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IE 324 SIMULATION

IE 324 SIMULATION. INTRODUCTION TO SIMULATION. WHAT IS SIMULATION?. To feign, to obtain the essence of, without reality. [Webster’s Collegiate Dictionary] The imitation of the operation of a real-world process or system over time. [Banks et al. (2005)]

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IE 324 SIMULATION

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  1. IE 324 SIMULATION INTRODUCTION TO SIMULATION

  2. WHAT IS SIMULATION? • To feign, to obtain the essence of, without reality. [Webster’s Collegiate Dictionary] • The imitation of the operation of a real-world process or system over time. [Banks et al. (2005)] • The process of designing a logical or mathematical model of a real system and then conducting computer based experiments with the model to describe, explain, and predict the behaviour of the real system. [Taylor (1984)]

  3. WAYS TO STUDY A SYSTEM System Experiment with the actual system Experiment with a model of the system Physical Model Abstract Model Analytical Model Simulation

  4. INPUT/OUTPUT PROCESS REAL-LIFE SYSTEM SIMULATION MODEL • Decision variables • Parameters System response (Y) (X) Y=f(X)

  5. EXAMPLE: HEALTH CENTER SIMULATION MODEL OF HEALTH CENTRE • Number of Doctors • Capacity of equipment • Arrival rate • Time in the system • Utilization of doctors • Waiting time

  6. EXAMPLE:SERIAL PRODUCTION LINE ……. 1 2 3 N • Length of the line • Size of buffers • Processing times SIMULATION MODEL OF PRODUCTION LINE • Throughput • Interdeparture time variability • Utilizations

  7. ORIGIN OF SIMULATION • Lie in statistical sampling theory, e.g., random numbers, random sampling (Before the 2nd world war) • Monte Carlo simulation (During the 2nd world war) • Modern Applications (After the 2nd world war)

  8. POPULARITY OF SIMULATION • Consistently ranked as the most useful, popular tool in the broader area of operations research / management science

  9. SYSTEM A system is a group of objects (or elements) that are joined together in some regular interactions towards the accomplishment of some stated objective or purpose

  10. COMPONENTS OF A SYSTEM Entity: is an object of interest in the system (which requires an explicit representation in the system model) Example: Health Center Patients, Doctors & Nurses, Rooms & beds Lab equipment, X-Ray machine, etc.

  11. COMPONENTS OF A SYSTEM Attribute: is a characteristic of an entity Example: Patient Type of illness, Age, Sex, etc.

  12. SYSTEM STATE • A collection of variables that contains all the information necessary to describe the system at any time Example: Health Center Number of patients in the system, Status of doctors (busy or idles), Number of idle doctors, Status of Lab equipment, etc

  13. EVENT • An instantaneous occurrence that may change the state of the system Example: Health Centre Arrival of a new patient, Completion of a service (i.e., examination) Failure of medical equipment, etc.

  14. VARIABLES Relevant variables Irrelevant variables affect the system performance ………..Don’t affect ……... Endogenous variables Exogenous variables

  15. EXOGENOUS VARIABLES • Input variables • External to the model (i.e., exist independently of the model) Exogenous variables Controllable variables (Decision Variables) Uncontrollable variables (Parameters) That can be manipulated to an extent by the DM Cannot be manipulated

  16. ENDOGENOUS VARIABLES • Output variables • Internal to the model and are functions of the exogenous variables and the model dynamics Examples: • Performance measures • State variables

  17. BE CAREFUL !!! • Classification of relevant vs. irrelevant variables depends on: • Purpose of the study • Scope (Level of Detail) • Classification of controllable vs. uncontrollable variables depends on: • Purpose of the study (existing vs. new) • Resources that are under control of the DM

  18. MODEL • Why do we study a system? • Why do we need a model? • Todesign new systems • To improve system performance • Tosolve problems affecting the system performance • The system does not exist (i.e., conceptual stage) • Impractical or too costly to experiment with the actual system

  19. MODEL A representation of a system for the purpose of studying the system ….by Banks et al. (2005).

  20. CLASSIFICATION OF MODELS Models Physical Models Abstract Models Resemble the real system physically (a small scale representation Use symbolic notation & mathematical equations to represent a systems BEGIN; EI=BI+PROD-DEMAND . END;

  21. ABSTRACT MODELS Prescriptive (Normative Models) Descriptive Models Used to formulate & solvea problem Used to describe the system behaviour Examples: Examples: • Linear Programming • Dynamic Programming • Simulation • Queuing Models

  22. ABSTRACT MODELS Analytical Numerical Employ computational procedures to solve the mathematical models Employ the deductive reasoning of mathematics to solve the model Examples: Examples: • Queuing models • Differential calculus • Simulation • Linear programming

  23. ABSTRACT MODELS Stochastic Deterministic Does not contain a random variable Contains one or more random variables Examples: Examples: • Simulation • Stochastic programming • LP, MIP and DP • Simulation

  24. ABSTRACT MODELS Static Dynamic Represents the system as it changes over time Represents the system at a particular point in time Examples: Examples: • Many optimization models covered in our curriculum • Monte Carlo simulation • Simulation • Dynamic Programming • Control Models • Queueing Models

  25. ABSTRACT MODELS Discrete Continuous May take on the value of any real number May only take a limited or specified values Examples: Examples: • Integer Programming • Simulation • Simulation • Queueing Models

  26. CHARACTERISTICS OF SIMULATION • Abstract • Numerical • Descriptive • Deterministic/Stochastic • Static/Dynamic • Discrete/Continuous

  27. ANALYTICAL VS SIMULATION • Use analytical model whenever possible • Use simulation when 1) Complete mathematical formulation does not exist or an analytical solution cannot be developed 2) Analytical methods are available, but the mathematical procedures are so complex that simulation provides a simpler solution 3) It is desired to observe a simulated history of the process over a period of time in addition to estimating certain system performances

  28. CAPABILITIES OF SIMULATION • Time compression and expansion • Explains “why?” • Allows to explore possibilities (What if?”) • Helps diagnosing problems & identify constraints • Requires fewer assumptions • Handles randomness and uncertainty • Handles dynamic behaviour • Flexible and easy to change • Credible and results are easier to explain

  29. LIMITATIONS OF SIMULATION • “Run” rather than “solve” • Random output obtained from stochastic simulations (Statistical analysis of output is required) • Cannot generate optimal solution on its own • Requires specialized training (probability, statistics, computer programming, modelling, system analysis, simulation methodology) • Costly (software and hardware)

  30. SIMULATION APPLICATIONS

  31. STEPS IN A SIMULATION STUDY Model conceptualization No Experimental Design Yes Setting of objectives and overall project plan Verified? Validated? Yes Model translation Problem formulation Production runs and analysis No Yes Yes More runs? Data collection No No Documentation and reporting Implementation

  32. PROBLEM FORMULATION • A statement of the problem • the problem is clearly understood by the simulation analyst • the formulation is clearly understood by the client • Problem, but not symptoms • Criteria for selecting a problem: • Technical, economic and political feasibility • Perceived urgency for a solution

  33. SETTING OBJECTIVES & PROJECT PLAN (PROJECT PROPOSAL) • Determine the questions that are to be answered • Identify scenarios to be investigated • Scope (Level of detail) • Determine the end-user • Determine data requirements • Determine hardware, software, & personnel requirements • Prepare a time plan • Cost plan and billing procedure

  34. MODEL DEVELOPMENT Real World System Conceptual model Logical model Simulation model

  35. CONCEPTUAL MODEL Real World System Subsystem of interest Conceptual model

  36. CONCEPTUAL MODEL • Questions to be answered • Scope (Level of detail) • Performance measures • Events, entities, attribute, exogenous variables, endogenous variables, & their relationships • Data requirements

  37. SCOPE • More detailed the model is, more representative it is of the actual system (if the modeling is done correctly) • A more detailed model requires: • more time and effort • longer simulation runs • more likely to contain errors

  38. Accuracy of the model Scope & level of detail Cost of model Scope & level of detail

  39. SCOPE Modeller Novice Modeller Experienced Modeller Tends toward too much detail Tends toward greater detail KISS

  40. LEVELS OF DETAIL • Evaluate if the candidate systems work • Compare two or more systems to determine better ones • Accurately predict the performance of selected system Scope

  41. LOGICAL (FLOWCHART) MODEL • Shows the logical relationships among the elements of the model start Read data check Set new event Generate data Calculate Stats check Print Stop

  42. SIMULATION (OPERATIONAL) MODEL • The model that executes the logic contained in the flow-chart model Coding Special Purpose Languages & Environments General Purpose Languages Examples: Examples: FORTRAN, C, PASCAL SIMAN, ARENA. AUTOSIM

  43. SIMAN MODEL --- MODEL FILE --- BEGIN; CREATE,1:,EXPO(40):EX(40):MARK(1); QUEUE,1; SEIZE:DOCTOR; DELAY:EXPO(30); TALLY:1,INT(1); RELEASE:DOCTOR; COUNT:1:DISPOSE; END: ----EXPERIMENTAL FILE ----- BEGIN; PROJECT,HEALTH_CENTRE, IHSA SABUNCUOGLU,24/1/2000; DISCRETE,100,1,1; RESOURCES:1, DOCTORS; DSTATS:1,NQ(!),NUMBER_IN_QUEUE: 2,NR(1),DOCTOR UTILIZATION; TALLIES:1, TIME IN HEALTH_CENTRE; COUNTERS:1,No. OF PATIENTS SERVED; END:

  44. ARENA MODEL

  45. Java Model // Loop until first "TotalCustomers" have departed while(NumberOfDepartures < TotalCustomers ) { Event evt = (Event)FutureEventList.getMin(); // get imminent event FutureEventList.dequeue(); // be rid of it Clock = evt.get_time(); // advance simulation time if( evt.get_type() == arrival ) ProcessArrival(evt); else ProcessDeparture(evt); } ReportGeneration(); }

  46. DATA COLLECTION & ANALYSIS • The client often collects the data & submit it in electronic format • Simulation Analyst: • Determines the random variables • Determines the data requirements • Analyses the data • Fits distribution functions

  47. VERIFICATION AND VALIDATION • Verification: the process of determining if the operational logic of the model is correct. • Validation:the process of determining if the model accurate representation of the system.

  48. VERIFICATION AND VALIDATION Real World System Conceptual model VALIDATION Logical model VERIFICATION Simulation model

  49. EXPERIMENTAL DESIGN • Alternative scenarios to be simulated • Type of output data analysis (steady state vs. transient state analysis) • Number of simulation runs • Length of each run • Initialization • Variance reduction

  50. ANALYSIS OF RESULTS • Determine the simulation runs necessary to estimate the performance measures • Statistical tests for significance and ranking • Interpretation of results

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