module 1 operations research

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Operations Research


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History

Origin - During Second world war . AT that time military

management in England called upon team of scientists to studythe strategic & tactical problems related to air, land defense of

the country . Since they were having very limited military

resources , it was necessary to decide upon the most effective

utilization of them

It has various names Operations Analysis, Operations

Evaluation , Operations Research , Systems Analysis , Systems

Research, Systems Evaluation , Management science.

Objective is OR model is more focused on Profit Maximization

Or Cost minimization

First Mathematical Model developed was Simplex Method

Apart from Military many other field started using OR activity

like Delhi cloth mill, Indian Railways, Indian Airlines, etc


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Introduction

-OR is a scientific method of providing executivedepartments with quantitative basis for decision

making regarding the operations under their control

- OR is the art of giving bad answers to problems to

which otherwise worse answers are given- OR is a scientific approach to problem solving for

executive management

- OR is a scientific method of providing executive with

analytical & objective basis for decisions


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Comments :

1 ) Every field like physics, chemistry, biology has its

history. It is very difficult to define OperationsResearch precisely as it is developed using

Mathematical Techniques & Tools which in

conjunction with a system approach are applied to

define operations2) Interdisciplinary approach is important

characteristics of Operations Research . In most of

the definitions this term is not used & are not

satisfactory3)


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Management Applications of OR

Finance Budgeting & Investments

Cash Flow Analysis , Long Range Capital Requirements ,Dividend Policies, Investment Portfolios

Purchasing Procurement

Rules for buying ,supplies, & stable or varying ,biddingpolicies, Replacement policies

Production Management

Physical distribution Location, size of warehouse, DCs &Retail outlets

Facilities planning Number & location of factories,

warehouses, loading unloading facilitiesManufacturing Production Scheduling & sequencing

Maintenance & Scheduling -


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Marketing

- Product Selection, timing, competitive actions

- No of salesman , frequency of calling counts percent,

HR ( Personnel Management )

- Selection of suitable person on minimum Salary , mixes of

age & skills

Research & Development- Determination of the areas of concentration

- Project Selection , Determination of time & cost trade-off,

& control of Self development Projects


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Employing techniques from other mathematical sciences,such as mathematical modeling, statistical analysis,

and mathematical optimization, operations research

arrives at optimal or near-optimal solutions to complex

decision-making problems.
http://en.wikipedia.org/wiki/Mathematical_modelhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Mathematical_optimizationhttp://en.wikipedia.org/wiki/Mathematical_optimizationhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Mathematical_model


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Modeling in Operations Research

Model is an representation of an actual object or situation. It shows relationships & inter-relationships of action &reaction in terms of cause & effect

Model is abstraction of reality

Classified according to following characteristics

A) Classification by Structure

- 1) Iconic Models scaling up or down e.g photographsdrawing , maps

- 2) Analogue models one set of properties is used to

interpret another set of properties such as e.g graphs,diagra, are used to represent properties such astime,number,percent, weight

- 3) Symbolic models ; It employs set of mathematicalsymbols


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B ) Classification by Purpose : It can be classified bypurpose of its utility.

1) Descriptive Models Simply describe some

aspects of a situation based on observations ,survey,

questionnaire . Result of opinion pollII ) Predictive Model : Such models can answer What

if type questions . Make predictions regarding

certain events

III) Prescriptive model : when above model is usedsuccessfully @ many number of times it can be used

to prescribe a source of action


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C) Nature of Environment :1) Deterministic assume conditions of certainty .e,g

transportation problems

II ) Probabilistic models : - Usually handle such situation

in certain things cannot be predicted with certaintyexample IN Insurance company

D) Classification by behavior :

I ) Static Model : These models do not consider the

impact of changes that takes place during the planninghorizon i.e. they are independent of time .

II ) Dynamic model : In these model time is considered &

it considers the impact of changes in time


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E ) Classification by method of Solution :1) Analytical models : These models have a specific

mathematical structure & thus can be solved by

known analytical or mathematical techniques. E.g

LPPII ) Simulation model : Purely cannot be solved by

using tools & techniques of mathematics. A

simulation model is essentially computer assisted

experimentation on mathematical structure of realtime structure.


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Principles of Modeling

Do not build complicated model when simple one will suffice

Beware of molding the problem to fit the technique e.g. An

expert on Linear Programming techniques may tend to viewevery problem he encounters as required in LP only . In fact notall optimization problems involve only Linear Functions.

The deduction phase of modeling must be conducted rigorously:The reason for requiring rigorous deductions is that one wantsto be sure that if model conclusions are inconsistent with reality, then the defect lies in assumptions

Models should be validated prior to implementation: e.g. Ifmodel is constructed to forecast the monthly sales of aparticular commodity it could be tested using historical data tocompare the forecasts it would have produced to the actual

sales. Model has to be validated prior to implementation A Model should never be taken too literally : For example

suppose that one has to construct an elaborate computer modelof Indian Economy with many competent researchers spendinga great deal of time & money in getting all kinds of complicatedinteractions & relationships. Under such situation it can bebelieved as if model duplicates itself the real system


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A model should neither be pressed to do , nor criticized forfailing to do that for which it was never intended :Model

used for forecasting Beware of Over- Selling a model: If any one is not aware

of how to use models than he or she should not go for it

A model cannot be any better than the Information that

goes into it : Models cannot replace Decision Makers :


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Simplification or Approximations of models

Model should be as accurate as possibleIs should be as easy as possible in solving

Model can be simplified by :

- Omitting certain variable

- Changing the nature of variables

- Aggregating the variables

- Changing the relationship between variables- Modifying the constraints


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General Methods For solving OR problems

A Analytic Method : If OR model is solved by usingclassical mathematics such as differential calculus ,

finite differences available for this task, then such type

solutions is called

B.Iterative Method: If classical method fail because ofcomplexities of the constraints or of the number of

variables then we are usually forced to adopt an

iterative method . First Trial soln is obtained ,

repeated again till optimal solution is obtainedThis is also called as Trial & Error method


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C) Monte Carlo Method

Step 1 We first draw a flow diagram of the system

Step 2 Take correct sample observations to select some

suitable model for the system. In this step we compute theprobability distributions for the variables of our interest

Step 3 Convert Probability distributions to a cumulativedistribution function

Step 4 A sequence of random numbers is now selected

with the help of random number tablesStep 5 Next we determine the sequence of Values of

variables of interest with the sequence of random numbersobtained in previous step

Step 6 Finally we construct some std mathematical

function to the values obtained


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Characteristics or Features

- Interdisciplinary Approach : In OR team of scientistsare from various disciplines are involved such asmathematics, statistics, economics, engineering,physics

- Wholistic Approach : It gives optimum solution (

decision ) relative to largest possible portion of thetotal organization. E. g Maintenance problem infactory

- Imperfections of Solutions : WE get better solutions

instead of good solution- Uses of scientific Research: It uses technique of

scientific research to reach optimum solution

- Optimize Total output : OR tries to optimize by

focusing more of profit with cost @ minimum


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Procedure/ Phases/steps of Operations Research

1) Formulating the Problem :Before proceeding to findthe solution of a problem first of all one must be ableto formulate the problem inn form of proper model

Who has to take decision, What are the objectives ,

What are the ranges of controlled variables, ,uncontrolled variables that may affect possible

solution , Constraints on the variables, constraints

on the variables ?

II) Constructing a Mathematical model : Reformulatethe problem in an appropriate form which is

convenient for analysis. It should have a) decision

variables b) Constraints c) Objective function


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III)Deriving the solutions from the model:This phase isdevoted to the computation of those values ofdecision variables that maximize or minimize the

objective function . Such solutions are called optimal

solution which is the best solution to problem under

consideration.

IV) Testing the model & its Solution ( Updating themodel):After completing the model it is once again

tested as a whole for the errors if any. A model maybe said to be valid if it can provide a reliable

prediction of the systems performance. Model

should be updated every time considering past,

present & Future


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V) Controlling the Solution :This phase establishescontrols over the solution with any degree ofsatisfaction. The model requires immediate

modification as soon as the controlled variables

change significantly otherwise the model goes out of

control.

VI) Implementing The Solution : Finally the testedresults of the model are implemented to work .


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Terms: Tools, Techniques & Methods

Here we Differentiate the terms Tools ,Techniques, &Methods which are frequently used in science.

Similarly calculus is a scientific Tool , employing

calculus to find an optimum value of a variable in a

mathematical model of a system is a scientific

technique & plan of utilizing a mathematical model to

optimize a system is a scientific method


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Scientific Method in Operations Research

It generally involves the three phases

a) Judgment Phase

- A determination of the operation

- The establishment of the objectives & values related

to the operation- The determination of the suitable measures of

effectiveness

b) Research Phase

- Observations & data collection for a betterunderstanding of what the problem is

- Formulation of hypothesis & models


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- Analysis of the available information & verification of

the hypothesis using pre-established measures of

effectiveness

- Predictions of various results from the hypothesis,

generalization of the result & consideration of

alternative methods

c) Action Phase- OR consists of making recommendations for decision

process by those who first posed the problem for

consideration or by someone to make decision

influencing the operation in which problem occurred


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Scope of OR

In agriculture Optimum allocation of Land to various crops

with the climatic conditions , distribution of water fromvarious resources like Canal for irrigation purpose.

2) In Finance - Helpful for government for careful planning

for the economic development . OR techniques help to

maximize the per capita income , to find out the profit planfor the company

3) In Industry - Industry manager OR is used for deciding

optimum allocation of various limited resources such as

men , machines,money,time,etc.4) In Marketing In the field of marketing it is useful to

decide where to distribute the products for sale so that the

total cost of transportation is minimum, minimum per unit

sale price.


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5) In Personnel management : To appoint the most

suitable persons on minimum salary , to determine

the best age of retirement for the employees.

6) In Production management : OR techniques is used

To find out the number & size of items to be produced ,

In scheduling & sequencing the production run by

proper allocation of machines.


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Outlines of OR models ( Quantitative

techniques of OR ) or Types of OR models

Distribution ( Allocation models ) : Distribution modelsare concerned with allotment of resources so as to

maximize or minimize profit subject to prescribed

restrictions. Methods for solving such type of problems

are known as mathematical programming techniques .

Production / Inventory Models : These are concerned

with the determination of the optimal ( economic ) order

quantity & ordering ( production ) intervals considering

the factors such as demand per unit time , cost ofplacing orders , cost associated with goods held up in

the inventory & the cost due to shortage of goods


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- Waiting Time Model : IN this

WE can know how much average time will be spent by

the customer in Queue? What will be the average

length of waiting Line or Queue

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module 1 operations research

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