introduction to econometric

1. Management Science (4102)
Distribution of Points
Category Points
(1) Assignment/ Class Attendance
(2) First Mid-Term
(3) Second Mid-Term
(4) Final Exam
(5) Class Performance
10%
15%
15%
60%
10%
Total 110

2. Meaning of Management Science
Many definitions of management science (MS) have
been offered, as well as many arguments as to why it
cannot be defined. The following definitions provide a
useful basis for an initial understanding of the nature
of MS:
A scientific method of providing executive
management with a quantitative base for decisions
regarding operations under their control (Mores-
Kimball 1943).

3. Meaning of MS
The application of the scientific method by inter-
disciplinary teams to problems involving the control
of organized (man-machine) systems so as to
provide solutions which best serve the purpose of
the organization as a whole (Ackoff- Sasieni 1968).
Scientific approach to problem solving for executive
management (Wagner 1969).

4. Meaning of MS
Optimal decision-making in, and modeling of,
deterministic and probabilistic systems that
originate from real life. These applications,
which occur in government, business,
engineering, economics, and the natural and
social sciences, are largely characterized by the
need to allocate limited resources. In these
situations, considerable insight can be obtained
from scientific analysis, such as that provided by
MS (Hiller-Lieberman 1974).
A branch of applied mathematics wherein the
application is to the decision-making process
(Gross 1979).

5. Definition of MS
Management science is the application of scientific
methods i.e. statistical or mathematical methods and
principles to business decision-making and problem-
solving processes. Applying scientific-style methods to
common management situations can help companies
develop a deeper understanding of business scenarios
and how to approach these issues from a managerial
standpoint. Management science may also take a
more theoretical approach to making business
decisions or solving problems rather than relying on a
manager’s personal judgment or perception of
business situations.

6. Example
Suppose a company produces both interior and exterior paints
from two raw materials namely 1 and 2. The following table
provides the basic data of the problem;
Exterior Paint
from per ton of
Raw Material
Interior Paint
from Per Ton of
Raw Material
Maximum Daily
Availability
(tons)
Raw Material 1
Raw Material 2
6
1
4
2
24
6
Profit per ton (in
1000 USD)
5 4
A market survey restricts the maximum daily demand of interior paint
to 2 tons. Additionally the daily demand for interior paint cannot
exceed that of exterior paint by more than 1 ton. Determine the best
product mix of interior and exterior paints for which the daily profit
will be maximum level. Now to solve this problem we apply the
scientific methods, techniques and tools which is called the
management science.

7. Solution
1
2
1 2
The variable x indicates the daily production in tons of exterior paint
The variable x indicates the daily production in tons of interior paint
The total daily profit is given by; z = 5x +4x
The objec 1 2
tive of the company is to maximize z = 5x +4x
The last element of the model deals with the constraints that
restrict raw materials usage and demand.
From the data of the problem we have
Usage of raw m 1 2
1 2
aterial 1 = 6x +4x
Usage of raw material 2 = x +2x

8. Solution
1 2
1
Now from the problem it is clear to us that the daily availabilities of
raw materials 1 and 2 are limited to 24 tons and 6 tons respectively, the
associated restrictions are given by;
6x +4x 24
x +2x

2 6
There are two types of demand restrictions (i) maximum daily demand of
interior paint is limited to 2 tons and (2) excess of daily production of interior
paint over that of exterior paint is at mos

2
t 1 ton. The first restriction is very
straightforward which expressed as
x 2
The second restriction can be translated to state that the difference between
the daily production of interior and exterio

2 1
r paints does not exceed 1.
Thus we can write that
x -x 1


9. Solution
1
2
1 2
An implicit (or understood-to-be) restriction on the model is that the variables
and must be positive. That is
x 0
x 0
The complete model of the problem can be written as;
Maximize: z = 5x +4x
Su


1 2
1 2
2
2 1
1
2
bject to;
6x +4x 24
x +2x 6
x 2
x -x 1
x 0
x 0







10. Example
Let a company produces two different products namely
refrigerator and TV. Production takes place in two separate
departments namely refrigerator are produced in department I
and TV are produced in department II. The company’s two
products are produced and sold in a monthly basis. The
monthly production cannot exceed 60 refrigerators in
department I and 120 TV in department II because of
limitation of available facilities and resources. The company
regularly employs a total of 60 workers. A refrigerator
requires 2 men-month of labors while a TV requires 1 man-
month of labor. A refrigerator contributes a profit of 6
thousand TK and TV contributes of 3 thousand TK.
Formulate the linear programming problem to maximize its
profit. How many units of refrigerators and TV should the
company produce to realize maximum profits? What is the
maximum profit?

11. Historical Background of MS
Management science generally refers to mathematical or
quantitative methods for business decision making. The
term "operations research" may be used interchangeably
with management science. Frederick Winslow Taylor
is credited with the initial development of scientific
management techniques in the early 1900s. In addition,
several management science techniques were further
developed during World War II. Some even consider the
World War II period as the beginning of management
science.
World War II posed many military, strategic, logistic, and
tactical problems. Operations research teams of engineers,
mathematicians, and statisticians were developed to use
the scientific method to find solutions for many of these
problems.

12. Historical Background of MS
Nonmilitary management science applications developed
rapidly after World War II. Based on quantitative methods
developed during World War II, several new applications
emerged. The development of the simplex method by George
Dantzig in 1947 made application of linear programming
practical. C. West Churchman, Russell Ackoff, and Leonard
Arnoff made management science even more accessible by
publishing the first operations research textbook in 1957.
Computer technology continues to play an integral role in
management science. Practitioners and researchers are able
to use ever-increasing computing power in conjunction with
management science methods to solve larger and more
complex problems. In addition, management scientists are
constantly developing new algorithms and improving
existing algorithms; these efforts also enable management
scientists to solve larger and more complex problems.

13. The Methodology of MS
MS is the scientific method of decision-making. In most
discussions of the general scientific method you would find
certain stages and essential processes, as depicted in the
following flowchart:

15. Elements of the Model of MS
MS model includes three basic elements
(i) Decision variables that we want to
determine
(ii) Objective (goal) that we want to
maximize or minimize
(iii) Constraints that we need to satisfy for
solving the objective function

16. Characteristics of MS
(i) It is system oriented
(ii) MS is the application of scientific method, techniques and
tools
(iii) MS is used by interdisciplinary team in order to present
complex functional relationships as mathematical models
(iv) MS deals with uncovering new problems for quantitative
analysis
(v) MS utilizes computer facilities like as software
(vi) MS deals with quantitative analysis
(vii) MS also deals with human factor
(viii) Management science may use the principles of
managerial economics when approaching various business
situation
(ix) The primary focus of MS is on decision making

17. Application of MS
(i) In order to take decision on scientific basis in the field of
business and industrial management, MS team will have to
consider different scientific techniques of producing goods
and returns. In production management, MS techniques will
help to change the overall structure like installation of new
machine, introduction of more automation etc.
(ii) MS techniques are widely applicable in the field of
industry for production, blending, product mix, inventory
control, demand forecast, sales, and purchase, transportation,
repair, and maintenance, scheduling and sequencing planning,
scheduling and control of projects etc.
(iii) MS is widely applicable in business and society. For
instance, it is widely applicable to decide the premium rates
of various policies. It is also extensively used in petroleum,
paper, chemical, metal, processing, aircraft, rubber, textile,
mining, transport and distribution industries.

18. Application of MS
(iv) MS is widely applicable both in developing and
developed economies for planning. In developing and
developed societies, economists, statisticians,
mathematicians, econometricians, administrators,
technicians, politicians, researchers and agricultural experts
workers together to solve the problem of poverty, hunger,
sustainable economic growth, infrastructure development,
optimum allocation of resources to fulfill our unlimited
demands,
(v) MS approach is equally applicable both in big and small
organizations. For example, whenever a departmental store
faces a problem like employing, additional sales, purchasing
additional van etc, techniques of MS can be applied to
minimize cost and maximize benefit for each such decision.

19. Application of MS
Forecasting: Using time series analysis to answer typical
questions such as: How big will demand for products be?
What are the sales patterns? How will this affect profits?
Finance and Investment: How much capital do we need?
Where can we get this? How much will it cost?
Manpower planning and Assignment: How many
employees do we need? What skills should they have? How
long will they stay with us?
Sequencing and Scheduling: What job is most important?
In what order should we do jobs?
Location, Allocation, Distribution and Transportation:
Where is the best location for an operation? How big
should facilities be? What resources are needed? Are there
shortages? How can we set priorities?

20. Applications of MS
Reliability and Replacement Policy: How well is
equipment working? How reliable is it? When
should we replace it?
Inventory Control and Stockout: How much stock
should we hold? When do we order more? How
much should we order?
Project planning and control: How long will a
project take? What activities are most important?
How should resources be used?
Queuing and Congestion: How long are queues?
How many servers should we use? What service
level are we giving?

21. Techniques of MS
The scope of management science techniques is broad. These
techniques include:
(i) Mathematical Programming:
MP attempts to optimize the objective or effectiveness function subject
to a set of requirements and limitations. LP, transportations, assigned
models, Simplex Method, Integer programming, and goal programming.
(ii) Branch and Bound:
Branch and bounds is a step by step procedure used when a very large
number of alternative exist for certain managerial problems. It is also
used to solve integer programming problems.
(iii) Decision Tables:
Allocation and investment problems involving a relatively small number
of possible solutions can be presented in a tabular form known as a
decision table.
(iv) Decision Tree:
The extension of decision tables for situations involving several decision
periods takes the shape of a tree.

22. Techniques of MS
(v) Forecasting
To predict the outcomes of managerial decisions, various
forecasting approaches are employed. Many of these are based on
statistics.
(vi) Network Models:
This is a family of tools designed for the purposes of planning and
controlling complex projects. The best known models are PERT
(Program Evaluation Review Technique) and CPM ( Critical Path
Model)
(vii) Inventory Model:
For inventory control problems, special models that attempt to
minimize the costs associated with ordering and carrying
inventories have been developed.

23. Techniques of MS
(viii) Markov Chain:
Markov chains are used for predicting the outcomes of processes
where systems or units change their condition over time.
(ix) Queuing Model:
This types of models have been developed to predict the performance
of service systems.
(x) Simulation Models:
For the analysis of complex systems where all other models fail, MS
uses descriptive type simulation models.
(xi) Decision Theory:
The rational process/technique for selecting the best of several
alternatives are applied in decision theory. The “goodness” of a
selected alternative depends on the quality of the data used in
describing decision situation.

24. Techniques of MS
(xiii) Transportation Models:
Transportation models have been developed to determine the
amounts shipped from each source to each destination that
minimize the total shipment cost while satisfying both the supply
limits and demand requirements. The model assumes that the
shipping cost on a given route is directly proportional to the
number of units shipped on that route. In general the
transportation model can be extended to areas other than the
direct transportation of a commodity. Including among others
inventory control, employment scheduling and personnel
assignment.
(xiv) Dynamic Programming:
Dynamic programming is an approach to decision that are
basically sequential in nature or can be reformulated so as to be
considered sequential.
(xv) Game Theory:
Game theory is an approach which is applied to formulate
optimal strategies in conflict and in competitive environment.

25. Application MS Techniques into Different Areas
Different areas where MS techniques have been applied are
given below;
(i) Inventory control
(ii) Facility design
(iii) Product mix determination
(iv) Portfolio analysis
(v) Scheduling and sequencing
(vi) Merger-growth analysis
(vii) Transportation planning
(viii) Design of information Systems
(ix) Allocation of limited resources
(x) Investment decision (new plants)
(xi) Project management-planning and control

26. Application MS Techniques into Different Areas
(xi) New product decision
(xii) Sales force decision
(xiii) Market research decision
(xiv) Research and development decision
(xv) Oil and gas exploration decision
(xvi) Pricing decision
(xvii) Competitive bidding decision
(xviii) Quality control decision
(xix) Machine set problems in production
(xx) Distribution decisions
(xxi) Manpower planning and control decisions
(xxii) Credit policy analysis
(xxiii) Research and development effectiveness

27. Phases of OR or MS
Like all other scientific researches, OR is based on
scientific methodology, which proceeds the following
lines
(i) Formulating the problem
(ii) Construction a model to represent the system under
study
(iii) Deriving the solution from the model
(iv) Testing the model and the solution derived from it
(v) Establishing controls over the solution
(vi) Putting the solution to work i.e. implementation
Give an Example

28. Limitation of MS
(1) MS deals with the mathematical models of quantitative
variables but do not take into account of qualitative factors
or emotional factors which are quite real.
Example: MS deals with the mathematical model of cost
minimization, profit maximization, output maximization
but cannot deal with the qualitative factors like as honesty,
sincerity, political impact, etc.
(2) Mathematical models are applicable to only specific
categories of problems
(3) Management which has to implement the advised
proposals may itself offer a lot of resistance due to
conventional thinking.
(4) The experts must deal with the problems in MS for
decision making which has to be implemented, but in our
country are not available.