Sample Problems in
Mathematical Modeling
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EMG181
Meeting 3
1
2
4
1
Problem 1
ABC Company produces 2 types of airconditioners X and Y.
The company records indicate that each X product sold brings
a profit of P3,000 and tha
Meetings23
Introduction to OR
Introduction to
Mathematical Modelling
EMG181 Quarter 1 SY2012-13
1
Definition of Operations
Research
Concerned with problems on how to conduct
and coordinate the operations of an
organization
Applies scientific methods and t
10/19/2012
Meeting 8
The Simplex Method
Developed by George Dantzig in 1947
Proven to be remarkably efficient in
solving huge problems.
Except for small problems, this method is
always executed on a computer.
LP Simplex Method
EMG181
Quarter 1 SY 2012-1
10/19/2012
Solution Techniques for
Minimization Problem
Meeting 9
1.
LP Simplex Method
The Minimization
Problem
EMG181 Quarter 1 SY 2012-13
2.
1
2.
3.
4.
5.
6.
Modify the constraints so that the RHS of each constraint is
nonnegative. This requires that ea
Lecture 3
Quality Orientations
Dr. Ma. Cecilia C. Carlos
From Previous Lecture:
Tangible Product Orientation
Customers perceive service as a product and
have expectations as to whether its features
meet or exceed expectationsor completely fail
to live up
Lecture 6
SERVICE QUALITY MODELS
SVM125 Quarter 3 SY 2010-11
1
Quality Models help us
understand the complexity of
service quality.
SVM125 Quarter 3 SY 2010-11
2
The Perceived Service Quality Model
(Gronroos, 1982)
Source: Gronroos, C. (1991). Quality Com
SVM125
Lecture 4 Dimensions of Service
Quality
Dr. Ma. Cecilia C. Carlos
10 Dimensions of Service
Quality
Parasumaran, Zeithaml and Berry
identified 10 determinants of service
quality in their research in 1985.
Tangibles
Physical evidence of service
App
Lecture 2
Product Quality vs. Service Quality
Dr. Ma. Cecilia C. Carlos
What is Quality?
From Previous Lecture:
the expected product/service being realized
products/services that are produced and
manufactured to specifications that are
appropriate to th
SERVICE QUALITY METRICS
Service quality isnt about internal
compliance.
Its about satisfying the customer.
SVM125 Quarter 3 SY 2010-11
2
What gets measured, gets
done.
BUT, measurement does not
lead to change when people
are what need to changenot
the met
For services, the assessment of
quality is made during the service
delivery process!
SVM125
Lecture 1 - Introduction
Dr. Ma. Cecilia C. Carlos
VOC + Affinity Diagram
External
Internal, Division
Metric
What is Quality?
fitness for use (Juran)
conformance
Meetings 14-15
Lecture 6
Integer Programming
Graphical Method
Branch and Bound Method
EMG181
QUarter 4 SY1011-12
1
Definition
Integer Programming (IP) models
are characterized by the fact that
some or all of the decision variables
are required to be integ
Meeting 22
Lecture 10
NETWORK MODELS
PERT-CPM
Network Models for Project
Management
Program Evaluation and Review Technique (PERT)
Used if the duration of each project is not known with certainty.
Can be used to estimate the probability that the project
Meeting 9
LP Simplex Method
The Minimization
Problem
EMG181Quarter4SY201112 1
Solution Techniques for
Minimization Problem
1.
2.
Big M Method - called the method of
penalty because artificial variables in the
objective function are penalized by
assigning
Meeting 8
LP Simplex Method
EMG181Quarter4SY2011121
The Simplex Method
Developed by George Dantzig in 1947
Proven to be remarkably efficient in
solving huge problems.
Except for small problems, this method is
always executed on a computer.
EMG181Quarter
Sample Problems in
Mathematical Modeling
0011 0010 1010 1101 0001 0100 1011
IE181
Meeting 4
1
2
4
Problem 1
0011 0010 1010 1101 0001 0100 1011
ABC Company produces 2 types
of airconditioners X and Y.
The company records indicate that each X product sold b
Meeting11
Lecture5
SensitivityAnalysis
EMG181Quarter4SY101112 1
Sensitivity Analysis
Sensitivity analysis refers to an analysis made to determine
how sensitive the optimal solution obtained is to changes in
the input data.
One of the major purposes of sen
Meeting 15
Lecture 7
Integer Programming
Gomory Cutting Plane
Method
Definition
The Gomory Cutting Plane Method is used to solve an IP
model which has more than 2 decision variables.
It uses the Gomory Cut which is an additional constraint
introduced to t
Meeting 21
Lecture 9
NETWORK MODELS
Shortest Route
Minimal Spanning Tree
Maximal Flow
Networks Defined
Networks Defined
An arrangement of paths connected at various
points, through which one or more items move
from one point to another.
Network models hav
Meeting 18
Lecture 8
Goal Programming
Definition
Goal Programming (GP) is a variation of LP that allows for
consideration of a single goal or multiple goals. First identified
by Charnes and Cooper, the technique was further extended
and refined by Ijiri.
Meeting10
DualityandDualSimplex
Method
EMG181Quarter4SY201112 1
DUALITY
With every LP maximization problem, there is an associated
minimization problem, and vice versa. LP problems exist in pairs.
The original problem is called the primal, and the complem
Meeting 23
Lecture 11
Game Theory
Introduction
Introduced in 1944 by John Von Neumann
and Oskar Morgenstern.
Concerned with decisions wherein one
party is in conflict with others resulting to a
competitive situation amongst the various
decision makers.
Meetings23
Introduction to OR
Introduction to
Mathematical Modelling
EMG181 Quarter 4 SY2011-12
1
Definition of Operations
Research
Concerned with problems on how to conduct
and coordinate the operations of an
organization
Applies scientific methods and t