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Introduction Introduction Operation Ope ration Res earch Research is is an an int erdisc ipl inary interdisciplinary branch br anch of  of appl ied appl ie d mathemati cs mathematics and and formal formal science science that that uses uses methods methods such such as as Mathematical modeling Mathematical modeling Statistic Statistic Algorithm Algorithm to to arrive arrive at at optimal optimal or or near near optimal optimal solutions solutions to to complex complex problems problems. It It is is typically typical ly concerned concerned with wit h determining determining the the ma xi mum maxi mum prof it profi t or or minimum minimum loss loss , , risk risk of of some some objective objective function function. Operation Operation Research Research helps helps management management achieve achieve its its goals goals using using scientific scientific methods methods.

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8/8/2019 Or Intro Slides

IntroductionIntroductionOperationOperation ResearchResearch isis anan interdisciplinaryinterdisciplinarybranchbranch of of appliedapplied mathematicsmathematics andand formalformalsciencescience thatthat usesuses methodsmethods suchsuch asas

Mathematical modelingMathematical modeling

StatisticStatistic

AlgorithmAlgorithm

toto arrivearrive atat optimaloptimal oror nearnear optimaloptimal solutionssolutions totocomplexcomplex problemsproblems.. ItIt isis typicallytypically concernedconcernedwithwith determiningdetermining thethe maximummaximum profitprofit ororminimumminimum lossloss ,, risk risk of of somesome objectiveobjective functionfunction..OperationOperation ResearchResearch helpshelps managementmanagement achieveachieveitsits goalsgoals usingusing scientificscientific methodsmethods..

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HistoryHistory

Modern Operation Research originated atModern Operation Research originated at

Bawdsey Research Station in UK in 1937.Bawdsey Research Station in UK in 1937.

It was theIt was the resultresult of an initiative of the station'sof an initiative of the station'ssuperintendent A.P Rowe.superintendent A.P Rowe.

He conceived the idea as a means to analyzeHe conceived the idea as a means to analyze

and improve the working of the UK's earlyand improve the working of the UK's early

His idea was successful.His idea was successful.

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HistoryHistory

Later Later onon duringduring worldworld war war IIII ,, thethe militarymilitarycommandscommands of of UU..K K.. andand UU..SS..AA engagedengaged severalseveralinterdisciplinaryinterdisciplinary teamsteams of  of scientistsscientists toto

undertakeundertake scientificscientific researchresearch intointo strategicstrategic andandtacticaltactical militarymilitary operationsoperations..

Their Their missionmission waswas toto formulateformulate specificspecific proposal proposal andand plans plans for for aidingaiding thethe MilitaryMilitary

CommandsCommands toto arrivearrive atat thethe decisiondecision onon optimaloptimalutilizationutilization of of scarcescarce militarymilitary resourcesresources andandeffortsefforts andand alsoalso toto implementimplement decisiondecisioneffectivelyeffectively..

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HistoryHistory

OR OR teamsteams werewere notnot actuallyactually involvedinvolved ininfightingfighting thethe war war but but theythey werewere onlyonly advisorsadvisorsandand significantlysignificantly instrumentalinstrumental inin winningwinning thethe

war war because because of of their their goodgood intellectualintellectual supportsupporttoto thethe strategicstrategic initiativesinitiatives of of thethe militarymilitarycommandscommands..

After After thethe war war thethe apparentapparent successsuccess of of militarymilitaryteam,team, itit attractedattracted thethe attentionattention of of thethe industryindustry..

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HistoryHistory

InIn IndiaIndia OperationOperation ResearchResearch waswas originatedoriginated

duringduring thethe lastlast phase phase of of worldworld war war IIII..

InitiallyInitially ,, anan OR OR centrecentre waswas formedformed atat thethe Air Air headquartersheadquarters toto tackletackle thethe problems problems relatingrelating toto

TheThe work work donedone by by thisthis groupgroup of of scientistscientist waswas

veryvery limitedlimited inin itsits scopescope..

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HistoryHistory

ActuallyActually inin IndiaIndia OR OR startedstarted inin 19491949 withwith thethe openingopeningupup of  of aa unitunit atat thethe RegionalRegional ResearchResearch Laboratory,Laboratory,HyderabadHyderabad for for usingusing OperationOperation ResearchResearch inin planning planningandand organizingorganizing researchresearch..

After After thatthat AhmedabadAhmedabad TextileTextile IndustryIndustry ResearchResearchAssociationAssociation organizedorganized anan OR  OR groupgroup for  for their  their industrialindustrial problem problem..

InIn 19531953 anan OR  OR unitunit waswas formedformed atat thethe IndianIndianStatisticalStatistical InstituteInstitute ,, CalcuttaCalcutta withwith aa viewview toto applyapply OR OR techniquestechniques toto nationalnational planning planning under under thethe guidanceguidance of of Prof Prof.. MahalnobisMahalnobis..

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HistoryHistory

OROR gotgot itsits formalformal recognitionrecognition inin thethe countrycountry withwith thetheformationformation OO..RR.. SocietySociety of of IndiaIndia inin 19571957..

TheThe societysociety becamebecame thethe member member of of thethe internationalinternationalFederationFederation of of SocietiesSocieties inin 19591959 andand organizedorganized itsits firstfirstconferenceconference atat allall IndiaIndia levellevel inin thethe samesame year year..

After  After thatthat publicationpublication of of thethe JournalJournal OPSEARCHOPSEARCH byby

ORSIORSI inin 19641964 further further addedadded toto thethe growthgrowth of of OROR..

ORSIORSI isis regularlyregularly organizingorganizing itsits annualannual conventionconvention sincesince19681968..

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OR Education In IndiaOR Education In India

OR education was formally initiated in India with theOR education was formally initiated in India with theformation of Indian Institute of Ahmedabad and Calcuttaformation of Indian Institute of Ahmedabad and Calcuttaduring the year 1961during the year 1961--62.62.

The university of Delhi started a full time Master¶s degree inThe university of Delhi started a full time Master¶s degree inOperation Research in 1963.Operation Research in 1963.

A Graduate Programme in operation research was introducedA Graduate Programme in operation research was introduced

by the Operation Research Society of India in 1973. by the Operation Research Society of India in 1973.

Today almost all the universities and Institutions in India areToday almost all the universities and Institutions in India areoffering the inputs of Operation Research In their Curriculum.offering the inputs of Operation Research In their Curriculum.

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Successful OR Applications in industrySuccessful OR Applications in industry

Company year Problem Annual Saving

errill ynch

esign Asset based anddirect online pricingoption for providing

Financial Services

8 million more

revenue

Continental Airlines

Optimize the reassignment of crews to flights whenschedule disruptionsoccur 4 million

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Phases of Operation ResearchPhases of Operation Research

Define the Problem of Interest and gathering relevantDefine the Problem of Interest and gathering relevant

Formulate mathematical model to represent theFormulate mathematical model to represent the

problem problem

Develop a computer Develop a computer--based procedure for deriving based procedure for deriving

solution to the problem from the modelsolution to the problem from the model

Test the model and refine it as neededTest the model and refine it as needed Prepare for ongoing application of the model asPrepare for ongoing application of the model as

prescribed by management & Implement prescribed by management & Implement

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Phases of ORPhases of OR

Define the Problem of Interest and gathering relevantDefine the Problem of Interest and gathering relevant

This IncludesThis Includes

DeterminingDetermining of of appropriateappropriate objectivesobjectives

ConstraintsConstraints

InterrelationshipsInterrelationships betweenbetween thethe areaarea toto bebe studiedstudied andand

otherother areasareas

PossiblePossible alternativealternative coursecourse of of actionaction

TimeTime limitlimit forfor makingmaking aa decisiondecision

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Phases of ORPhases of OR

ExampleExample:: DefineDefine thethe ProblemProblem of of InterestInterest andand gatheringgatheringrelevantrelevant datadata

AnAn OR  OR studystudy donedone for for SanSan FranciscoFrancisco PolicePolice DepartmentDepartmentresultedresulted inin thethe computerizedcomputerized systemsystem for  for optimallyoptimallyschedulingscheduling andand deployingdeploying police police patrol patrol officersofficers..

TheThe newnew systemsystem provided provided annualannual savingsaving of of \$\$1111million,million, andand

aa 2020%% improvementimprovement inin responseresponse timestimes.. InIn assessingassessing thetheappropriateappropriate objectivesobjectives for for thisthis studystudy ,, threethree fundamentalfundamentalobjectivesobjectives werewere identifiedidentified

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Phases of ORPhases of OR

Objectives of the study were identified as:Objectives of the study were identified as:

Maintain a high level of citizen safety.Maintain a high level of citizen safety. Maintain a high level of officer Morale.Maintain a high level of officer Morale.

Minimize the cost of operations.Minimize the cost of operations.

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Phases of ORPhases of OR

ExampleExample:: InIn thethe latelate 19901990ss fullfull serviceservice financialfinancial serviceservice

firmsfirms camecame under under assaultassault fromfrom electronicelectronic

MerrillMerrill LynchLynch respondedresponded by by conductingconducting major major

OR OR studystudy thatthat ledled toto completecomplete overhauloverhaul inin howhow

itit chargedcharged for for itsits services,services, rangingranging fromfrom aa aa fullfull

serviceservice assetasset based based optionoption toto aa lowlow costcost optionoption

for for clientsclients wishingwishing toto investinvest onlineonline directlydirectly..

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Phases of ORPhases of OR

DataData collectioncollection andand processing processing played played aa keykeyrolerole inin thethe studystudy

ToTo analyzeanalyze thethe impactimpact of of individualindividual clientclient behavior  behavior inin responseresponse toto differentdifferent optionsoptions thetheteamteam neededneeded toto assembleassemble aa comprehensivecomprehensive datadata

of of 200200 gigabytesgigabytes involvinginvolving 55 millionmillion clients,clients,1010 millionmillion accounts,accounts, 100100 millionmillion tradetrade records,records,andand 250250 millionmillion ledger ledger recordsrecords..

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Formulate mathematical model toFormulate mathematical model to

represent the problemrepresent the problem ExampleExample

AnAn OR  OR studystudy donedone for for MonsantoMonsanto waswas concernedconcerned withwith

optimizingoptimizing production production operationoperation inin MonsantoMonsanto chemicalchemical plant plant toto minimizeminimize thethe costcost of  of meetingmeeting targettarget for for thethe

amountamount of of certaincertain chemicalchemical product product toto be be produced produced inin

settingsetting for for eacheach of of thethe catalyticcatalytic reactor reactor usedused toto produce produce

thisthis product, product, wherewhere settingsetting determinesdetermines thethe costcost of  of

operatingoperating thethe reactor reactor andand amountamount produced produced..

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Phases of Operation ResearchPhases of Operation Research

Develop a computer Develop a computer--based procedure for  based procedure for

deriving solution to the problem from thederiving solution to the problem from the

modelmodel

Test the model and refine it as neededTest the model and refine it as needed

Prepare for ongoing application of the modelPrepare for ongoing application of the model

as prescribed by management & Implementas prescribed by management & Implement

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O.R. APPROACHO.R. APPROACH

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Classification Of odelsClassification Of odels

Models can be classified according to followingModels can be classified according to following

characteristicscharacteristics

Classification by structureClassification by structure

Iconic Models Iconic Models

Analogue Models Analogue Models

Symbolic Model Symbolic Model

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Classification Of odelsClassification Of odels

Classification by PurposeClassification by Purpose

Descriptive Model  Descriptive Model

Predictive Model  Predictive Model

Prescriptive Model  Prescriptive Model

Classification by nature of EnvironmentClassification by nature of Environment

Deterministic Models Deterministic Models  Probabilistic Models Probabilistic Models

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Classification Of odelsClassification Of odels

Classification By behaviorClassification By behavior

Static Model Static Model

Dynamic Model Dynamic Model  Classification By Method of SolutionClassification By Method of Solution

Analytical Models Analytical Models

Simulation ModelsSimulation Models

Heuristic ModelsHeuristic Models