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SYLLABIPAPER 6 (ii) : OPERATIONS RESEARCHUNIT-I Operations Research—Meaning, Significance and

Scope. Introduction to Linear Programming, Formulation of

Linear Programming—Problem, Graphical Method,Simplex Method.Duality in Linear Programming, Definition of Dual Problem, General Rules in Converting any Primal into its Dual,

Transportation problem, Assignment problem.

UNIT-II Inventory – Types, Nature and Classification,

Economic Lot Size Models, Quality Discounts, Basic Concept of Network Models,

Preparation of the Network Diagrams, Project Duration and Critical Path, probability Statements of Project Durations.

Games Theory : Two persons zero sum games, Pure Strategies, Mixed Strategies, Dominance, Introduction to frequency problems,

Classification of Sequencing Problems, Processing in Job through Two Machines.

PRACTICAL WORK :

One project report in following areas : Packages in LPP, PERT-CPM in any industry, Inventory application in any company.

STYLE OF THE PAPERSection A – Covering Full Syllabus2 Theory 4 Practical and you have to attempt any 4

of 5 Marks each Total 20

MarksSection B– Covering Unit I of the Syllabus1 Theory 3 Practical and you have to attempt any 2

of 15 Marks each Total 30

MarksSection C– Covering Unit II of the Syllabus1 Theory 3 Practical and you have to attempt any 2

of 15 Marks each Total 30

MarksHighest Score You can expect in this Paper 80/80 +

20/20 in Internals Assessment

SOME FACTS ABOUT MY PAST RESULTSMore than 75% of my students get

more than 75% marks in my subject.

I find some students who get 100 out of 100 in my subject

How amongst will achieve this only you will know but I assure you

I find some students who get 100 out of 100 in my subject

LET’S START

OPERATIONS RESEARCH : NAMES

Operations Research is also known as:

Decision Science Management ScienceOperations ManagementQuantitative Techniques

OPERATIONS RESEARCH: HISTORY The roots of OR can be traced back many

decades, when early attempts were made to use a scientific approach in the management of organizations.

However, the beginning of the activity called operations research has generally been attributed to the military services early in World War II.

Because of the war effort, there was an urgent need to allocate scarce resources to the various military operations and to the activities within each operation in an effective manner.

Therefore, the British and then the U.S. military management called upon a large number of scientists to apply a scientific approach to dealing with this and other strategic and tactical problems.

In effect, they were asked to do research on (military) operations. These teams of scientists were the first OR teams.

By developing effective methods of using the new tool of radar, these teams were instrumental in winning the Air Battle of Britain.

Through their research on how to better manage convoy and antisubmarine operations, they also played a major role in winning the Battle of the North Atlantic.

Similar efforts assisted the Island Campaign in the Pacific.

A key person in the post-war development of OR was George B Dantzig. In 1947, he developed linear programming and its solution method known as simplex method.

Besides linear programming, many other tools of OR such as statistical control, dynamic programming queuing theory and inventory theory were well developed before the end of the 1950s.

O.R. as a formal subject is about fifty five years old, origins may be traced to the latter half of World War II. The impetus for its origin was the development of radar defense systems for the Royal Air Force, and the first recorded use of the term Operations Research is attributed to a British Air Ministry official named A. P. Rowe who constituted teams to do “operational researches” on the communication system and the control room at a British radar station.

The studies had to do with improving the operational efficiency of systems (an objective which is still one of the cornerstones of modern O.R.). This new approach of picking an “operational’’ system and conducting “research” on how to make it run more efficiently soon started to expand into other arenas of the war.

Perhaps the most famous of the groups involved in this effort was the one led by a physicist named P. M. S. Blackett which included physiologists, mathematicians, astrophysicists, and even a surveyor. This multifunctional team focus of an operations research project group is one carried forward to this day. Blackett’s biggest contribution was in convincing the authorities of the need for a scientific approach to manage complex operations, and indeed he is regarded in many circles as the original operations research analyst.

OPERATIONS RESEARCH : DEFINITIONS Operations Research (OR) – The science

that applies mathematical and computer science tools to support decision making.

Operations Research is concerned with scientifically deciding how to best design and operate man-machine systems usually requiring the allocating of scarce resources. -Operations Research Society, America

OR is the art of winning wars without actually fighting. -Arthur Clarke

OR is a scientific method of providing executive departments with a quantitative basis for decision regarding the operations under their control. -Morse and Kimbal

OR is the art of giving bad answers to problems where otherwise worse answers are given.

-T.L. Satty

CHARACTERISTICS OF OPERATIONS RESEARCH OR is a system approach OR is an Inter-disciplinary team approach.OR increases creative ability of the decision makerOR is Scientific approach (i) Defining (ii) Observing (iii) Formulating (iv) Testing (v) AnalyzingOR is Objectivistic approach Digital computerQuantitative solutionOR is a continuing processOptimizing natureHuman judgment

CHARACTERISTICS OPERATIONS RESEARCH Operation Research is the applications of scientific

methods, techniques and tools to problems involving the operations of a system so as to provide those in control of the system with optimum solutions to the problems. The significant features of operation research are as below :

1. OR is a system approach: The essence of systems approach is to find all significant and indirect effects on all parts of a system and to evaluate each action in terms of the effects for the system as a whole. e.g., a new strategy of marketing department can effect all the other departments of the organisation and so in evaluating the strategy, not only its effects on the marketing department should be considered but also the effects of the proposal on other departments as well.

2. OR is an Inter-disciplinary team approach: OR is interdisciplinary in nature and needs a team approach solving economic, physical, psychological, biological, sociological and engineering aspects of any problem by the assistance of mathematicians statisticians, engineers, economists, management and computer experts, this team for a given problem tries to analyse the cause and effect relationship between various parameters and evaluates the outcome of various alternative strategies.

3. OR increases creative ability of the decision maker: OR is a powerful tool in increasing the effectiveness of managerial decision. OR techniques help the decision maker to improve his creative and judicious capabilities, analyse and understand the problem situation leading to better control, co-ordination, system finally better decisions.

4. OR is Scientific approach : OR gives scientific methods for the purpose of solving problems, and there is no place of whims a guesswork in it. It is a formulized process of reasoning and consists of the following steps:

(i) Defining: The problem to be analyzed clearly and defining the conditions for observations.

(ii) Observing: Observations are made under different conditions to determine the behaviour of the system.

(iii) Formulating: A hypothesis describing how the various factors involved are believed to interact and the best solution to the problem is formulated on the basis of above observations.

(iv) Testing: Finally the result of experiment is design and executed, observations are made and measurements are recorded.

(v) Analysing: Finally the result of experiment are analysis and check weather hypothesis is accepted or not. Of the hypothesis is accepted it means the solution obtained is optimum.

5. OR is Objectivistic approach : OR attempts to find out the strategic or optimal solution to the problem under consideration. For this purpose, it is required that a measure of effectiveness be defined which is based on the objectives of the organisation. This measure is then used as the basis to compare the alternative courses of action.

6. Digital computer : Use of digital computer has become an integral part of the operations research approach to decision-making. The computer may be required due to the complexity of the model, volume of data required or the computations to be made. Many quantitative techniques are available in the form of ‘canned’ programmes.

7. Quantitative solution. Operation research assists the management with a quantitative basis for decision making. OR attempts to provide a systematic and scientific rational approach for quantitative solutions to the various managerial problems.

8. OR is a continuing process : OR is a continuing process. It continues with the emergence of new problems, finding and implementing solutions and interpreting the results of such implementation. Problems continue to arise in the modern dynamic environment. As such OR becomes a continuing process.

9. Optimizing Nature : OR ties to optimize total return by maximizing the profit and minimizing the cost or loss.

10. Human judgment : In deriving quantitative solution, sometimes human factors, play significant role, in the problems, are ignored. So, study of the OR is incomplete without a study of human factors.

5. OR is Objectivistic approach : OR attempts to find out the strategic or optimal solution to the problem under consideration. For this purpose, it is required that a measure of effectiveness be defined which is based on the objectives of the organisation. This measure is then used as the basis to compare the alternative courses of action.

6. Digital computer : Use of digital computer has become an integral part of the operations research approach to decision-making. The computer may be required due to the complexity of the model, volume of data required or the computations to be made. Many quantitative techniques are available in the form of ‘canned’ programmes.

7. Quantitative solution. Operation research assists the management with a quantitative basis for decision making. OR attempts to provide a systematic and scientific rational approach for quantitative solutions to the various managerial problems.

8. OR is a continuing process : OR is a continuing process. It continues with the emergence of new problems, finding and implementing solutions and interpreting the results of such implementation. Problems continue to arise in the modern dynamic environment. As such OR becomes a continuing process.

9. Optimizing Nature : OR ties to optimize total return by maximizing the profit and minimizing the cost or loss.

10. Human judgment : In deriving quantitative solution, sometimes human factors, play significant role, in the problems, are ignored. So, study of the OR is incomplete without a study of human factors.

WHY OPERATIONS RESEARCH You may ask, “Why must we learn the Operations

Research techniques?” Here are a few motivating reasons:

Organizations are becoming more complex, Huge numbers of choices and relentless time pressures and margin pressures make the decisions you face more daunting and more difficult.

Environments are changing so rapidly that past practices are no longer adequate. Meanwhile, new enterprise applications and software are generating massive amounts of data – and it can see like an overwhelming task to turn that data into insight and answers.

The costs of making bad decisions have increased.

OPERATIONS RESEARCH HELPS Deciding where to invest capital in order to

grow Getting more value out of ERP(Enterprise

Resource Planning), CRM (Customer Relationship Management), and other software systems

Figuring out the best way to run a call center

Locating a warehouse or depot to deliver material s over shorter distances at reduced cost

Forecasting sales for a new kind of product that has never marketed before

Solving complex scheduling problems

Planning for a potential terrorist attack Deciding when to discount, and how much Getting more cycles out of manufacturing

equipment Optimizing a portfolio of investments,

whether it contains financial securities or pharmaceutical product inventory

Deciding how large a budget to devote to Internet vs. traditional sales

Planting crops in the face of uncertainty about weather and consumer demand

SCOPE OF OPERATION RESEARCH

(The Multidisciplinary and Interdisciplinary Nature of Operations Research)

I. IN DEFENCE OPERATIONS Administration Intelligence Operations, andTraining and supply.

II.IN INDUSTRYApplications of operations research in the area of

management1. Production Management : The production manager can

apply OR methods for The remunerative policy with regard to time and piece rate. Determination of optimum product mix. Production, scheduling and sequencing the production run

by allocation of machines. Work study operation including time study. Selecting plant location and design of the sites. Distribution policy Loading and unloading facility for road transportation. Maintenance crew sizes.

2. MARKETING MANAGEMENT The marketing manager can apply OR

method for Product selection, timing and formulation of competitive strategies.

Marketing research.Distribution strategies.Sales forecasting.Sales promotion.Selection of advertising media and terms of cost and time factor

To find optimum number of Salesmen.

3. FINANCIAL MANAGEMENT The financial manager can apply OR method

for Apply cash flow analysis for capital budgeting Formulate credit policies, evaluate credit risksDetermine optimum replacement strategies.Frame claim and complaint procedures.Frame policies regarding capital structure.Long range capital requirement. Investments portfolio.Dividend policies.

4. PERSONAL MANAGEMENT The personal manager can apply OR method for Forecasting the manpower requirement, framing of

recruitment policies, assignment of jobs to machines or workers etc.

Selection of suitable personnel with due consideration for age, education skills training etc.

Determination of optimum number of persons for each service centre.

The promotional policies. Mixes of age and skills.

5. PURCHASE DEPARTMENT The purchased department can apply OR

method for Determining the quantity and timing of purchase of raw materials, machinery etc.

Bidding policies.Rules for buying and supplies under varying pries.Equipment replacement policies.Determination of quantities and timing of purchases.

6. RESEARCH AND DEVELOPMENT DEPARTMENT

The research and development department can apply OR method for

Determining the areas for research and development.

Scheduling and control of R and D projects.Resource allocation and crashing in projects.Project selection.Reliability and alternative design.

7. MANUFACTURING DEPARTMENT

The manufacturing department can apply OR method for :

Inventory control Projection marketing balance.Production scheduling Production smoothing.

8. ORGANIZATION BEHAVIOUR DEPARTMENT The OB department can apply OR

method forPersonnel selection and planning.Scheduling of training programs.Skills balancing.Recruitment of Employees.

9. ACCOUNTING DEPARTMENT The accounting department can apply OR

method for Cash flow and fund flow planning.Credit policy analysis.Planning of delinquent account strategy.

10. TECHNIQUES AND GENERAL MANAGEMENT

The Techniques & General Management can apply OR method for

Decision support systems and MIS; forecasting.Organizational design and controlProjection management, strategic planning.

III. IN GOVERNMENT PLANNING IV. AGRICULTURE: With the explosion of population and

consequent shortage of food, every country is facing the problem of :

Optimum allocation of land and various crops in accordance with the climatic conditions;

Optimum distribution of water from various resources like canal for irrigation purposes.

Thus there is a need of determining best policies under the prescribed restrictions. Hence a good amount of work can be done in this direction.

V. IN HOSPITALS VI. IN LIFE INSURANCE CORPORATIONVII. IN CONSTRUCTION PROJECTSVIII. OPERATIONS RESEARCH MANAGEMENT INFORMATION

SYSTEMSIX. OPERATIONS RESEARCH AS SYSTEM SCIENCE:

Extensions

Unification

The Needs: Explication, Understanding, Prediction

Observation of the phenomenon

Modeling New Theories

Using Existing Models

Constructing Hypothesis

Obtaining Experimental Data

Testing for Confirmation Or

Attempt of Refutation

METHODOLOTY OF OR METHODS

 OrientationProblem DefinitionValidation and Output AnalysisSolutionImplementation and MonitoringData CollectionModel Formulation

Basis of Classification

STRUCTURE PURPOSE TIME/BEHAVIOUR DEGREE OF SOLUTION CERTAINITY PROCEDURE

Descriptive Normative Model Model Predictive Model Static Dynamic Analytical Simulation Physical Symbolic Model Model Model Model Model Model Model

Probabilistic Non- Probabilistic Iconic Analogue Verbal Mathematic Model Model Model Model Model Model

CLASSIFICATION OF OR MODEL (A) Classification Based on Structure 1. Physical Model : These models provide a physical appearance of the real object under study either reduced in size or scaled up. These models cannot be manipulated and not very useful for prediction, therefore, problems such as portfolio section, media selection, production scheduling, etc. cannot be analysed with a physical model. Physical models are classified into the following two categories.Iconic Models : Iconic models retain some of the physical and

characteristics of the system they represent. An iconic model is either in an idealized form or a scaled version of the system. It is said to be scaled down when the dimensions of the model are smaller than those of the real object and model said to be scaled up when it is bigger than the real object. In other words, it is an image.

Examples : A globe representing the earth. Blue prints of a home. Model of a cell in biology. A baby toy car as a model of an automobile.

PHYSICAL MODELSAnalogue Model: These models represent a system or object by using

set of properties different from the ones, held by the original object or system. There is no ‘look-alike’ relation between the model and the original. i.e. These models represent a system by the set of properties different from that of the original system and does not resemble physically. After the problem is solved, the solution is re-interpreted in terms of the original system.

Example : Organizational chart represent the state of formal relationships existing between

members of the organization. Maps in different colours may represent water, desert, mountains etc. Graphs of time series, stock market etc. may be used to represent quantitative

relationship between any two properties. Both models are easier to manipulate and can represent dynamic situations; so

analogue model is more popular than iconic models.

SYMBOLIC MODELSThese models use symbols like letters, numbers etc.to represent

the properties of the system. These models are also used to represent relationships which can be represented in a physical form. Symbolic models can be classified into two categories:

Verbal Models: These models describe a situation in written or spoken language.

Example: Written sentences, books, newspapers, journals etc.Mathematical Models: These models represent the

characteristics of a situation or reality by using a set of mathematical symbols and relationships. These models are widely used in OR due to their capacity to depict the complex relationship among the variables of a problem. Example : ‘+’, ‘–‘, ‘×’, ‘÷’.

CLASSIFICATION BASED ON PURPOSE The models based on the purpose of their utility include :Descriptive Models: Descriptive models simply describe some features of a

situation based on observation survey or other available data of a situation and do not predict or recommend.

Example : Result of a n opinion poll. Block diagram representing an algorithm or method for solving a problem.Predictive Models: These models indicate that ‘if this occurs then that will

follow’. They related dependent and independent variables and permit trying out, ‘what if’ questions. In other words, these models are used to predict the outcomes due to a given set of alternatives for the problem.

Example : Television network try to predict the election results before the counting of all the

votes. Rain forecast before actual rainfall.Normative Models : When a model has been repeatedly successful, it can be

used to develop objective decision rules or criteria for optimal solutions. These models are applicable to repetitive problems.

Example : Linear programming is a normative or prescriptive model, because it prescribes what

the managers should do.

CLASSIFICATION BASED ON BEHAVIOUR

Static models : these models are considered independent of time. They do not take into account the effect of changes taking place during a particular time period. It involve only one decision for duration of a given time period.

Example :an inventory models can be developed and solved to determine economic order quantity for the next period assuming that the demand in planning period would remain the same as that for today.Dynamic models : these models consider time as one of the important variables and taken into account the effect of changes generated by time. This involves not only one, but a series of interdependent decisions are required.

Example : dynamic programming in which all possible results are analyzed and best solution is selected.

CLASSIFICATION BASED ON DEGREE OF CERTAINTY

Deterministic Models : These models make assumption of certainty and perfect knowledge. In this model the parameters are completely defined. Examples: Linear Programming Problems, Assignment Problems, Transportation Problems , Break even models etc.

 Probabilistic Models : Models in which at least one parameter or decision variable is a random variable are called probabilistic models. Variables are independent which is the function of dependent variable(s). This means payoff due to certain changes in the independent variable cannot be predicted with certainty. However, it is possible to predict a pattern of values of both the variables by their probability distribution. Example : Probabilistic inventory models are used the conditions of uncertain demand to decide the economic ordering quantity (EOQ). A game theory where saddle points or equilibrium points of the player does not exists, we apply probabilistic model.

CLASSIFICATION BASED ON SOLUTION PROCEDURE

Analytical Models : These models have a specific mathematical structure and problems can be solved by running specific solution procedures. Any optimization model (which requires maximization or minimization of an objective function) is an analytical model.

Example :A general linear programming problem.Special structured transportation and assignment problem.Simulation Models : These models also have a

mathematical structure but are not solved by applying mathematical techniques to get a solution. Instead, a simulation model is essentially a computer assisted experimentation on a mathematical structure of a real life problem in order to describe and evaluate its behaviour under certain assumptions over a period of time.

LIMITATIONS OF OPERATIONS RESEARCHOperation Research has certain limitations. However,

these limitations are mostly related to the problems of model building and the time and money factors involved in its application rather than its practical utility.

Some of them are as follows: MAGNITUDE OF COMPUTATIONSO.R tries to find out optimal solution taking into

account all the factors. In the modern society these factors are enormous and expressing them in quantity and establishing relationships among these are required complicated calculations which can only be handled by machines.

NON-QUANTIFIABLE FACTORSO.R provides solution only when all elements

related to a problem can be qualified. All relevant variables do not lend themselves to quantification. Factors which cannot be quantified, find no place in O.R.

GAP BETWEEN MANAGER AND OPERATIONS RESEARCHER

O.R being specialist’s job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Management itself may offer a lot of resistance due to conventional thinking.

MONEY AND TIME COSTSWhen the basic data are subjected to frequent

changes, incorporation them into the O.R models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R solution available after sometime.

IMPLEMENTATIONImplementation of decisions is a delicate task. It

must take into account the complexities of human relations and behaviour. Sometimes resistance is offered only due to psychological factors.

SELECTION OF TECHNIQUEOperations Research techniques are very useful

but they cannot be used indiscriminately. Choice of technique depends upon the nature of problem, operating conditions, assumptions, objectives, etc. Thus, identification and use of an appropriate technique is essential.

NOT A SUBSTITUTE OF MANAGEMENTOperations Research only provides the tools and

cannot be a substitute of management. It only examines the results of alternative courses of action and final decision is made by management within its authority and judgment.

SUB- OPTIMISATIONSub- optimisation is deciding in respect of a

relatively narrow aspect of the whole business situation or optimisation of a sub- section of the whole. Functional heads some times, without taking care of wider implications, sub- optimise their functions. This may cause loss in that part of the organisation which is left out of the exercise and as such should be avoided.

THANK YOU

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OM SHANTI !