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Developments during world war Developments during world war II II

Operation Research - Relation withOperation Research - Relation with applied Mathematics, Statistics, applied Mathematics, Statistics,

Developments in computer ScienceDevelopments in computer Science

Presented by Prof.Dr.Nirmal S.KamboPresented by Prof.Dr.Nirmal S.Kambo

Department of Industrial EngineeringDepartment of Industrial Engineering

EMU EMU

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Branch of science dealing with Branch of science dealing with modeling and analyzing techniques for modeling and analyzing techniques for optimizing the performance of optimizing the performance of organization systems. organization systems.

Taking optimal decisions especially Taking optimal decisions especially those dealing with the allocation of those dealing with the allocation of limited recourses.limited recourses.

Operations Research (O.R.) Several definitions

Finding “best” decisions is main Finding “best” decisions is main concern of human beings concern of human beings

Ancient humans worried about Ancient humans worried about problems like ‘what is the shortest problems like ‘what is the shortest route from my home to the river?’route from my home to the river?’

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Origin of O.ROrigin of O.R Roots can be traced back to early Roots can be traced back to early

1900’s.1900’s. Major scientific approach started in early Major scientific approach started in early

world war IIworld war II British and American military management British and American military management

formed formed groupsgroups of ofo Scientists – Scientists –

Mathematicians ,Physicists ,Statisticians , ...Mathematicians ,Physicists ,Statisticians , ...o Engineers – Aeronautical ,Naval , Engineers – Aeronautical ,Naval ,

Communication ,… Communication ,… o Know-how persons – Army , Navy , Air Know-how persons – Army , Navy , Air

force ,…force ,… 66

PurposePurpose

Study various military operations Study various military operations and activities in an effective and activities in an effective manner in view of manner in view of scarce resourcesscarce resources (human beings, arms & ammunition (human beings, arms & ammunition , aero planes , ships , food etc. , aero planes , ships , food etc.

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Type of problemsType of problems

Allocation(optimal) of limited resourcesAllocation(optimal) of limited resources Deployment of armiesDeployment of armies Opening war ??? (where ? How many ?)Opening war ??? (where ? How many ?) Deployment of missiles – Cause Deployment of missiles – Cause

Maximum damage Maximum damage Allocation of aero planes , ships , etc.Allocation of aero planes , ships , etc. Bombardment areas…Bombardment areas… Supply lines… Supply lines…

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Results of group activitiesResults of group activities a)a) Won air battle of BritainWon air battle of Britain

Won Island campaign in the PacificWon Island campaign in the Pacific

Won battle of North Atlantic….Won battle of North Atlantic….

b)b) Impetus to O.R studies & techniques Impetus to O.R studies & techniques

Motivation to research in O.R.Motivation to research in O.R.

An important contribution is by George An important contribution is by George Dantzing (1949) ‘Simplex Method of LP’Dantzing (1949) ‘Simplex Method of LP’

- Karwarkaz’s method for LP (1984)- Karwarkaz’s method for LP (1984)

Major contributions in LP ,DP , Queuing , Major contributions in LP ,DP , Queuing , inventory etc. developed before 1950.inventory etc. developed before 1950.

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c)c) Growth of computersGrowth of computers Fast developments in O.R.Fast developments in O.R. Expansion of organizationsExpansion of organizations Large size O.R. problemsLarge size O.R. problems Large amount of computationsLarge amount of computations … … Led to Led to Computers RevolutionComputers Revolution

... From large size electronic digital ... From large size electronic digital computers tocomputers to

Mainframe computersMainframe computers Mini computersMini computers Micro computersMicro computers Super computersSuper computers

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Commonly Used ToolsCommonly Used Tools Mathematics & StatisticsMathematics & Statistics

1)1) Linear Algebra, MatricesLinear Algebra, Matrices

2)2) Calculus , analysis (Real and Calculus , analysis (Real and Complex)Complex)

3)3) Differential EquationsDifferential Equations

4)4) Probability TheoryProbability Theory

5)5) Stochastic ProcessStochastic Process

6)6) Statistical MethodsStatistical Methods

7)7) etcetc1111

Computing machinesComputing machines Computer softwareComputer software Simulation TechniqueSimulation Technique .. ..

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QueuesQueues

Waiting time of customers to get Waiting time of customers to get serviceservice

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Queues of Queues of personspersons at a bank at a bank PartsParts waiting for processing on machines waiting for processing on machines MachinesMachines waiting for repair waiting for repair JobsJobs waiting for processing on computer waiting for processing on computer Aero planesAero planes waiting to land or take off waiting to land or take off Telephone callsTelephone calls waiting at exchange waiting at exchange StudentsStudents waiting for registration waiting for registration Traffic flowTraffic flow Communication / Computer networkCommunication / Computer network

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o To model such situation. Process worked To model such situation. Process worked A.K.Erlang (1909) for A.K.Erlang (1909) for tolerance callstolerance calls

o Characteristics of queuesCharacteristics of queues Arrival of customers (Random / Deterministic)Arrival of customers (Random / Deterministic) Service times (Random)Service times (Random) Servers (Single , Finite , infinite)Servers (Single , Finite , infinite) Queue discipline (FCFS ,LCFS ,SIRO ,Priority ,Queue discipline (FCFS ,LCFS ,SIRO ,Priority ,

…)…) System capacity (Finite or Infinite)System capacity (Finite or Infinite) Population of customers (Finite or Infinite) Population of customers (Finite or Infinite)

Random characteristics – Knowledge of Random characteristics – Knowledge of probability , stochastic processes (For probability , stochastic processes (For Modeling) ,Statistics (For estimation), etc.Modeling) ,Statistics (For estimation), etc.

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Performance MeasuresPerformance Measures(Steady-State)(Steady-State)

Average number of customers in system , LAverage number of customers in system , L Average number of customers in queue , LAverage number of customers in queue , Lqq

Average waiting time of customers in queue Average waiting time of customers in queue , w, wqq

Average waiting time of customers in Average waiting time of customers in system , wsystem , w

Throughout – rate of completion of jobsThroughout – rate of completion of jobs Fundamental result (LITTLE’S FORMULAS)Fundamental result (LITTLE’S FORMULAS)

λλ= Average arrival – rate of = Average arrival – rate of customers entering the systemcustomers entering the system 2020

Why steady?Why steady?Costs involvedCosts involved Service costs ( no of servers, service Service costs ( no of servers, service

rates,..)rates,..) Waiting time costsWaiting time costs System capacity costsSystem capacity costs

To avoid congestionTo avoid congestion To design optimal systemTo design optimal system ……

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