TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 4
SENSITIVITY ANALYSIS
1. A Graphical Introduction to Sensitivity Analysis
Sensitivity is concerned with how changes in an LPs parameters affect
the LPs optimal solution.
2. Example: The Giapetto problem in Wi
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 2
Example Problem
A new company Wyndor Glass Company has:
3
2
Products =
plants
products.
making
8' glass door : product 1
4 6' window : product 2
Resources : Production Capacities in 3 plants are as follow
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 1
Introduction
Operations Research (OR) / Management Science
A scientific approach to decision that involves the operations
of organizational systems.
The art of giving bad answers to problems which otherwise
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 3
Dr. Lazar Spasovic
THE SIMPLEX METHOD
An algorithm will solve an LP if it:
(a) demonstrates that there is a feasible solution
(b) determines an optimal solution
Unbounded feasible region: A feasible region t
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 10
THE METHOD OF LEAST SQUARES
Given a set of n points (x1, y1), (x2, y2), .(xn, yn) and a positive integer m, which polynomial of
degree m is closest to the given points? Lets focus on linear polynomial in th
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 8
STOCHASTIC PROCESSES AND
QUEUING THEORY
Review of Probability Theory
Event a specified outcome of a random phenomenon
Simple event: single possible outcome
3 heads from 3 coins HHH
Compound event:
2 or more
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 7
Nonlinear Programming (NLP)
Examples:
Product Mix Problem with Price Elasticity
p(x)
price
P(x)
profit
P(x)=x[p(x)-c]
c
Unit cost
Amount
x demand
x
Firms profit P ( x ) = x * p( x ) c * x (a nonlinear functi
TRAN/CE 650
URBAN SYSTEMS
ENGINEERING
Lecture 6
Networks Models
Definition:
Graph:
Nodes or Vertices
Arcs or Edges
Network: Graph with Flow
Chain: A sequence of edges connecting i and j.
Path: Directed Chain
Connected Graph: If there exists ( ) a chain co
Big M example:
Problem: We have 3 different liquids that can be blended to make a 5-oz
cocktail.
-Each unit of liq1 has 2 units alcohol and 3 units juice. Cost is $3.
-Each unit of liq2 has 3 units alcohol and 1 unit juice. Cost is $2.
-Each unit of liq3