Transcript c - Industrial Engineering Department EMU-DAU

Developments during world war II
Operation Research - Relation with
applied Mathematics, Statistics,
Developments in computer Science
Presented by Prof.Dr.Nirmal S.Kambo
Department of Industrial Engineering
EMU
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Operations Research (O.R.)
Several definitions

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Branch of science dealing with modeling and
analyzing techniques for optimizing the
performance of organization systems.
Taking optimal decisions especially those
dealing with the allocation of limited
recourses.
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Finding “best” decisions is main concern of
human beings
 Ancient humans worried about problems
like ‘what is the shortest route from my
home to the river?’
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Origin of O.R
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Roots can be traced back to early 1900’s.
Major scientific approach started in early world
war II
British and American military management formed
groups of
Scientists – Mathematicians ,Physicists
,Statisticians , ...
Engineers – Aeronautical ,Naval , Communication
,…
Know-how persons – Army , Navy , Air force ,…
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Purpose

Study various military operations and
activities in an effective manner in view
of scarce resources (human beings, arms
& ammunition , aero planes , ships ,
food etc.
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Type of problems
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Allocation(optimal) of limited resources
Deployment of armies
Opening war ??? (where ? How many ?)
Deployment of missiles – Cause Maximum
damage
Allocation of aero planes , ships , etc.
Bombardment areas…
Supply lines…
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Results of group activities
a) Won air battle of Britain
Won Island campaign in the Pacific
Won battle of North Atlantic….
b) Impetus to O.R studies & techniques
Motivation to research in O.R.
An important contribution is by George
Dantzing (1949) ‘Simplex Method of LP’
- Karwarkaz’s method for LP (1984)
Major contributions in LP ,DP , Queuing ,
inventory etc. developed before 1950.
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c) Growth of computers
Fast developments in O.R.

Expansion of organizations

Large size O.R. problems

Large amount of computations

… Led to Computers Revolution
... From large size electronic digital computers to
 Mainframe computers
 Mini computers
 Micro computers
 Super computers

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Commonly Used Tools
Mathematics & Statistics
1) Linear Algebra, Matrices
2) Calculus , analysis (Real and Complex)
3) Differential Equations
4) Probability Theory
5) Stochastic Process
6) Statistical Methods
7) etc
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Computing machines
Computer software
Simulation Technique
.
.
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Queues
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Waiting time of customers to get service
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Queues of persons at a bank
Parts waiting for processing on machines
Machines waiting for repair
Jobs waiting for processing on computer
Aero planes waiting to land or take off
Telephone calls waiting at exchange
Students waiting for registration
Traffic flow
Communication / Computer network
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To model such situation. Process worked
A.K.Erlang (1909) for tolerance calls
o Characteristics of queues
 Arrival of customers (Random / Deterministic)
 Service times (Random)
 Servers (Single , Finite , infinite)
 Queue discipline (FCFS ,LCFS ,SIRO ,Priority ,…)
 System capacity (Finite or Infinite)
 Population of customers (Finite or Infinite)
Random characteristics – Knowledge of probability ,
stochastic processes (For Modeling) ,Statistics (For
estimation), etc.
o
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Performance Measures
(Steady-State)
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Average number of customers in system , L
Average number of customers in queue , Lq
Average waiting time of customers in queue , wq
Average waiting time of customers in system , w
Throughout – rate of completion of jobs
Fundamental result (LITTLE’S FORMULAS)
λ= Average arrival – rate of customers
entering the system
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Why steady?
Costs involved
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Service costs ( no of servers, service rates,..)
Waiting time costs
System capacity costs
To avoid congestion
To design optimal system
…
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Thank you for your time and attention
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