NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
Multicriteria Decisions
To introduce the topic of multicriteria decision making, we consider a
technique referred to as goal programming.
This technique has been developed to handle multiplecriteria situations
within the general framework of linear progra
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
1
Overview
Linear Programming Problem
Problem Formulation
A Simple Maximization Problem
Graphical Solution Procedure
Extreme Points and the Optimal Solution
A Simple Minimization Problem
Special Cases
2
Linear Programming
Linear programming has not
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
DYNAMIC PROGRAMMING
Dynamic programming is an approach to problem
solving that decomposes a large problem that may
be difficult to solve into a number of smaller
problems that are usually much easier to solve.
Dynamic programming approach allows break up
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
Inventory Models
Inventory refers to idle goods or materials held by an
organization for use sometime in the future.
Items carried in inventory include;

raw materials
purchased parts
components
subassemblies
workinprocess
finished goods
supplies.
Inve
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
Transportation
The transportation problem arises frequently in planning for the
distribution of goods and services from several supply locations to
several demand locations.
Typically, the quantity of goods available at each supply location (origin)
is li
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
Overview
LP has seen wide application in the field of:
Marketing: To help marketing managers allocate a fixed
advertising budget to various advertising media.
Financial Research: To help financial managers
maximize expected return on their investment or
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
PERT/CPM
PERT
Program Evaluation and Review Technique
Developed by U.S. Navy for Polaris missile project
Developed to handle uncertain activity times
CPM
Critical Path Method
Developed by Du Pont & Remington Rand
Developed for industrial projects for whi
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
Sensitivity Analysis
Sensitivity analysis (or postoptimality analysis) is used to
determine how the optimal solution is affected by changes,
within specified ranges, in:
The objective function coefficients
The righthand side (RHS) values
It helps in a
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
MINIMAL SPANNING TREE
In network terminology, the minimal spanning tree
problem involves using the arcs of the network to
reach all nodes of the network in such a fashion that
the total length of all the arcs used is minimized.
Let us consider the communi
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
EOQ MODEL WITH QUANTITY DISCOUNTS
Quantity discounts occur in numerous situations in
which suppliers provide an incentive for large order
quantities by offering a lower purchase cost when
items are ordered in larger quantities.
Here we discuss how EOQ mod
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
INVENTORY MODEL WITH PLANNED SHORTAGES
A shortage, or stock out, is a demand that cannot be supplied.
In many situations, shortages are undesirable and should be avoided.
In some cases it may be desirablefrom an economic point of viewto plan
for and allow
NED University of Engineering & Technology, Karachi
operation research
MATH 523

Fall 2016
NED UNIVERSITY OF ENGINEERING & TECHNOLOGY
RESOURCE SCHEDULING BY OPERATION RESEARCH
TECHNIQUE FOR TELENOR 4G IMPLEMENTATION AND CIVIL
WORK
REPORT BY:
AYISHA IRSHAD
SEAT NO: UE08
MEM (TRANSPORTATION INFRASTRUCTRE MANGEMENT
OPERATION RESEARCH (EM505)
SUB
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 02
TE [TC]
Digital Signal Processing
Effects of Resampling in Discrete Time Signals
OBJECTIVE: The useful, and fascinating, process of sample rate conversion is a scheme for
changing the original sampling rate of a discrete signal after the s
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 03
TE [TC]
Digital Signal Processing
Effects of Quantization in Discrete Time Continuous Valued Signals
OBJECTIVE: The purpose of this lab is to observe the quantization effects on sampled signals and
to understand how quantization leads to qu
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 06
TE [TC]
Digital Signal Processing
Quadrature Signals: Complex, But Not Complicated
OBJECTIVE: The goal of this laboratory is to gain familiarity with complex numbers and their
use in representing sinusoidal signals such as () = cos(t + ) as
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Assignment02
TE [TC]
Digital Signal Processing
Sampling and Aliasing
Q1)
Q2)
Q3)
Q4)
Q5)
What is stroboscopic effect?
Are there any useful applications of aliasing effect?
What is the usage of anti aliasing in sounds, images and video games?
Is there any
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 07
TE [TC]
Digital Signal Processing
Understanding of Time & Frequency Domain
OBJECTIVE: The goal of this laboratory is to develop the understanding of time and frequency
domains, their visualization and their usage.
INTRODUCTION:
Complex expo
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 04
TE [TC]
Digital Signal Processing
DiscreteTime Convolution
OBJECTIVE:
The goal of this laboratory is to gain familiarity with the importance of Convolution
technique in signal processing and to also verify the different characteristics of
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 01
TE [TC]
Digital Signal Processing
Effects of Sampling and Aliasing in Discrete Time Signals
OBJECTIVE: The purpose of this lab is to study the relationship between discretetime and
continuoustime signals by examining sampling and aliasing
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 08
TE [TC]
Digital Signal Processing
Continuous Time Fourier Series [CTFS] Properties and Applications
OBJECTIVE: The goal of this laboratory is to observe and learn about Fourier Series and Fourier
Transform properties and their applications.
NED University of Engineering & Technology, Karachi
Intro to geo digits
MATH 989

Fall 2016
Lab Session 05
TE [TC]
Digital Signal Processing
DiscreteTime Correlation
OBJECTIVE: In this laboratory, we will examine a discrete time correlation method which
is most widely used in signal processing for detection purposes.
INTRODUCTION:
Correlation i