
J.R. Birge, F. Louveaux, Stochastic Programming
Decision problems under uncertai
IE 426
Optimization models and applications
Lecture 19 November 15, 2010
I
Minimum Spanning Tree
I
Network Design
Announcements:
I
Case studies will be assigned by the end of the week. Form
into groups of 4.
The Minimum Spanning Tree Problem
I
Given a gra
ISE 426
Optimization models and applications
Lecture 17 October 27, 2016
I
I
I
Good and bad formulations
Branch&bound for MILP
Examples of B&B
Reading:
I Hillier & Lieberman, Chapter 13, 13.4 to 13.5
I Winston & Venkataramanan, Chapter 9
I Winston, Chapte
ISE 426
Optimization models and applications
Lecture 18 November 8, 2016
I
The Traveling Salesperson Problem (TSP)
I
The Quadratic Assignment Problem (QAP)
I
Piecewise linear functions
The Traveling Salesperson Problem (TSP)
A salesperson has to visit n c
ISE 426
Optimization models and applications
Lecture 7 September 20, 2016
Duality
Reading:
I
W.&V. Sections 6.56.7, pages 295-308
I
H.&L. Section 6.16.4, pages 151-169
First: playing with equations and inequalities
I
Trivial: if a b and c d, then a + c b
ISE 426
Optimization models and applications
Lecture 20 November 10, 2016
I
Bin Packing Problem
I
Cutting Stock Problem
I
Column generation
The bin packing problem
I
Given a set of N bins of volume V and ni objects of
volumes vi , i = 1, . . . , n.
I
We w
NAME
IE 111
_
Exam 2 * 8:00 Section * Fall 2015
Instructions
Open book, open notes
Clearly indicate your answer
You must show all relevant work and justify your answers appropriately. Partial credit will
be given, but not without sufficient support.
E
IE 111
Note Set #5 Random Variables
Random Variables
The concepts of random variables and probability distributions are extremely important
in probability and statistics. Once you see clearly in your mind what they are, and how
they work, you will be in g