ISyE 3833: Engineering Optimization
October 4, 2015
Solution Midterm 1 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 My company assembles electronic parts and sells the assembled nal products.
1. We sell two nal products. Selling price of
Engineering Optimization ISyE 3833 - Quiz 2 - Solution
1. A metallurgy company makes two grades of bronze: high grade and low grade. Both types
of bronze are made by mixing copper and tin. High grade bronze must be between 70%
and 85% copper (by weight),
ISYE3133A - Engineering Optimization
Midterm 1 - October 1st, 2012
NAME:
GTID:
SIGNATURE:
Time: 1hr 20 minutes
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work.
You will only receive credit for the work written on the exam i
Problem Set 1 - Solutions
This problem set is meant to be an opportunity for you to review Linear Algebra. Chapter 2 of the
textbook/ hints given here should help you to solve these problems.
1
Summation and For all notation
1. Write each of the following
Problem Set 2 - Solutions
Linear Programming
1. Solution:
In this problem we have 4 types of possible suppliers (Abundo (A), Colmado (C), Maximo (M),
and Saboro (S) which we can buy, and also 3 types of coee (Hotel (H), Restaurant (R), Market
(M) that we
Extra Practice Problems for Exam 2
1. For each of the following problems, do the following:
Graph the feasible region (if it exists)
Determine if the feasible region is bounded or unbounded
Solve the LP graphically
If there exists multiple optimal sol
ISyE 3833: Engineering Optimization
September 22, 2015
Lecture 11
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
XOR variables
Given
x1 =
1 if decision 1 is taken
0 otherwise
x2 =
1 if decision 2 is taken
0 otherwise,
we want to model:
x3 =
1 exactly one
ISyE 3833: Engineering Optimization
September 17, 2015
Lecture 10
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Fixed Cost
1.1
An Investment Problem
Solution:
Variables:
xi : equals 1 if production occurs in month i, and equals 0 otherwise, i cfw_1, , 6;
ISyE 3833: Engineering Optimization
September 15, 2015
Lecture 9
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
If-Then Constraints
We want to model the following kind of problem.
I need to manufacture cars such that:
1. the total number of cars is at mos
ISyE 3833: Engineering Optimization
September 10, 2015
Lecture 8
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Scheduling
Solution:
Variables:
xi : number of nurses beginning on day i, for all i cfw_1, 2, , 7
Individual variables restrictions:
For all i
ISyE 3833: Engineering Optimization
September 8, 2015
Lecture 7
Lecturer: Santanu S. Dey
Scribe: Santana, A.
In this lecture we do one more linear program formulation and then we move on to
integer formulation problems.
1
Min Max Formulations
Next is anot
ISyE 3833: Engineering Optimization
November 3, 2015
Solution Midterm 2 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 Consider a linear program given in standard form with 2 rows and 5 variables.
Suppose we know it is feasible.
1. Can the
ISyE 3833: Engineering Optimization
September 1, 2015
Lecture 5
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Transportation
Note that m and n are data, not variables. As well as si , dj and ci,j . This is a problem in a
general form. The particular case
ISyE 3833: Engineering Optimization
August 27, 2015
Lecture 4
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Blending
Solution:
Variables: As some of the data provided are given in terms of percentage it is more convenient
in this problem to dene the vari
ISyE 3833: Engineering Optimization
August 27, 2015
Lecture 4
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Blending
Solution:
Variables: As some of the data provided are given in terms of percentage it is more convenient
in this problem to dene the vari
ISyE 3833: Engineering Optimization
September 3, 2015
Lecture 6
Lecturer: Santanu S. Dey
Scribe: Santana, A.
From now on we will start doing some more complex formulations, for instance, in some
cases we will have to use auxiliary variables as in the next
ISyE 3833, HW 3 Solutions
1. Beerco manufactures ale and beer from corn, hops, and malt. At present, 40 lb of corn, 30 lb of
hops, and 40 lb of malt are available. A barrel of ale sells for $40 and requires 1 lb of corn, 1 lb of
hops, and 2 lb of malt. A
Greenhouse gas emission: 563 tons CO2e
Energy Use: 8.33 TJ
Total Air Emissions(Fugitive + Stack): 178 kg
Water Use: 8900 kGal
Greenhouse gas emission: 1390 tons CO2e
Energy Use: 23.7 TJ
Total Air Emissions(Fugitive + Stack): 327 kg
Water Use: 22300 kGal
P
4
ISyE 3044B/Spring 2016: Solutions to Homework #5
1. See the attached file 3044hw5s16-p1.spfx. Potential improvements include:
(a) add more staff member(s), especially toward the end of a day;
(b) provide incentives to shift arrivals towards the morning
This article has been accepted for publication in Computer but has not yet been fully edited.
Some content may change prior to final publication.
1
Cloud Computing for Mobile Users: Can
Offloading Computation Save Energy?
Karthik Kumar and Yung-Hsiang Lu
Supply Chain Modeling: Logistics
ISyE 3103
Lecture Notes
Instructor: Alejandro Toriello
Version: September 2, 2016
1
Course Overview
A supply chain is a network of organizations, within an enterprise or across several enterprises,
connected through the pr
Supply Chain Modeling: Logistics
ISyE 3103
Lecture Notes
Instructor: Alejandro Toriello
Version: September 2, 2016
1
Course Overview
A supply chain is a network of organizations, within an enterprise or across several enterprises,
connected through the pr
ISyE 3833 - HW 1
Due: Jan 27 / 28
1. (From Winston, Section 2.1, Problem 1) For
1 2 3
A= 4 5 6
7 8 9
find:
1 2
B = 0 1
1 2
and
(a) A,
(e) B T ,
(b) 3A,
(f) AB, and
(c) A + 2B
(g) BA.
(d) AT ,
2. (From Winston, Section 2.1, Problem 2) Only three brands o