OPERATION RESEARCH BBA-N406 unit 1 Notes

 

Operation Research

Decision making in business and industry is extremely difficult since the world is full of uncertainty. In past, businessmen generally make their decisions with experience or intuition but in this world it does not make any sense. They realized that in this way they are net able to make an effective decision so that they need  some scientific methods which help them to take an appropriate decision in a particular, situation. Every organization has limited resources. Operations research provides the solution that how to optimum utilizes scarce resources? Operations research provides  a facility to, decision maker to evaluate the given problems, identify the alternative solutions, recognize the constraints and then assist the decision maker to have the best possible solution available as optimal solution.

 

Definition of OR

1. Operations Research is a scientific method of providing executive departments with a quantitative

basis for decision regarding the operations under their control.

P M Morse & GE & Kimball

2. Operations Research is a scientific approach to problem solving for executive Management.

H.M. Wagner

3. Operations Research is the art of finding bad answers to problems to which otherwise worse

answers are given.

T.L. Saaty

4. Operations Research is concerned with scientifically deciding how to best design & operate manmachine

system usually requiring the allocation of scarce recourses.

Operations Research Society, UK

5. Operations Research is the art of winning war without actually fighting it

Miller & Starr

6. Operations Research is the systematic, method oriented study of the basic structure, characteristics,

functions and relationships of an organization to provide the execute with a sound, scientific and

quantitative basis for decision making.

E.L. Arnoff M.J.Netzorg

7. Operations Research-is the systematic application of quantitative methods, techniques and tools to

the analysis of problems involving the operation of system.

Daellenbach & George

8. Operations Research may be described as a scientific approach to decision making that involves the

operations of organizational system.

F S Hiller & G J Lieberman

9. This new decision making field has been characterized by the use of scientific knowledge through

interdisciplinary team effort for the purpose of determining the best utilization of limited resources.

H A Taha

 

Characteristics of OR

Following are the characteristics of Operations Research

1. Interdisciplinary team approach – The problems an OR of analyst faces are heterogeneous in

nature, involving the number Variables and constraints which are beyond the analytical ability of a

person. So a number of people from various disciplines are required to understand the problem.

They apply their specialized knowledge and experience to get a better understanding and solution to the problem on hand.

2. System approach – Any organization is it a business or government of a defence organization can

be considered as a system having various sub systems. The decision made by any sub systems made

by will have its effect on other sub systems. Like decision taken by finance department will have its

effect on marketing department. When dealing with OR problem the system should be treated as a

whole so that the interrelation between sub systems and the problem on the entire system are kept

in mind. Hence OR is a system approach.

3. Scientific method – OR uses scientific methods for the following steps:

a. The problem is defined and analyzed

b. Observations are made under different conditions.

c. On the basis of observations, a hypothesis is formulated how the various factors interact for the

best solution to the problem.

d. An experiment is designed and executed to test the hypothesis.

e. Finally the results of the experiments are analyzed and the hypothesis is either accepted or

rejected.

4. It helps increasing the creative ability of the decision market – OR provides the managers

mathematical took, techniques and models to analyze the problem on hand and to evaluate the result

of all alternatives and make lair Optimal choice, thereby helping him in faster and better decisions.

Hence a manager who uses OR techniques will have a better creativity ability than a manager who

does not use these techniques.

5. Helpful in finding: optimum decisions – OR techniques always try to provide the best or optimum

decisions regarding to the organization. It provides the solution by considering all the constraints.

6. Quantitative solutions – OR techniques provide quantitative basis for decision making to the

management. Different problems related to business and management like Assignment problem,

Transportation problem, Game Theory, Simulation, and Markov Chain etc. are solved in quantitative

form.

7. Use of computer – Since OR techniques are mathematical in nature therefore it requires a

computers to solve the complex mathematical models. A large amount of calculations are required so use of digital computer has become an integral part of the Operations research approach to decision making

 

Use of OR

Personnel Management

• Recruitment policies and assignment of jobs

• Manpower planning, wage/salary administration

• Negotiation in a bargaining situation

• Skills and wages balancing

• Establishing equitable bonus system

Production Management

1. Project planning

a. Location and size of warehouse or new plant, distribution centres and retail outlets.

b. Logistics layout and engineering design

c. Transportation, planning and scheduling

2. Manufacturing

a. Aggregate production Planning, assembly line, blending, purchasing and inventory control

b. Allocating R&D budgets-most affectively

3. Maintenance and project scheduling.

a. Maintenance policies and preventive maintenance

b. Maintenance crew size and scheduling

c. Project scheduling and allocation of resources

Government

• Economic planning, natural resources, social planning and energy

• Urban and housing problems.

• Military, police, pollution control

Research and development

• Determination of areas of concentration of R&D

• Control of development projects

• Determination of cost and time requirements

 

PHASES OF OPERATIONS RESEARCH

The most important feature of OR is the use of scientific methods and building of decision models. The three

phases of the scientific methods are as follows

a. Judgement Phase – This phase includes:

• Identification of real-life problem

• Selection of an appropriate objective & the values of various variables related to that ob.jective

• Application of appropriate scale of measurement

• Formulation of an appropriate model of the problem.

b. Research Phase: This phase includes:

• Observations and data collection for a better understanding of the problem

• Formulation of hypothesis and models

• Observation and experimentation to lest the hypothesis

• Analysis of the availably information and verification of the hypothesis

• Predictions Of various result-from the hypothesis

• Generalization of the result and consideration of alternative methods.

c. Action Phase: This phase consist of making, recommendations for implementing the decision. There must be awareness of environment in which the problem occurred, objective, assumption and omission of the model of the problem.

MODELS IN OR

Classification based on structure

This can be classified as

• Physical model- These models provide a physical appearance of the real object under study either

reduced in site or scaled up. Physical models are useful only in design problems because they are easy to Structure

Iconic model—These models retain some of the physical properties and characteristics of the system.

Iconic model is an object or system, represented on a small scale. These models can simulate the actual

performance of a product. The main advantages of these models arc that it is concrete, specific & easily

understandable.

Example: Maps, Globes, Blueprint of a home, Photograph Model' of train, engine etc.

Analogue model – These models do not look like die real situation but represent and behave like a

system under study. These models are easier to manipulate. They are less specific and concrete.

Example a) Organizational chart represents the structure, authority and responsibilities relationship

with boxes and arrows.`

b) The map in different colors represents roads, -highway, water, deserts, towns and other geographical

features.

c) Graphs of time series, stock market changes, frequency curves etc. may be used to represent

qualitative relationships between any two properties and predict how a change in one property affects

the other.

• Symbolic model – These models use a set of mathematical symbols and functions to represent the

decision variables and their relationships to describe the behavior of the system. These models are also

used to represent relationships which can be representing in, a physical form. Symbolic models are

classified into the following two categories

Verbal Model—These models describe a situation in written or spoken language.

Example – Written sentences, books etc.

Mathematical Model – These models involve the use of mathematical symbols, letters, numbers and

mathematical operators (+, -, *, /) to represent relationships among various variables of the system to

describe its properties or behavior.

Example: The relationship among time, distance and speed

Descriptive model – The use of this model it to investigate the outcomes of various alternative courses

of action. In this model there is no guarantee that an alternative is selected by descriptive analysis is optimal. These models are usually used in decision situations where optimizing models are not

applicable. These are used in predicting the behavior of a system under various conditions. Example:

Simulation

• Predictive model – These models indicate “if this occurs, then that will follow”. They relate dependent and

independent variables. These models do not have an objective function as apart of the model to evaluate

decision alternatives.

Static model – Static model represent a system at some specified time and do not account for changes

over time.

Example – Inventory model

· Dynamic model – In a dynamic model, time is considered as one of the variables and allow the impact

of changes due to change in time.

Example – Dynamic Programming

 Some of the problems which can be analysed by operations research are given hereunder:

1. Finance, Budgeting and Investment:

i. Cash flow analysis, long range capital requirement, investment portfolios, divi­dend policies,

ii. Claim procedure, and 

iii. Credit policies.

2. Marketing:

ADVERTISEMENTS:

i. Product selection, competitive actions,

ii. Number of salesmen, frequencies of calling on, and 

iii. Advertising strategies with respect to cost and time.

3. Purchasing:

i. Buying policies, varying prices,

ii. Determination of quantities and timing of purchases,

ADVERTISEMENTS:

iii. Bidding policies,

iv. Replacement policies, and 

v. Exploitation of new material resources.

4. Production Management:

i. Physical distribution: Location and size of warehouses, distribution centres and retail outlets, distribution policies.

ii. Facilities Planning: Number and location of factories, warehouses etc. Loading and unloading facilities.

iii. Manufacturing: Production scheduling and sequencing stabilisation of produc­tion, employment, layoffs, and optimum product mix.

iv. Maintenance policies, crew size.

v. Project scheduling and allocation of resources.

5. Personnel Management:

i. Mixes of age and skills,

ii. Recruiting policies, and 

iii. Job assignments.

6. Research and Development:

i. Areas of concentration for R&D.

ii. Reliability and alternate decisions.

iii. Determination of time-cost trade off and control of development projects.

Characteristics (Features) of Operation Research:

Main characteristics of operations research (O.R.) are follows:

(i) Inter-Disciplinary Team Approach:

This requires an inter-disciplinary team includ­ing individuals with skills in mathematics, statistics, economics, engineering, mate­rial sciences, computer etc.

(ii) Wholistic Approach to the System:

While evaluating any decision, the important interactions and their impact on the whole organisation against the functions originally involved are reviewed.

(iii) Methodological Approach:

O.R. utilises the scientific method to solve the problem

(iv) Objective Approach:

O.R. attempts to find the best or optimal solution to the prob­lem under consideration, taking into account the goals of the organisation.

Methodology of Operation Research:

Operation Research, is a scientific approach for decision-making, and therefore must follow following steps:

1. Formulating the Problem:

The problem must be first clearly defined. It is common to start the O.R. study with tentative formulation of the problem, which is reformulated over and again during the study. The study must also consider economical aspects.

While formulating the O.R. study, analyists must analyse following major components:

(i) The environment:

Environment involves physical, social and economical factors which are likely to affect the problem under consideration. O.R. team or analysts must study the organisation contents including men, materials, machines, suppliers, consumers, competitors, the government and the public.

(ii) Decision-makers:

Operation analyst must study the decision-maker and his rela­tionship to the problem at hand.

(iii) Objectives:

Considering the problem as whole, objectives should be defined.

(iv) Alternatives:

The O.R. study determines as to which alternative course of action is most effective to achieve the desired objectives. Expected reactions of the competitors to the alternative must also be considered.

2. Deriving Solution:

Models are used to determine the solution either by simulation or by mathematical analysis. Mathematical analysis for deriving optimum solution includes ana­lytical or numerical procedure, and uses various branches of mathematics.

3. Testing the Model and Solution:

A properly formulated and correctly manipulated model is useful in predicting the effect of changes in control variables on the overall system effectiveness. The validity of the solution is checked by comparing the results with those ob­tained without using the model.

4. Establishing Controls over the Solution:

The solution derived from a model remains effective so long as the uncontrolled variables retain their values and the relationship. The solution goes out of control, if the values of one or more variables vary or relationship between them undergoes a change. In such circumstances the models need to be modified to take the changes into account.

5. Implementing the Solution:

Solution so obtained should be translated into operating procedure to make it easily understandable and applied by the concerned persons. After apply­ing the solution to the system, O.R. group must study the response of the system to the changes made.

Operation Research Models:

Operation Research model is an idealised representation of the real life situation and repre­sents one or more aspects of reality. Examples of operation research models are: a map, activity charts balance sheets, PERT network, break-even equation, economic ordering quantity equation etc. Objective of the model is to provide a means for analysing the behaviour of the system for improving its performance.

Classification of Models:

Models can be classified on the basis of following factors:

1. By degree of Abstraction:

i. Mathematical models.

ii. Language models.

2. By Function:

i. Descriptive models.

ii. Predictive models.

iii. Normative models for repetitive problems.

3. By Structure:

i. Physical models.

ii. Analogue (graphical) models.

iii. Symbolic or mathematical models.

4. By Nature of Environment:

i. Deterministic models.

ii. Probabilistic models.

5. By the Time Horizon:

i. Static models.

ii. Dynamic models.

Characteristics of a Good Model:

i. Assumptions should be simple and few.

ii. Variables should be as less as possible.

iii. It should be able to asscimilate the system environmental changes without change in its framework.

iv. It should be easy to construct.

Constructing the Model:

A mathematical model is a set of equations in which the system or problem is described. The equations represent objective func­tion and constraints. Objective function is a mathematical expressions of objectives (cost or profit of the operation), while constraints are mathematical expressions of the limitations on the fulfillment of the objectives.

These expressions consist of controllable and uncontrollable variables.

The general form of a mathematical model is:

O = f (xi, yi)

where O = Objective function

xi = Controllable variables

yi = Uncontrollable variables

f = Relationship between O, and xi, yi.

Since model is only an approximation of the real situation, hence it may not include all the variables.

Simplification in Operation Research Models:

While constructing the model, efforts should be made to simplify them, but only up to the extent so that there is no significant loss of accuracy.

Some of the common simplifications are:

i. Omitting certain variables.

ii. Aggregating (or grouping) variables.

iii. Changing the nature of variables e.g., considering variables as constant or continuous.

iv. Changing relationship between variables i.e., considering them as linear or straight line.

v. Modify constraints.

Techniques of Operation Research:

Important techniques of Operation Research are being described hereunder:

(i) Inventory Control Models:

Operation Research study involves balancing inventory costs against one or more of the following costs:

i. Shortage costs.

ii. Ordering costs.

iii. Storage costs.

iv. Interest costs.

This study helps in taking decisions about:

i. How much to purchase.

ii. When to order.

iii. Whether to manufacture or to purchase i.e., make and buy decisions.

The most well-known use is in the form of Economic Order Quantity equation for finding economic lot size.

(ii) Waiting Line Models:

These models are used for minimising the waiting time and idle time together with the costs associated therewith.

Waiting line models are of two types:

(a) Queuing theory, which is applicable for determining the number of service facilities and/or the timing of arrivals for servicing.

(b) Sequencing theory which is applicable for determining the sequence of the servicing.

(iii) Replacement Models:

These models are used for determining the time of replacement or maintenance of item, which may either:

(i) Become obsolete, or

(ii) Become inefficient for use, and

(iii) Become beyond economical to repair or maintain.

(iv) Allocation Models:

These models are used to solve the problems arising when:

(a) There are number of activities which are to be performed and there are number of alternative ways of doing them,

(b) The resources or facilities are limited, which do not allow each activity to be performed in best possible way. Thus these models help to combine activities and available resources so as to optimise and get a solution to obtain an overall effectiveness.

(v) Competitive Strategies:

Such type of strategies are adopted where, efficiency of deci­sion of one agency is dependent on the decision of another agency. Examples of such strategies are game of cards or chess, fixing of prices in a competitive market where these strategies are termed as “theory”.

(vi) Linear Programming Technique:

These techniques are used for solving operation problems having many variables subject to certain restrictions. In such problems, objectives are—profit, costs, quantities manufactured etc. whereas restrictions may be e.g. policies of government, capacity of the plant, demand of the product, availability of raw materials, water or power and storage capacity etc.

(vii) Sequencing Models:

These are concerned with the selection of an appropriate sequence of performing a series of jobs to be done on a service facility or machine so as to optimise some efficiency measure of performance of the system.

(viii) Simulation Models:

Simulation is an experimental method used to study behaviour over time.

(ix) Network Models:

This is an approach to planning, scheduling and controlling complex projects.

Applications of Operation Research:

These techniques are applied to a very wide range of problems.

Here only some of the common applications are being mentioned:

(i) Distribution or Transportation Problems:

In such problems, various centres with their demands are given and various warehouses with their stock positions are also known, then by using linear programming technique, we can find out most economical distribution of the products to various centres from various warehouses.

(ii) Product Mix:

These techniques can be applied to determine best mix of the products for a plant with available resources, so as to get maximum profit or minimum cost of produc­tion.

(iii) Production Planning:

These techniques can also be applied to allocate various jobs to different machines so as to get maximum profit or to maximise production or to minimise total production time.

(iv) Assignment of Personnel:

Similarly, this technique can be applied for assignment of different personnel with different aptitude to different jobs so as to complete the task within a minimum time.

(v) Agricultural Production:

We can also apply this technique to maximise cultivator’s profit, involving cultivation of number of items with different returns and cropping time in different type of lands having variable fertility.

(vi) Financial Applications:

Many financial decision making problems can be solved by using linear programming technique.

Some of them are:

(i) To select best portfolio in order to maximise return on investment out of alternative investment opportunities like bonds, stocks etc. Such problems are generally faced by the managers of mutual funds, banks and insurance companies.

(ii) In deciding financial mix strategies, involving the selection of means for financing firm, projects, inventories etc.

Limitations of Operations Research:

i. These do not take into account qualitative and emotional factors.

ii. These are applicable to only specific categories of decision-making problems.

iii. These are required to be interpreted correctly.

iv. Due to conventional thinking, changes face lot of resistance from workers and some­times even from employer.

v. Models are only idealised representation of reality and not be regarded as absolute.