DETERMINISTIC EQUIVALENTS FOR OPTIMIZING
AND SATISFICING UNDER CHANCE
CONSTRAINTS!
A. Chames
Northwestern University, Bvanston, III
and W. W. Cooper
Carnegie Institute of Technology, Pittsburgh, Pa
(Eeceived December 27, 1961)
Chance constrained programmi
Z00_REND1011_11_SE_MOD4 PP3.QXD
2/21/11
12:49 PM
Page M4-1
MODULE
4
Game Theory
LEARNING OBJECTIVES
After completing this supplement, students will be able to:
1. Understand the principles of zero-sum, two-person
games.
2. Analyze pure strategy games and
ANSWERS to Midterm 2 questions
1. (20 points.) Prove that the intersection of two convex set is also convex. (Hint: use definition of convex
set and formal definition of intersection of two sets: ( ) )
Take two arbitrary points x and y in ( ).
Since x and
Chapter 2
Linear programming
1
Introduction
Many management decisions involve trying to make the
most effective use of an organizations resources.
Resources typically include machinery, labor, money, time,
warehouse space, or raw materials.
Resources m
ANSWERS TO MIDTERM EXAM 1 QUESTIONS
1. (30 pts.)
x1 = the number of soldiers produced per week
x2 = the number of trains produced per week
si+ = amount by which the ith goal level is exceeded.
si- = amount by which the ith goal level is underachieved
The
College of Management, NCTU
Operation Research I
Fall, 2008
Chap 4 The Simplex Method
The Essence of the Simplex Method
Recall the Wyndor problem
Max Z = 3x1 + 5x2
4
S.T. x1
2x2 12
3x1 + 2x2 18
x1, x2 0
8 corner point solutions. 5 out of
them are CPF sol
CHAPTER
LINEAR
PROGRAMMING
AND APPLICATIONS
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.to
Basic Concepts Linear Programming
in
Degenerate
LP's-Graphical Solution
Natural Occurrence Linear Constraints
of
The Simplex Method of SolvingLinear ProgrammingProblems.
104 CHAPTER 2 Systems of Linear Equations and Matrices
where xi , x2 x3 x4 represent the amount, in millions of dollars, that must be produced to satisfy internal and external
demands of the four sectors; N is the total workforce required
for a particular
A Tutorial on Convex Optimization
Haitham Hindi
Palo Alto Research Center (PARC), Palo Alto, California
email: [email protected]
Abstract In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it
64446_CH01xI.qxd
6/22/04
7:41 PM
Page 1
C H A P T E R
1
Decision Analysis
CONTENTS
1.1
A Decision Tree Model and its Analysis
Bill Sampras Summer Job Decision
1.2
Summary of the General Method of Decision Analysis
1.3
Another Decision Tree Model and its A
Kendall Crab & Lobster Case
Summer 2003
Why Learn Decision Trees?
Organize limited data
Make assumptions explicit
Learn useful managerial tools
Enhance thinking skills
Make better decisions
Communicate more effectively
Prepare foundation for further study
Rob J Hyndman
Forecasting using
8. Stationarity and Differencing
OTexts.com/fpp/8/1
Forecasting using R
1
Outline
1 Stationarity
2 Ordinary differencing
3 Seasonal differencing
4 Unit root tests
5 Backshift notation
Forecasting using R
Stationarity
2
Stat
Introductory Time Series with R
Paul S.P. Cowpertwait and Andrew V. Metcalfe
2009
1.
1.1.
Time Series data
Purpose
1. Time series are analysed to understand the past and to predict the future.
2. Kyoto Protocol; Singapore Airlines;
3. Time series methods
Forecasting Methods
Erkan Tre
Forecasting
Forecas(ng is the es(ma(on of the value of a
variable (or set of variables) at some future point in
(me.
Applica(ons for forecas(ng include:
Inventory control / produc0on plann
Rob J Hyndman
Forecasting using
3. Autocorrelation and seasonality
OTexts.com/fpp/2/
OTexts.com/fpp/6/1
Forecasting using R
1
Outline
1 Time series graphics
2 Seasonal or cyclic?
3 Autocorrelation
Forecasting using R
Time series graphics
2
Time series gra
Applied Time Series Analysis
FS 2012 Week 01
Marcel Dettling
Institute for Data Analysis and Process Design
Zurich University of Applied Sciences
[email protected]
http:/stat.ethz.ch/~dettling
ETH Zrich, February 20, 2012
Marcel Dettling, Zurich Uni
Introductory Time Series with R
Paul S.P. Cowpertwait and Andrew V. Metcalfe
2009
4.1.
Basic Stochastic Models
4.1.1.
Purpose
1. The rst is based on an assumption that there is a
xed seasonal pattern about a trend. We can estimate the trend by local avera
Introductory Time Series with R
Paul S.P. Cowpertwait and Andrew V. Metcalfe
2009
2.1.
Correlation
2.1.1.
Purpose
1. In many cases, consecutive variables will be correlated. If we identify such correlations, we can improve our forecasts, quite dramaticall
Applied Time Series Analysis
FS 2012 Week 02
Marcel Dettling
Institute for Data Analysis and Process Design
Zurich University of Applied Sciences
[email protected]
http:/stat.ethz.ch/~dettling
ETH Zrich, February 27, 2012
Marcel Dettling, Zurich Uni
Example
A company is planning the manufacture of a product for
March, April, May and June of next year. The demand
quantities are 520, 720, 520 and 620 units, respectively.
The company has 10 employees at the beginning and can
meet fluctuating production
NAME
1.
MATH 304
Examination 2
Page 1
[18 points]
(a) Find the following determinant. However, use only properties of determinants,
without calculating directly (that is without expanding along a column or row or
otherwise). Explain your answer.
1 3 2 1
5
What is Operation Research?
What is Operation Research?
What is Operation Research?
During World War II, British military leaders asked
scientists and mathematicians to analyze several
military problems, involving
the deployment of radar
the management
Linear programming modeling and examples
Example 1
Each gallon of milk, pound of cheese, and pound of
apple produces a known number of milligrams of
protein and vitamins A, B, and C, as given in following.
The minimum weekly requirements of the nutritiona
OPIM 915
Final Examination Spring 2015
Read at least twice before looking at the exam questions.
Sign the NO CHEATING FORM and indicate the time at which you started the exam. An
exam without this form signed and dated will not be graded.
If you want to g
A Solution Manual and Notes for:
The Elements of Statistical Learning
by Jerome Friedman, Trevor Hastie,
and Robert Tibshirani
John L. Weatherwax
David Epstein
21 June 2013
Introduction
The Elements of Statistical Learning is an inuential and widely studi
DSO 530: Simple Linear Regression
Abbass Al Sharif
Predicting House Value from Percent of Low Income Household
We are going to use a dataset called Boston which is part of the MASS package. It recordes the median value
of houses for 506 neighborhoods arou
Regression and Classication with R
Yanchang Zhao
http:/www.RDataMining.com
R and Data Mining Workshop @ AusDM 2014
27 November 2014
Presented at Australian Customs and UJAT
1 / 44
Outline
Introduction
Linear Regression
Generalized Linear Regression
Decisi
AM
L
y
E = 0 E
AM
L
x
top
3.5
3
E
E
2.5
Error
2
1.5
1
E
Early stopping
out
0.5
E in
0
0
1000
2000
3000
4000
5000
Epochs
6000
7000
8000
9000
10000
bottom
AM
L
AM
L