Download - 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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