Practice Final AEM 412
You should be able to finish your test in 2:30 minutes comfortably. Read the questions carefully. For each question read all its subquestions before starting answering it. I also suggest that you read all the questions before start
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
(slides adapted from: M. Hilliers, J. Orlins, and H. Sarpers)
Example of Sensitivity Analysis and
Economic Interpretation of Duality
Sensitivity Analysis: Computer Analysis
Glass Example
x1
Computational Methods for Management and Economics
AEM 4120

Fall 2014
1 
2 
3 
and y1 + y2 + y3 + y4 + y5 + y6 = 1
[TAs do not give the solution to the students directly just tell them to use
auxiliary binary variables].
Computational Methods for Management and Economics
AEM 4120

Fall 2014
`AEM 4120
Homework Assignment 5
Due date: Thursday, November 6 (via blackboard)
1.
Use the branch and bound algorithm presented in class to solve the
following problem:
2.
The Research and Dev
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM 4120
Homework Assignment #4
Due date: Thursday, October 23rd (submit it via Blackboard)
Use Excel or any LP package (e.g., MPL, AMPL, or Lindo) for the problems that require
solving the LP. The solution should include the values for the decision varia
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM 4120
Homework Assignment 2
Due date: Thursday, September 11th, 1 PM
(Submit it via blackboard)
Directions: This homework consists of answering questions about linear programming
problems. Make sure that your work is original and completed individually
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM 4120
Homework Assignment 1
Due date: Thursday, September 4th (at the beginning of class)
United Airlines Station Manpower Planning System Summary: Key Points
Background:

highly competitive industry: minimizing costs is essential to firms survival
ex
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM 4120
Homework Assignment 7
Due date: Thursday December 4th (1 pm, via blackboard)
1  The sales manager for a publisher of college textbooks has six traveling
salespeople to assign to three different regi
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Practice Final AEM 412
You should be able to finish your test in 2:30 minutes comfortably.
Read the questions carefully. For each question read all its subquestions
before starting answering it. I also suggest that you read all the questions
before start
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Midterm AEM 412
Duration: 1:15 minutes
Solution
Your Name:
_
Your Email Address:
_
You should be able to finish your test in 1:15 minutes comfortably.
Read the questions carefully. For each question read all its subquestions
before starting answering it.
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Practice Midterm AEM 4120
Duration: 1:15 minutes
Your Name:
_
Your Email Address:
_
You should be able to finish your test in 1:15 minutes comfortably.
Read the questions carefully. For each question read all its subquestions
before starting answering it
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM 4120
Homework Assignment #4
Due date: Thursday, October 23rd (submit it via Blackboard)
Use Excel or any LP package (e.g., MPL, AMPL, or Lindo) for the problems that require
solving the LP. The solution should include the values for the decision varia
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Solving LP Algebraically:
Simplex
Simplex as an algebraic procedure:
augmented standard form with slack variables
System of m (3) functional constraints and n (5) variables (original +
slack
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM4120  2016
Homework 3
Due: Thursday, Sep 27th, 1:25 PM
Submit via Blackboard
Directions: This homework consists of answering questions about Simplex
Method. Make sure that your work is original and completed individually.
1
Problem 1: Simplex Method (
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM4120
Computational Methods for
Management and Economics
Carla P. Gomes
Module 1
Introduction
Overview of this Lecture
Course Administration
Course Themes, Goals, and Syllabus
Computational modeling and solution
approaches
Mathematical Programs
Int
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Duality
Duality: Guessing upper bounds on
the value of the objective function
Let x1 = the number of doors to produce
x2= the number of windows to produce
Maximize Z= 3 x1 + 5 x2
subject to
x1
Computational Methods for Management and Economics
AEM 4120

Fall 2014
An Example of Simplex Method
Solve the following problem using Simplex Method:
maximize
Z = x1 + 2x2
subject to: x1 + 3x2 8
x1 + x2 4
x1 0, x2 0.
(a) Use graphical analysis to identify all the cornerpoint feasible (CPF) solutions for this model.
Answer.
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
LP Complexity
Different LP solvers
Revisiting the LP assumptions
LP Complexity
Complexity of Simplex Method
Complexity of simplex we can measure it in terms of
its runtime or e.g., number
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Lecture 3
Outline
Recap of LP Graphical Solution and Special
Cases
LP Terminology
Sensitivity Analysis
Finding the Optimal Solution
Production rate
W
for windows
Our objective function is:
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Lecture 4
Outline
Sensitivity Analysis additional comments
Additional LP example
Main LP Categories (intro)
Sensitivity Analysis
How does the optimal solution change
when we change the par
Computational Methods for Management and Economics
AEM 4120

Fall 2014
This article was downloaded by: [128.84.124.29] On: 25 August 2016, At: 10:18
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
INFORMS is located in Maryland, USA
Interfaces
Publication details, including instructions for
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Lecture 10
Duality and Sensitivity Analysis
Economic Interpretation of Duality
Sensitivity Analysis
How would changes in the problems objective function
coefficients or righthand side value
Computational Methods for Management and Economics
AEM 4120

Fall 2014
AEM4120  2016
Homework 2
Due: Thursday, Sep 15th, 1:25 PM
Submit via Blackboard
Directions: This homework consists of answering questions about linear
programming problems. Make sure that your work is original and completed
individually.
1
Web Mercantile
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Lecture 5
Main Categories of LP problems:
ResourceAllocation Problems
Costbenefittradeoff problems
DistributionNetwork Problems
Mixed Problems
Distribution Network Problems
The Big M Dist
Computational Methods for Management and Economics
AEM 4120

Fall 2014
Computational Methods for
Management and Economics
Carla Gomes
Lecture 2
Reading: Chapter 2, and 3.1 of textbook
Outline of Lecture
Mathematical Programs
Intro Linear Programming:
Example Wyndor Problem
Graphical Solution
Sensitivity Analysis
Specia