1. INTRODUCTION TO SIMULATION
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
with a model
of the system
Physical
Model
Abstract
Model
Analytical
Model
Simulation

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

5. EXAMPLE: HEALTH CENTER
Number of Doctors
Capacity of equipment
Arrival rate
SIMULATION MODEL OF
HEALTH CENTRE
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 need a model? Why do we study a system?
To design new systems
To improve system performance
To solve problems affecting the system performance
Why do we need a model?
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
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 & solve a problem
Used to describe the system behaviour
Examples:
Examples:
Linear Programming
Dynamic Programming
Simulation
Queuing Models

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

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

24. ABSTRACT MODELS Static Dynamic Examples: Examples:
Represents the system at a particular point in time
Represents the system as it changes over 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 Examples: Examples:
May only take a limited or specified values
May take on the value of any real number
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
Model
translation
Verified?
Yes
Validated?
Problem
formulation
Production runs
and analysis No
Yes
Yes
More runs?
Data
collection No No
Implementation
Documentation
and reporting

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 Conceptual model Logical model Simulation model
Real World System
Conceptual model
Logical model
Simulation model

35. CONCEPTUAL MODEL 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. Tends toward too much detail Tends toward greater detail
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 -----
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;

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

51. DOCUMENTATION General model logic Key elements of the model
Data structures
Alternative scenarios
Performance measures or criteria used
Results of experiments
Recommendations

52. IMPLEMENTATION ?
FAILURE
SUCCESS