Quantitative management is not a modern business idea but a management theory that came into existence after World War II. Business owners initially used it in Japan to pick up the pieces of the devastation caused by the war and started taking baby steps toward reconstruction. It focuses on the following elements of business operations: Customer satisfaction Business value enhancement Empowerment of employees Creating synergy among teams Creating quality products Preventing defects Being responsible for quality Focusing on continuous improvement Leveraging statistical measurement Remaining focused on the processes Commitment to refinement and learning Quantitative techniques in management as a collection of mathematical and statistical tools. They’re known by different names, such as management science or operation research. In modern business methods, statistical techniques are also viewed as a part of quantitative management techniques. When appropriately used, quantitative approaches to management can become a powerful means of analysis, leading to effective decision-making. These techniques help resolve complex business problems by leveraging systematic and scientific methods.

1. QUANTITATIVE TECHNIQUES
Chapter I - Introduction
Meaning and Definition of Quantitative Techniques, Linkage between
Business Decision Making and Quantitative Techniques, Different
Quantitative Techniques, Areas for Application of Quantitative
Techniques in Business. Types of Decisions; Steps in Decision Making;
Quantitative Analysis and Decision Making; Different types of Models
Quantitative Analysis and Decision Making; Different types of Models
and their Uses; Model Building Steps.
Prepared by
Mr. Dayananda Huded M.Com, NET, KSET
Teaching Assistant,
Rani Channamma University, PG Centre, Jamkhandi
E-Mail: dayanandch65@gmail.com

2. HISTORY
 Quantitative management is not a modern business idea but a
management theory that came into existence after World War
II. Business owners initially used it in Japan to pick up the
pieces of the devastation caused by the war and started taking
baby steps toward reconstruction. It focuses on the following
elements of business operations:
 Customer satisfaction
 Business value enhancement
Business value enhancement
 Empowerment of employees
 Creating synergy among teams
 Creating quality products
 Preventing defects
 Being responsible for quality
 Focusing on continuous improvement
 Leveraging statistical measurement
 Remaining focused on the processes
 Commitment to refinement and learning

3. MEANING
 Quantitative techniques in management as a collection of
mathematical and statistical tools. They’re known by
different names, such as management science or operation
research. In modern business methods, statistical techniques
are also viewed as a part of quantitative
management techniques.
 When appropriately used, quantitative approaches to
management can become a powerful means of analysis,
leading to effective decision-making. These techniques help
resolve complex business problems by leveraging systematic
resolve complex business problems by leveraging systematic
and scientific methods.
 Quantitative techniques in management involve using
various elements of quantities, including numbers, symbols
and mathematical expressions. They act as supplements to
help decision-makers in making the proper judgment. These
are powerful business tools that allow managers to optimize
outcomes with limited resources.
 The term Decision Science / Quantitative Techniques (QT)
/Operations Research (OR) describes the discipline that is
focused on the application of Information Technology (IT) for
well-versed decision-making.

4.  Quantitative Techniques adopt a scientific approach to
decision-making. In this approach, past data is used in
determining decisions that would prove most valuable in the
future.
 The use of past data in a systematic manner and
constructing it into a suitable model for future use comprises
a major part of scientific management.
 For example, consider a person investing in fixed deposit in
a bank, or in shares of a company, or mutual funds, or in
Life Insurance Corporation. The expected return on
Life Insurance Corporation. The expected return on
investments will vary depending upon the interest and time
period. We can use the scientific management analysis to
find out how much the investments made will be worth in
the future.
 There are many scientific method software packages that
have been developed to determine and analyze the problems.

5. DEFINITIONS OF QT
 According to C.R. Kothari :
 "Quantitative Techniques may be defined as those technique which
provide the decision maker with a systematic and powerful means
of analysis and help, based on quantitative in exploring policies for
achieving pre-determined goals”.
 Quantitative techniques are those statistical and programming
techniques, which help decision makers solve many problems,
especially those concerning business and industry.
 Quantitative techniques are those techniques that provide the
decision makers with systematic and powerful means of analysis,
based on quantitative data, for achieving predetermined goals.
based on quantitative data, for achieving predetermined goals.
 Quantitative research is defined as a systematic investigation of
phenomena by gathering quantifiable data and performing
statistical, mathematical, or computational techniques.
 Quantitative research collects information from existing and
potential customers using sampling methods and sending out online
surveys, online polls, questionnaires, etc., the results of which can
be depicted in the form of numerical. After careful understanding of
these numbers to predict the future of a product or service and
make changes accordingly.

6.  Operational research/QT is the application of the methods of
science to complex problems in the direction and management of
large systems of men, machines, materials, and money in the
industry, business, govt. and defence.
- Operations Research Society, UK
 QT is concerned with scientifically deciding how to best design and
operate man machines systems usually requiring the allocation of
scarce resources.
-Operations Research Society, US
 Operation research/QT is applied design theory. It uses any
 Operation research/QT is applied design theory. It uses any
scientific, mathematical or logical means to attempt to cope with
the problems that confront the executive, when he tries to achieve
a through going rationality in dealing with his decision problems.
- D. W. Miller & M. K. Stan
 Operation research/QT is a scientific approach to problem solving
for executives management.
- H. M. Wagner

7. LINKAGE BETWEEN BUSINESS DECISION MAKING AND
QUANTITATIVE TECHNIQUES
 Quantitative techniques include methods or tools, which focus on
objective measurement, and analysing numbers in order to draw
conclusion about given problems.
 These are more relevant to problems of complex business situations.
 Quantitative methods seek to measure various offering-, consumer-, or
market-related phenomena in an entire population and to explain
patterns of predefined offering-, consumer-, or market-related
phenomena through causal inference or teleological explanation.
 QT used to collect quantitative data from the research study.
If any organization would like to conduct a customer satisfaction
 If any organization would like to conduct a customer satisfaction
survey, a customer satisfaction survey template can be used. Through
this survey, an organization can collect quantitative data and metrics
on the goodwill of the brand or organization in the mind of the
customer based on multiple parameters such as product quality,
pricing, customer experience, etc.
 collecting feedback from the event attendees about the value that they
see from the event. By using an event survey template, the
organization can collect actionable feedback about satisfaction levels of
customers during various phases of the event such as the sales, pre
and post-event, the likelihood of recommending the organization to
their friends and colleagues, hotel preferences for the future events
and other such questions.

8. DIFFERENT QUANTITATIVE
TECHNIQUES/CLASSIFICATION/TYPES OF QT
Different
QT/Classification/Types
of QT
Mathematical QT Statistical QT Programming QT
1. Permutation
2. Matrix
3. Determinants
4. Differentiation
5. Integration
6. Vestors
1. Collection of Data
2. Index Numbers
3. Time Series
4. Interpolation
5. Probability Theory
6. Sampling Analysis
1. Linear Programming
2. Assignment
3. Game Theory
4. Decision Theory
5. Simulation
6. Inventory Control Theory

9. I.
 1. Permutation: Permutation means arrangement of objects in a definite
order. The number of arrangements depends upon the total number of
objects and the number of objects taken at a time for arrangement.
 Determine the number of possible arrangement.
 Ex: 2 Pants (Red & Black) and 2 Shirts (Green & Blue)
 2. Matrix: Matrix is an orderly arrangement of certain given numbers or
 2. Matrix: Matrix is an orderly arrangement of certain given numbers or
symbols in rows and columns. It is a mathematical device of finding out the
results of different types of algebraic operations on the basis of the relevant
matrices.
 An arrangement(array) of m rows and n columns is called matrix.
 Number of rows and columns in a matrix is called its Dimention

10.  3. Determinants: It is a powerful device developed
over the matrix algebra. This device is used for finding
out values of different variables connected with a
number of simultaneous equations.
 4. Differentiation: It is a mathematical process of
finding out changes in the dependent variable with
reference to a small change in the independent variable.
 5. Integration: Integration is the reverse process of
 5. Integration: Integration is the reverse process of
differentiation.
 6. Differential Equation: It is a mathematical
equation which involves the differential coefficients of
the dependent variables.

11. II STATISTICAL QT
 1. Collection of Data: One of the important statistical methods is
collection of data. There are different methods for collecting primary and
secondary data.
 2. Index numbers: Index numbers measure the fluctuations in various
Phenomena like price, production etc over a period of time, They are
described as economic barometers.
 3. Correlation and Regression Analysis: Correlation is used to study
the degree of relationship among two or more variables. On the other hand,
regression technique is used to estimate the value of one variable for a
given value of another.
given value of another.
 4. Time series Analysis: Analysis of time series helps us to know the
effect of factors which are responsible for changes.
 5. Probability Theory: Theory of probability provides numerical values of
the likely hood of the occurrence of events.
 6. Ratio analysis: Ratio analysis is used for analyzing financial
statements of any business or industrial concerns which help to take
appropriate decisions.
 7. Testing of hypothesis: Testing of hypothesis is an important statistical
tool to judge the reliability of inferences drawn on the basis of sample
studies.

12. III. PROGRAMMING QT
 1. Linear programming: Linear programming technique is used
in finding a solution for optimizing a given objective under certain
constraints.
 2. Queuing theory: Queuing theory deals with mathematical
study of queues. It aims at minimizing cost of both servicing and
waiting.
 3. Game Theory: Game theory is used to determine the optimum
strategy in a competitive situation.
 4. Decision Theory: This is concerned with making sound
 4. Decision Theory: This is concerned with making sound
decisions under conditions of certainty, risk and uncertainty.
 5. Inventory theory: Inventory theory helps for optimizing the
inventory levels. It focuses on minimizing cost associated with
holding of inventories.
 6. Simulation: It is a technique of testing a model which resembles
real life situations.
 7. Sequencing: Sequencing tool is used to determine a sequence in
which given jobs should be performed by minimizing the total
efforts.

13. NATURE OF QT
 QT is a very powerful tool by using this we judge our production,
maximise profits, minimise costs and production methods can be
oriented for the accomplishment of certain pre-determined objectives.
 1. Decision Making: It is a support system in decision making
process. It provides decision makers with appropriate tools of
evaluation and presentation.
 2. Deployment of Resources: QT, if properly applied, leads to
optimal allocation of available limited resources. It avoids wastage and
less efficient usage of resources and conservation of them.
 3. Scientific Method: QT for decision making are examples for the
use of scientific methods of management. It offers a systematic and
objective experimentation, observation, and best evaluation of best
strategies.
 4. Network Programming: It is a technique of planning, scheduling,
controlling, monitoring and coordinating large and complex projects
comprising of a number of activities and events. It serves as an
instrument in resources allocation and adjustments of time and cost up
to the optimum level. It includes CPM, PERT etc.

14.  5. Branch and Bound Technique: It is a recently developed technique.
This is designed to solve the combinational problems of design making
where there are large number of feasible solutions, problems of plan
location, problems of determining minimum cost of production etc are the
examples of combinational problems.
 6. Quantification: Critical factors affecting a decision situation is
transformed into quantitative or numerical form. It is easy to comprehend,
understand and delegate an issue in numeric form.
 7. Numerical Analysis: Another basic feature of QT is numerical
expression of variables and analysis there-on. Even qualitative
characteristics or phenomenon can be transformed to numbers and symbols
using QT.
using QT.

15. SCOPE OF QT OR AREAS OF APPLICATION OF QT
 Finance and Accounting: Cash flow analysis, Capital budgeting,
Dividend and Portfolio management, Financial planning.
 Marketing Management: Selection of product mix, Sales resources
allocation and Assignments.
 Production Management: Facilities planning, Manufacturing,
Aggregate planning, Inventory control, Quality control, Work
scheduling, Job sequencing, Maintenance and Project planning and
scheduling.
scheduling.
 Personnel Management: Manpower planning, Resource
allocation, Staffing, Scheduling of training programmes.
 General Management: Decision Support System and Management
of Information Systems, MIS, Organizational design and control,
Software Process Management and Knowledge Management.
 Research and Development:

16. ROLE AND IMPORTANCE OF QT
 These techniques are especially increasing since World War II in the
technology of business administration. These techniques help in solving
complex and intricate problems of business and industry.
 1. Provide a Tool for Scientific Analysis: These technique provides
executives with a more precise description of the cause and effects,
relationship and risks. Underlying business operations in measurable
terms and this eliminates the subjective bias on which managements used
to formulate their decisions decades ago.
 2. Provides Solutions for Various Business Problems: QT used in the
field of production, procurement, marketing finance and allied field.
field of production, procurement, marketing finance and allied field.
Problems like how best can be managers and executives allocate the
available resources.
 3. Helps in Minimising Waiting and Servicing Costs: This will the
management in minimising the total waiting and servicing costs. This
technique also helps to analyse the best feasibility of adding facilities.
 4. Assists in Choosing Optimum strategy: Game theory is especially
used to determine the optimum strategy in a competitive situation and
enables the businessmen to maximise profits or minimise losses by
adapting the profitable decisions.

17.  5. Enable proper deployment of resources: It render valuable help in
proper deployment of resources. All this helps in the deployment of the
resources from one activity to another to enable the project completion on time.
This techniques, thus, provides for determining the probability of completing
an event or project itself by a specified date.
 6. They render great help in optimum resource allocation: Linear
programming technique is used to allocate scarce resources in an optimum
manner in problem of scheduling, product – mix and so on.
 7. Enable the management to decide when to buy and how much to
buy: The techniques of inventory planning enables the management to decide
when to buy and how much to buy.
 8. They facilitate the process of decision making: Decision theory enables
 8. They facilitate the process of decision making: Decision theory enables
the businessmen to select the best course of action when information is given
to probabilistic form. Through decision tree techniques executive’s judgement
can systematically be brought into the analysis of the problems.
 9. Through various quantitative techniques management can know
the reactions of the integrated business systems: The Integrated
Production Models techniques are used to minimise cost with respect to work
force, production and inventory. This technique is quite complex and is usually
used by companies having detailed information concerning their sales and
costs statistics over a long period. Besides, various other O.R. techniques also
help in management people taking decisions concerning various problems of
business and industry

18. LIMITATIONS OF QT
 1. The inherent limitation concerning mathematical expressions:
Quantitative techniques involve the use of mathematical models, equations
and similar other mathematical expressions. Assumptions are always
incorporated in the derivation of an equation and such an equation may be
correctly used for the solution of the business problems when the
underlying assumptions and variables in the model are present in the
concerning problem. IF this caution is not given due care then there always
remains the possibility of wrong application of the quantitative techniques.
Quite often the operations researchers have been accused of having many
solutions without being able to find problems that fit.
 2. High costs are involved in the use of quantitative techniques:
Quantitative techniques usually prove very expensive. Services of
specialised persons are invariably called for while using quantitative
techniques. Even in big business organisations we can expect that
quantitative techniques will continue to be of limited use simply because
they are not in many cases worth their cost. Thus, the use of quantitative
techniques is a costlier affair and this in fact constitutes a big and
important limitation of such techniques.

19.  3. Quantitative techniques do not take into consideration
the intangible factors i.e., non measurable human factors:
Quantitative techniques make no allowances for intangible
factors such as skill, attitude, vigour of the management people in
taking decisions but in many instances success or failure hinges
upon the consideration of such non-measurable intangible factors.
There cannot be any magic formula for getting an answer to
management problems; much depends upon proper managerial
attitudes and policies.
4. Quantitative techniques are just the tools of analysis
 4. Quantitative techniques are just the tools of analysis
and not the complete decision making process: It should
always be kept in mind that quantitative techniques, whatsoever
it may be, alone cannot make the final decision. They are just
tools and simply suggest best alternatives but in final analysis
many business decisions will involve human element. Thus,
quantitative analysis is at best a supplement rather than, a
substitute for management; subjective judgement is likely to
remain a principal approach to decision making.

20. TYPES OF DECISIONS
 1. Programmed and non-programmed decisions: Programmed decisions
are concerned with the problems of repetitive nature or routine type matters.
 These decisions are taken generally by lower level managers. Decisions of this type
may pertain to e.g. purchase of raw material, granting leave to an employee and
supply of goods and implements to the employees, etc.
 Non-programmed decisions relate to difficult situations for which there is no
easy solution.
 These matters are very important for the organisation. For example, opening of a
new branch of the organisation or a large number of employees absenting from the
organisation or introducing new product in the market, etc., are the decisions
which are normally taken at the higher level.
which are normally taken at the higher level.
 2. Routine and strategic decisions:
 Routine decisions are related to the general functioning of the organisation.
They do not require much evaluation and analysis and can be taken quickly. Ample
powers are delegated to lower ranks to take these decisions within the broad policy
structure of the organisation.
 Strategic decisions are important which affect objectives, organisational goals
and other important policy matters. These decisions usually involve huge
investments or funds. These are non-repetitive in nature and are taken after
careful analysis and evaluation of many alternatives. These decisions are taken at
the higher level of management.

21.  3. Tactical (Policy) and operational decisions:
 Decisions pertaining to various policy matters of the organisation are
policy decisions. These are taken by the top management and have long
term impact on the functioning of the concern. For example, decisions
regarding location of plant, volume of production and channels of
distribution (Tactical) policies, etc. are policy decisions.
 Operating decisions relate to day-to-day functioning or operations of
business. Middle and lower level managers take these decisions.
 An example may be taken to distinguish these decisions. Decisions
concerning payment of bonus to employees are a policy decision. On the
other hand if bonus is to be given to the employees, calculation of bonus in
other hand if bonus is to be given to the employees, calculation of bonus in
respect of each employee is an operating decision.
 4. Organisational and personal decisions:
 When an individual takes decision as an executive in the official capacity,
it is known as organisational decision. If decision is taken by the
executive in the personal capacity (thereby affecting his personal life), it
is known as personal decision.
 Sometimes these decisions may affect functioning of the organisation also.
For example, if an executive leaves the organisation, it may affect the
organisation. The authority of taking organizational decisions may be
delegated, whereas personal decisions cannot be delegated.

22.  5. Major and minor decisions:
 Decision pertaining to purchase of new factory premises is a major
decision. Major decisions are taken by top management.
 Purchase of office stationery is a minor decision which can be
taken by office superintendent.
 6. Individual and group decisions:
 When the decision is taken by a single individual, it is known as
individual decision.
Usually routine type decisions are taken by individuals within the
 Usually routine type decisions are taken by individuals within the
broad policy framework of the organisation.
 Group decisions are taken by group of individuals constituted in
the form of a standing committee.
 Generally very important and pertinent matters for the
organisation are referred to this committee. The main aim in
taking group decisions is the involvement of maximum number of
individuals in the process of decision making.

23. STEPS IN DECISION MAKING

24.  Step 1: Identify the decision: You realize that you need to make a decision. Try to clearly
define the nature of the decision you must make. This first step is very important.
 Step 2: Gather relevant information: Collect some pertinent information before you make
your decision: what information is needed, the best sources of information, and how to get it. This
step involves both internal and external “work.” Some information is internal: you’ll seek it
through a process of self-assessment. Other information is external: you’ll find it online, in books,
from other people, and from other sources.
 Step 3: Identify the alternatives: As you collect information, you will probably identify several
possible paths of action, or alternatives. You can also use your imagination and additional
information to construct new alternatives. In this step, you will list all possible and desirable
alternatives.
 Step 4: Weigh the evidence: Draw on your information and emotions to imagine what it would
be like if you carried out each of the alternatives to the end. Evaluate whether the need identified
in Step 1 would be met or resolved through the use of each alternative. As you go through this
difficult internal process, you’ll begin to favor certain alternatives: those that seem to have a
difficult internal process, you’ll begin to favor certain alternatives: those that seem to have a
higher potential for reaching your goal. Finally, place the alternatives in a priority order, based
upon your own value system.
 Step 5: Choose among alternatives: Once you have weighed all the evidence, you are ready to
select the alternative that seems to be best one for you. You may even choose a combination of
alternatives. Your choice in Step 5 may very likely be the same or similar to the alternative you
placed at the top of your list at the end of Step 4.
 Step 6: Take action: You’re now ready to take some positive action by beginning to implement
the alternative you chose in Step 5.
 Step 7: Review your decision & its consequences: In this final step, consider the results of
your decision and evaluate whether or not it has resolved the need you identified in Step 1. If the
decision has not met the identified need, you may want to repeat certain steps of the process to
make a new decision. For example, you might want to gather more detailed or somewhat
different information or explore additional alternatives.

25. METHODOLOGY OF QUANTITATIVE TECHNIQUES

26.  Step 1. Formulating the Problem: As a first step, it is necessary to clearly understand the
problem situations. It is important to know how it is characterized and what is required to be
determined. Firstly, the key decision and the objective of the problem must be identified from the
problem. Then, the number of decision variables and the relationship between variables must be
determined.
 Step 2. Defining the Decision Variables and Constraints: In a given problem situation,
defining the key decision variables are important. Identifying these variables helps us to develop
the model.
 For example, consider a manufacturer who is manufacturing three products A, B and C using
two machines, I and II. Each unit of product A takes 2 minutes on machine I and 5 minutes on
machine II. Product B takes 1 minute on machine I and 3 minutes on machine II. Similarly,
product C takes 4 minutes and 6 minutes on machine I and machine II, respectively. The total
available time on machine I and machine II are 100 hours and 120 hours, respectively. Each unit
of A yields a profit of Rs. 3.00, B yields Rs. 4.00 and C yields Rs. 5.00. What should be level of
production of products A, B and C that should be manufactured by the company so as to
production of products A, B and C that should be manufactured by the company so as to
maximize the profit?
 The decision variables, objective and constraints are identified from the problem.
 The company is manufacturing three products A, B and C. Let A be x1, B be x2 and C be x3. x1,
x2 and x3 are the three decision variables in the problem. The objective is to maximize the
profits. Therefore, the problem is to maximize the profit, i.e., to know how many units of x1, x2
and x3 are to be manufactured. There are two machines available, machine I and machine II
with total machine hours available as 100 hours and 120 hours. The machine hours are the
resource constraints, i.e., the machines cannot be used more than the given number of hours.
 To summarize,
 l Key decision : How many units of x1, x2 and x3 are to be manufactured
 l Decision variables : x1, x2 and x3
 l Objective : To maximize profit
 l Constraint : Machine hours

27.  Step 3. Developing a Suitable Model: A model is a mathematical
representation of a problem situation. The mathematical model is in the form
of expressions and equations that replicate the problem. For example, the
total profit from a given number of products sold can be determined by
subtracting selling price and cost price and multiplying the number of units
sold. Assuming selling price, sp as Rs. 40 and cost price, cp as Rs. 20, the
following mathematical model expresses the total profit, tp earned by selling
number of unit x.
TP = (SP – CP) x
= (40 – 20) x
TP = 20 x
 The applications of models are wide, such as:
 Linear Programming Model
 Sensitivity Analysis
 Sensitivity Analysis
 Goal Programming
 Non Linear Programming
 Queuing Theory
 Inventory Management Techniques
 PERT/CPM (Network Analysis)
 Decision Theory
 Games Theory
 Transportation and Assignment Models. Etc.
 Step 4. Acquiring the Input Data: Accurate data for input values are
essential. Even though the model is well constructed, it is important that the
input data is correct to get accurate results. Inaccurate data will lead to wrong
decisions.

28.  Step 5. Solving the Model:
 Solving is trying for the best result by manipulating the model to
the problem. This is done by checking every equation and its
diverse courses of action. A trial and error method can be used to
solve the model that enables us to find good solutions to the
problem.
 Step 6. Validating the Model: A validation is a complete test of
the model to confirm that it provides an accurate representation of
the real problem. This helps us in determining how good and
realistic the solution is. During the model validation process,
inaccuracies can be rectified by taking corrective actions, until the
inaccuracies can be rectified by taking corrective actions, until the
model is found to be fit.
 Step 7. Implementing the Results: Once the model is tested
and validated, it is ready for implementation. Implementation
involves translation/application of solution in the company. Close
administration and monitoring is required after the solution is
implemented, in order to address any proposed changes that call
for modification, under actual working conditions.

29. QUANTITATIVE ANALYSIS AND DECISION MAKING
 1. Linear programming: is used in finding a solution for
optimizing a given objective such as profit maximization or
cost minimization under certain constraints.
 This technique is primarily concerned with the optimal
allocation of limited resources for optimizing a given function.
 The name linear programming is because of the fact that the
model in such cases consists of linear equations indicating
linear relationship between the different variables of the
system.
system.
 Linear programming technique solves product-mix and
distribution problems of business and industry.
 It is a technique used to allocate scarce resources in an
optimum manner in problems of scheduling, product-mix, and
so on.
 Key factors under this technique include an objective
function, choice among several alternatives, limits or
constraints stated in symbols and variables assumed to be
linear.

30.  2. Waiting line: deals with mathematical study of queues.
Queues are formed whenever the current demand for service
exceeds the current capacity to provide that service.
 Waiting line technique concerns itself with the random
arrival of customers at a service station where the facility is
limited.
 Providing too much of capacity will mean idle time for
 Providing too much of capacity will mean idle time for
servers and will lead to waste of money.
 On the other hand, if the queue becomes long, there will be
a cost due to waiting of units in the queue.
 Waiting line theory, therefore, aims at minimizing the costs
of both servicing and waiting.

31.  3. Inventory control/planning aims at optimizing inventory
levels.
 Inventory may be defined as a useful idle resource which has
economic value, e.g., raw-materials, spare parts, finished products,
etc.
 Inventory planning, in fact, answers the two questions, viz., how
much to buy and when to buy?
 Under this technique, the main emphasis is on minimizing costs
associated with holding inventories, procurement of inventories
and shortage of inventories.
and shortage of inventories.
 4. Integrated production models aims at minimizing cost with
respect to workforce, production and inventory.
 This technique is highly complex and is used only by big business
and industrial units.
 This technique can be used only when sales and costs statistics for
a considerable long period are available.

32.  5. Dynamic programming refers to the systematic search
for optimal solutions to problems that involve many highly
complex inter relations that are, moreover, sensitive to
multistage effects such as successive time phases.
 6. Heuristic programming also known as discovery
method, refers o step by step search toward an optimum
when a problem cannot be expressed in the mathematical
programming form.
 The search procedure examines successively a series of
combinations that lead to stepwise improvements in the
solution and the search stops when a near optimum has been
solution and the search stops when a near optimum has been
found.
 7. The theory of replacement is concerned with the
prediction of replacement costs and the determination of the
most economic replacement policy.
 There are two types of replacement models
 one type of models deal with replacing equipment that deteriorate
with time and
 the other type of models helps in establishing replacement policy
for those equipment which fail completely and instantaneously.

33. DIFFERENT TYPES OF MODELS AND THEIR USES
 1. Physical Models: These models are usually used by engineers and
scientists. In managerial research one finds the utilisation of physical
models in the realm of marketing in testing of alternative packaging
concepts.
 2. Mathematical Models: The mathematical models use symbolic
notation and equations to represent a decision-making situation. The
system attributes are represented by variables and the activities by
mathematical functions that interrelate the variables.
 Ex. EOQ
Sta4c models assume the system to be in
 3. Static vs. Dynamic Models: Sta4c models assume the system to be in
a balance state and show the values and relationships for that only.
Dynamic models, however, follow the changes over time that result from
the system activities. Obviously, the dynamic models are more complex and
more difficult to build than the static models.
 4. Descriptive model: Such Models are used to describe the behaviour of
a system based on certain information. For example, a model can be built to
describe the behaviour of demand for an inventory item for a stated period,
by keeping the record of various demand levels and their respective
frequencies.

34.  5. Explanatory model: Such models are used to explain the
behaviour of a system by establishing relationships between its
various components. For example, a model can be built to explain
variations in productivity by establishing relationships among
factors such as wages, promotion policy, education levels, etc.
 6. Predictive model: Such models are used to predict the status
of a system in the near future based on data. For example, a model
can be built to predict stock prices (within an industry group), for
given any level of earnings per share.
 7. Prescriptive (or normative) model: A prescriptive model is
one which provides the norms for the comparison of alternative
solutions which result in the selection of the best alternative (the
most preferred course of action). Examples of such models are
allocation models.

35. MODEL BUILDING STEPS
 The approach used for model building or model development for
managerial decision-making will vary from one situation to another.
However, we can enumerate a number of generalized steps which can be
considered as being common to most modelling efforts. The steps are
Step 1
• Identifying and formulating the decision problem
Step 2
• Identifying the objective(s) of the decision maker(s)
• System elements identification and block building
Step 3
• System elements identification and block building
Step 4
• Determining the relevance of different aspects of the system
Step 5
• Choosing and evaluating the model form
Step 6
• Model calibration (The measuring devise)
Step 7
• Implementation

36. THE SEVEN-STEP MODEL-BUILDING PROCESS
Step 1
•Formulate the problem
Step 2
•Observe the system
Step 3
•Formulate a mathematical model of a problem
•Verify the model & use the model for prediction
Step 4
•Verify the model & use the model for prediction
Step 5
•Select a suitable alternative
Step 6
•Present the results & conclusion of the study to the organisation
Step 7
•Implement and evaluate recommendations

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