Texts: Gordon G N Deo J Banks et al

 Definition  Advantages and disadvantages  Suitability  Applications  Models  Components of system  Simple examples  Steps in simulation study

 Copy the behavior of a system or phenomena  Imitation of real world process  Generation of artificial history of a system

 Subject of study  Aggregation or Assemblage of objects / processes that interact  Examples:  Traffic, Bank, Restaurant, Petrol bunk, Water reservoir, Inventory, Queue, Training pilots, etc

 New policies/procedures/decisions can be explored without interruption of existing system  No resource commitment  Time can be compressed or expanded while simulating  Interaction of variables can be understood  Importance of variables can be understood  Bottleneck analysis possible  Will know better about system working  What-if questions can be answered

 Model building is difficult  Different experts may come up with two different models  Simulation results may be difficult to interpret  Modeling and analysis may be time consuming and expensive  Good for cases where analytical soultion is not possible

 Suited when:  Analytical solution not available  Model is trustable  Reinforcement of analytical results  If cost effective

 Analytical solution not available  Common sense problems  Numerical simulation not good if direct experiments can be performed  Cost exceeds the savings  Resources or time not available  Data not available  Verification and validation cannot be done  Under unreasonable expectations  Too complex

 List is vast  Here are few:  Manufacturing – Analysis of storage and retrieval strategies in a ware house, Electronics assembly operations, Dynamics in a service oriented supply chain …  Construction – Dam, Activity scheduling in a project, Tunnel construction …  Military – Design of automatic missile, Multi trajectory performance, …

 Logistics, Transportation, Distribution – Evaluating benefits of rail traffic, Analysis of passenger flows in an air port, Product distribution in newspaper industry, …  Business process – Personnel forecasting and work force planning, …  Human system – Modeling human performance in complex systems, Study human element in air traffic control, …

Models Physical Mathematical Static Dynamic Numeric Analytic Numeric System simulation

 Miniaturized dam – with scaled down height, strength, water pressure  Wind tunnels in aircraft system, Water tanks in ship design  Automobile shock absorber and electric circuit have similar differential equations  Hence build a circuit and experiment with changes in volts and resistance  If car wheel bounces too much then the similar effect is indicated in the analogous system with oscillations in voltages  Mathematical model is unsatisfactory in case of builldings

 Is focus of study in this course  Static is when the system is in equilibrium  Dynamic means system changes with time  Examples- Economic model and shock absorber  Both of these are dynamic and analytical  But not all real problems are this simple  If analytical solutions don’t exist numeric solutions are to be generated - simulation

 Deterministic and stochastic ◦ Clerk scrutinizing files in order, Board game playing (to some extent) are deterministic ◦ Card game is probabilistic -Inputs are unpredictable  Discrete and continuous ◦ Queue is discrete – change is abrupt ◦ Inventory, Reservoir, Motion problems are continuous – change is smooth

 System is a group of interacting objects  Example – machines, parts, workers operate coordinately to produce an automobile  Sometimes forces outside the system affect the performance – cyclone affecting production rate of automobiles – exogenous events  Activities that are infrequent and remotely affecting system - exogenous  Such events can be excluded mostly  Events that are part of the system – increase in insurance investments during financial year end – endogenous  In defining components we discuss endogenous events

 Entity – object of interest  Attribute – property of entity useful in study of simulation  Activity – time of specified length  State – collection of variable necessary to describe the system  Event – instantaneous occurrence of that may change state of the system

 Banking system  Objective: Measure wait time of customers  Entity – Customers  Attribute – Entry time, Transaction type, Exit time  Activity – Transaction  State – Customers in the bank  Event – Arrival, Departure of customers

 Banking system  Objective – Measure deposits and withdrawals  Entity – Customers  Attribute – Amount deposited or withdrawn  Activity – Transaction  State – Volume of cash in the bank  Event – Act of transaction – not much of a difference between this and attribute

 Inventory  Objective – Work out minimum cost  Entity – Customer  Attribute – Demand of item  Activity – Buying  State – Number of items  Event – Buying

 Inventory  Objective – Customer satisfaction  Entity – Customer  Attribute – Demand of customer  Activity – Buying  State – Number of items  Event – Buying Same as example 3. However we need not calculate holding cost, ordering cost. Loss of good will cost is important here

 Petrol bunk  Objective – Measure waiting lines  Entity – Vehicle  Attribute – Volume ordered (keep track of two / four wheeler / card / cash)  Activity – Filling fuel  State – Number of vehicles  Event – Buying fuel

 Petrol bunk  Objective – Measure in and out flow of fuel  Entity – Vehicle  Attribute – Volume ordered (keep track of two / four wheeler)  Activity – Filling fuel  State – Volume of fuel  Event – Buying fuel

 Coffee shop  Traffic in a bus stand  Traffic in a port  Barber shop  Hospital emergency room  Grocery store  Taxi cab company

1. Problem formulation 2. Setting objectives 3. Model conceptualization, data collection 4. Model translation 5. Verification 6. If step 5 is failure then back to 4 Else 7. Validation 8. If step 7 is failure then back to 3 Else 9. Experimental design 10. Perform runs 11. If number of runs if not enough in step 10 then back to 10 Else 12. Print statistics and stop

Formulate problem, Identify objectives Fix model, collect data Translate model Verify-success? Validate-success? Design Enough runs? Print results Perform runs no yes no yes no

 Definition – any text  Advantages and disadvantages – Chapter1 of Banks  Suitability – Chapter 1 of Banks  Applications – Chapter 1 of Banks  Models – Chapter 1 of Gordon  Components of system – Gordon, Banks – chapter 1 of both  Simple examples - Gordon, Banks – chapter 1 of both  Steps in simulation study - Gordon, Banks – chapter 1 of both