IE426 Optimization models and applications
Fall 2013 Homework #3
This homework accounts for 5% of the nal grade. It is due on
Thursday, October 31st, in class. There are 20 points available.
For all problems where an AMPL model is required, include the
mo
ISE 426
Optimization models and applications
Lecture 16 October 24, 2013
More IP
a xb c xd
Extreme points and relaxations
Fun with logic
Consider propositions a, b, c . . ., all in cfw_T, F. They can all be
modeled with binary variables xa , xb , xc . . .
IE426 Optimization models and applications
Fall 2012 Quiz #2, November 15, 2012
First name
Last name
Lehigh email
You have 75 minutes. This quiz accounts for 10% of the nal grade. There
are 40 points available. Please write clear and concise statements. U
IE426 - Optimization models and application
Fall 2013 - Homework #3 Answer
1
Goal Programming
1. Check that the original LP is infeasible by solving it with AMPL.
Answer: we can build the LP model in AMPL as
set row = 1.5;
# number of linear constraints
s
ISE426 Optimization models and applications
Fall 2013 Homework #2
This homework accounts for 5% of the nal grade. It is due on
Thursday, October 3, in class. There are 20 points available. For all
problems where an AMPL model is required, include the mode
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
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 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 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
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
IE 426
Optimization models and applications
Lecture 3 September 6, 2016
I
Upper & lower bounds
I
Relaxations: an example
I
Linear programming
Convex constraints
I
A constraint g(x)b, with g : Rn R, defines a subset S of
Rn , that is,
S = cfw_x Rn : g(x) b
IE 426
Optimization models and applications
Lecture 2 September 1, 2010
Convexity; Relaxations; Lower and upper bounds.
I
Winston, chapter 1, or
I
Winston & Venkataramanan, chapter 1, or
I
Hillier & Lieberman, chapter 2.
Convexity
Convex sets
Def.: A set
ISE 426
Optimization models and applications
instructor:
phone:
office hrs:
email:
web page:
Katya Scheinberg
Mohler Lab #479
(610) 758 4039
after class on Tuesdays (if I am available)
and by appointment
katyas at lehigh dot edu
http:/coral.ie.lehigh.edu/
IE 426
Optimization models and applications
Lecture 5 September 15, 2016
I
AMPL
I
Q & A session
I
Transportation problem + AMPL
Reading:
WV Transportation problem
Chap. 1 of draft found here
http:/www.4er.org/CourseNotes/
AMPL
I
a modeling language for op
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
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 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
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
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
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 final grade. There are 40 points available. Please write clear
ISE 426
Optimization models and applications
Lecture 10-11 October 1, 2015
I
I
I
basic feasible solutions
simplex method
connection with dual variables
Reminders:
I Homework #2 is due in class 10/06. No late homework
will be accepted!
I Quiz on 10/08, pra
ISE 426
Optimization models and applications
Lecture 9 September 29, 2015
Duality, continued
Reading:
W.&V. Sections 6.56.7, pages 295-308
H.&L. Section 6.16.4, pages 151-169
Reminders:
Quiz on 10/08, practice on 10/06.
Primal problem, dual problem
Primal
ISE 426
Optimization models and applications
Lecture 22 November 20, 2014
Nonlinear Programming (NLP)
Least squares example
Quadratic Programming
Reading:
Winston&Venkataramanan, Ch. 12 up to 12.4; 12.10
Nonlinear Programming (NLP)
Consider the continuous
IE426 Optimization models and applications
Fall 2016 Homework #3
This homework accounts for 5% of the final grade. It is due on
Friday, November 18 by 04:30 pm. There are 25 points available.
Please give detailed answers for full credit For all problems w