Fundamentals of Quantitative Analysis

Fundamentals of Quantitative
Analysis
Theoretical Representation

What is Quantitative Analysis?
Quantitative Analysis is the systematic,
method oriented study of the basic structure,
characteristics, functions and relationship of
an organization to provide the executive with
a sound, scientific and quantitative basis for
decision making.
-------E.L. Arnoff & M.J. Netzorg

Perspective of Quantitative Analysis
QA can be viewed from Three Perspectives
1. Its Characteristics
2. Its Process
3. Its Tools

The Characteristics
The major characteristics are:
• A primary focus on managerial decision making.
• The application or employment of a scientific approach.
• Problems and decisions are viewed from a system perspective.
(Its system orientation)
• The use of methods and knowledge from several disciplines.
(The use of interdisciplinary team)
• Application of formal mathematical model. (Scientific method)
• Human factors

Quantitative Analysis Process / Approach: The
quantitative analysis approach consists of
a. Defining the problem
b. Develop a model
c. Acquiring input data
d. Develop a solution
e. Testing the solution
f. Model validation and sensitivity analysis
e. Implementation

The Tools
QA works with tools that enable to analyze a problem to predict the future
development of the problem and to suggest the best result. Some standard
tools are:
• a. Linear programming model for allocation problem.
• b. Statistical techniques for taking decisions under probability
• c. Decision tables: The solutions of allocation and investment problems
can be presented in a tabular form known as a decision table.
• d. Decision trees: The extension of decision tables for situations
involving several decision periods takes the shape of a “tree”.

The Tools
• e. Game theory: Game theory provides a systematic approach to
decision making in competitive environments and a framework for the
study of conflict.
• f. Forecasting: To predict the outcome of managerial decisions.
• g. Mathematical programming: M. Programming is used to
maximize the attainment level of one goal subject to a set of
requirements and limitations.
• h. Network model: This tools are used for planning and controlling
complex projects, such as PERT, CPM etc.
• I. Inventory model: It is used for certain inventory control problems.

Question: What do you mean by problem
solving and decision making?
A decision is the conclusion of a process by which one chooses between two
or more available alternative courses of action for the purpose of attaining a
goal(s). the process is called decision making.
Decision making and problem solving involves 4 steps:
1. Defining the problem. 2. Searching for alternative courses of action.
3. Evaluating the alternative. 4. Selecting one alternative.
Actually problem solving involves the total process that is the 4 steps. The
specific step 4, i.e ‘selecting an alternative’ is the decision or solution of the
problem.

Question: What is Model? What are the
different types of Model?
A model is a simplified, substantially reduced and some what
abstracted representation of reality.
Types of model: A model can be classified as following types:
1. Verbal model: Reality expressed in textual form is called a verbal
model.
Example: The higher the price of commodity X (Þx) the lower will be its quantity
demanded (QDx) of time, other factors remaining constant. i.e. if price increased
than demand decreased.

2. Mathematical model: Reality expressed in mathematical symbols is called
mathematical model.
Example:
QDx = f (Þx) , Cet. Par
- If Þx ↑ then QDx ↓
- If Þx ↓ then QDx ↑
Cet. Par
Where,
Þx = Price of commodity X
QDx = Quantity demanded of commodity X
Cet. Par = Ceteris Paribus, meaning other factors
remain unchanged.

3. Graphical model: Reality expressed in graphical form is called a graphical
model.
Þx Demand Curve
D
QDx
4. Image model: Reality expressed in photograph, paintings is called a Image
model. Example: Any photograph
5. Iconic model: Iconic models are the physical representation of reality.
Example: Toy car, teddy bear, Architect’s model of a building.
6. Analogue model: Models represent reality to certain extent, and deviate
from reality in certain other extent. Example: Fighter planes, Robots etc.

Mathematical models categorized by risk:
Deterministic Model: Some mathematical models do not involve risk or
chance. We assume that we know all values usd in the model with
complete certainty. These are called deterministic models. A company, for
example, might want to minimize manufacturing costs while maintaining a
certain quality level. If we know all these values with certainty, the model is
deterministic.
Probabilistic Model: Other models involve risk or chance. For example,
the market for a new product might be “ good” with a chance of 60% ( a
probability of 0.6) or “not good” with a chance of 40% ( a probability of
0.4). Models that involve chance or risk, after measured of a probability
value, are called probabilistic models.

How to develop a Quantitative Analysis Model?
We know, Profit = Revenue – Expenses
Profit = ( Price per unit)(Number of units sold) – ( Variable cost per unit)
(number of units) – Fixed Cost.
i.e P = Pq- Vq –F,
now If P = 10, V = 5, F = 1000
Then P = 10q – 5q -1000 = 5q -1000
• Ex: If sales i.e q = 0 , Then P= -1000 (loss 1000)
If sales, i.e, q =1000, Then P = 4000
At BEP, P = 0, which implies, 0 = 5q – 1000
q = 200 units, which is called Break Even Quantity.

Question: What are the advantages of
Mathematical Modeling?
1. Models can accurately represent reality. If properly
formulated, a model can be extremely accurate. A valid
model is one that is accurate and correctly represent the
problem or system under investigation.
2. Model can help a decision maker to formulate problems.
3. Models can given us insight and information. For example,
using the profit model, we can see what impact changes in
revenues and expenses will have on profits. Studying the
impact of changes in a model, such as a profit model, is
called sensitivity analysis.

Question: What are the advantages of
Mathematical Modeling?
4. Models can save time and money in decision making and
problem solving. If usually takes less time, effort, and
expense to analyze a model.
5. A model may be the only way to solve some large or
complex problems in a timely fashion.
6. A model can be used to communicate problems and
solutions to others. A decision analyst can share his or
her work with other decision analysts. Solutions to a
mathematical model can be given to managers and
executives to help them make final decisions.

Question: What is the objective of a firm. Discuss
Rational Behavior Concepts.?
The objective of a firm is to maximize the profit or alternately minimize the
cost. Rationality of a firm consists in optimization of some objective function.
This is the Neo-classical concept of Rational Behavior. This concept consists
two requirements.
a. Unlimited computational capacity. b. Perfect and cost-less
information.
But Herbert Simon contradicts with this concept and introduced ‘Bounded
Rational’. He highlights the new term which is called sub optimal level/
satisfying Behavior. This is limited by
a. Computational capacity is always limited. b. Information is imperfect.
It is costly.
So a firm can play the sub optimal level or satisfying behavior.

A system is a collection of people, resources, concepts, and procedures that is
intended to perform some identifiable function or to serve a goal.
Copyright 2006 John Wiley & Sons, Inc. 1-17
INPUT
•Material
•Machines
•Labor
•Management
•Capital
TRANSFORMATION
PROCESS
OUTPUT
•Goods
•Services
Feedback
Question: Define system. Discuss the structure of
a system.?.

• The structure of a system divided into three parts:
1. Input 2. Process 3. Output and they are surrounded by an
environment and are frequently connected by a feedback mechanism.
• Inputs: Inputs include those elements that enter the system.
• Process: All the elements necessary to convert the inputs into outputs are
included in the processes.
• Output: Outputs describes the finished products.
• Feedback: The flow of information to the decision maker concerning the
system’s output is called feedback. Based on this information the decision
maker can modify the inputs, or the processes or both.
• The environment: There are several elements that lie outside the system in
the sense that they are not inputs, outputs or processes. However, they
have an impact on the system’s performance and consequently on the
attainment of its goal. These are termed the environment.

Types of System
There are two types of System:
1. Open System and
2. Closed System.
The system which is isolated from the environmental
influences and are totally independent is called
closed system, where as the open system
exchanging information, material or energy with the
environment and are very dependent.

What is System Approach?
Operations Research recognizes that a decision made in one
segment of the organization may have a significant effect, not only on
the operation of that particular segment, but on the operation of other
segment as well. Therefore, when possible, the overall organization
point of view is adopted. Such an approach is termed a system point
of view or systems approach.

Question: Discuss the formulation of
Mathematical Modeling.
Modeling or formulation the problem involves conceptualization
of the problem and its abstraction to a mathematical form. The
dependent and independent variables are identified and the
equations describing their relationships established. Simplification
are made, whenever necessary through a set of assumptions.
The modeling involves the following steps:
• The components of the model.
• The structure of the model.
• The mathematical relationship.
• The validation of the model

Formulation of Mathematical Modeling
• The components of the model: Consists of
• Result variable: Which reflects the level of effectiveness of the
system. That is, they tell how well the system performs or attains
its goals. Result variable are the outputs of the system.
• Decision variable: Describe elements in the problem for which a
choice must be made. These can be manipulated and controllable
by the decision maker.
• Uncontrollable variables: In any decision situation there are factors
that effect the result variables but that are not under the control
of the decision maker. Such as interest rate, tax, prices of supplies
etc.

b. Structure of the model: The components of a mathematical
model are expressed as variables. These are then tied together by sets
of mathematical expressions such as equations or inequalities to form a
system.
c. The mathematical relationship: Mathematical relationship
includes two major tools:
The Objective function: The objective function express the dependent variables
in the model as they relate to the independent variables. The objective is to
maximize the profit.
The constraints: The constraints express the limitations imposed on managerial
systems due to regulations, competition, scarcity of resources, technology or
other uncontrollable variables

d. The validation of the model: After a model has been
constructed, it is necessary to know how well it represents reality. That
is we need to know whether the model is correct or not.

Fundamentals of Quantitative Analysis

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Fundamentals of Quantitative Analysis