The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework #4
Due Monday 12 December.
1. Recall the AF recruiting MOLP from Homework 2:
The Air Force (AF) is evaluating a new marketing plan for recruiting women and
minorities. A television ad geared towards women has been developed, and the AF
e
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 2 Section 1.4
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Mappings
Develop America's Airmen Today . for Tomorrow
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 2 Section 1.4
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Mappings
Develop America's Airmen Today . for Tomorrow
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 3 Section 1.4, 2.12.3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Cones
Develop America's Airmen Today . for Tom
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 3 Section 1.4, 2.12.3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Cones
Develop America's Airmen Today . for Tom
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 3 Section 1.4, 2.12.3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Cones
AFIT
Develop America's Airmen Today . fo
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 4 Section 2.42.5
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Alternate views of Efficiency and
Domination
Develo
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 3 Section 1.4, 2.12.3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Cones
AFIT
Develop America's Airmen Today . fo
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 4 Section 2.42.5
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Alternate views of Efficiency and
Domination
Develo
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 5 Chapter 3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Weighted Sum Method
Develop America's Airmen Today . for
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 5 Chapter 3
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Weighted Sum Method
Develop America's Airmen Today . for
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Where were going
Develop America's Airmen Today . for Tomorrow
Concept Review & Notation
Types of Efficiency
Introduction:
What is Scalarization?
Why is it used?
Motivation for additional Scalarization Techniques
Three scalarization techniques
The Ep
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Weighted Sums
Idea
Write a single objective as a linear
combination of multiple objective functions
F ( x) = li * fi ( x)
li = weight given to ith objective function
Typically li =1
Constraints unchanged
Notation
Y
= a vector of weights and p
S (l
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Weighted Sums
Idea
Write a single objective as a linear
combination of multiple objective functions
F ( x) = li * fi ( x)
li = weight given to ith objective function
Typically li =1
Constraints unchanged
Notation
Y
= a vector of weights and p
S (l
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 13 Chapter 8.2
Capt Christopher Arendt
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
Multiobjective Combinatorial
Optimization
Develo
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 1 Sections 1.1 1.2
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Intro to MCO
Develop America's Airmen Today . for
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
Develop America's Airmen Today . for Tomorrow
OPER 621
Lecture 1 Sections 1.1 1.2
Dr Jeff Weir
Air University: The Intellectual and Leadership Center of the Air Force
Integrity  Service  Excellence
AFIT
Intro to MCO
Develop America's Airmen Today . for
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework #4
Due Monday 12 December.
1. Recall the AF recruiting MOLP from Homework 2:
The Air Force (AF) is evaluating a new marketing plan for recruiting women and
minorities. A television ad geared towards women has been developed, and the AF
e
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework #4 Solutions
1. Recall the AF recruiting MOLP from Homework 2:
The Air Force (AF) is evaluating a new marketing plan for recruiting women and
minorities. A television ad geared towards women has been developed, and the AF
estimates each
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework # 3
1. Solve the following lexicographic optimization problem with linear objectives and linear
constraints:
f (x ) ( f1 (x)
x1 x2 x3 , f 2 (x) x2 , f 3 ( x)
x1 2 x2 )
lexmin
Subject to
x1 x2 1
x1
x2
x3
4
x1 , x2 , x3 0
What is the optim
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework 1
Due Wednesday , October 19
1. Provide a general description of a real world multicriteria optimization problem (MOP).
2. Relations, mappings and functions:
a. Give an example of a bijective (onetoone and onto) function f : .
b. Is it
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework 1
Due Wednesday, October 24th
1. Provide a general description of a real world multicriteria optimization problem (MOP).
2. Relations, mappings and functions:
a. Give an example of a bijective (onetoone and onto) function f : .
b. Is i
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework #4
1. Recall the AF recruiting MOLP from Homework 2:
The Air Force (AF) is evaluating a new marketing plan for recruiting women and
minorities. A television ad geared towards women has been developed, and the AF
estimates each showing of
The University of Texas at San Antonio San Antonio
OPER 641

Spring 2014
OPER 621
Homework 2
Due with Homework 2 (Wednesaday, 2 Nov)
1. Find the ideal and nadir points, y I and y N , respectively, for the MOP in Exercise 1.1 on
page 20 of textbook, which is as follows:
Minimize
Subject to
f ( x ) = ( f1 ( x ) = 5 x 2 , f 2 ( x