Presented by Prof.Dr.Nirmal S.Kambo Department of Industrial Engineering EMU

1. 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

2. Operations Research (O.R.)Several definitions • 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.

3. 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?’

6. Origin of O.R • 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 ,…

7. 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.

8. Type of problems • 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…

9. 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.

10. 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

11. Commonly Used Tools • Mathematics & Statistics • Linear Algebra, Matrices • Calculus , analysis (Real and Complex) • Differential Equations • Probability Theory • Stochastic Process • Statistical Methods • etc

12. Computing machines • Computer software • Simulation Technique • . • .

15. Queues • Waiting time of customers to get service

18. 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

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

20. Performance Measures(Steady-State) • 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

21. Why steady? Costs involved • Service costs ( no of servers, service rates,..) • Waiting time costs • System capacity costs • To avoid congestion • To design optimal system • …

22. Thank you for your time and attention