IE 324 SIMULATION INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? To feign, to obtain the essence of, without reality. [Webster’s Collegiate Dictionary]
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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)]
WAYS TO STUDY A SYSTEM
System
Experimentwith the
actual system
Experimentwith a modelof the system
Physical Model
Abstract Model
AnalyticalModel
Simulation
INPUT/OUTPUT PROCESS
SIMULATION MODEL
REAL-LIFE SYSTEM
• Decision variables
• Parameters System response
(X) (Y)
Y=f(X)
SIMULATION MODEL OF HEALTH CENTRE
• Number of Doctors
• Capacity of equipment
• Arrival rate
• Time in the system
• Utilization of doctors
• Waiting time
EXAMPLE: HEALTH CENTER
EXAMPLE:SERIAL PRODUCTION LINE
SIMULATION MODEL OF PRODUCTION LINE
• Length of the line
• Size of buffers
• Processing times
• Throughput
• Interdeparture time variability
• Utilizations
1 2 3 N…….
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)
POPULARITY OF SIMULATION
• Consistently ranked as the most useful, popular tool in the broader area of operations research / management science
SYSTEMA 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
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.
COMPONENTS OF A SYSTEM
Attribute: is a characteristic of an entity
Example: Patient
Type of illness,
Age,
Sex, etc.
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
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.
VARIABLES
Relevant variables Irrelevant variables
affect the system performance ………..Don’t affect ……...
Endogenous variables Exogenous variables
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
ENDOGENOUS VARIABLES
• Output variables• Internal to the model and are functions of the
exogenous variables and the model dynamics
Examples:
• Performance measures
• State variables
BE CAREFUL !!!
• Classification of relevant vs. irrelevant variables depends on:
• Classification of controllable vs. uncontrollable variables depends on:
• Purpose of the study
• Scope (Level of Detail)
• Purpose of the study (existing vs. new)
• Resources that are under control of the DM
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
• The system does not exist (i.e., conceptual stage)
• Impractical or too costly to experiment with the actual system
CLASSIFICATION OF MODELS
Models
Physical Models Abstract Models
Use symbolic notation & mathematical equations to represent a systems
Resemble the real system physically (a small scale representation
BEGIN;
EI=BI+PROD-DEMAND
.
END;
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
ABSTRACT MODELS
Analytical Numerical
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
ABSTRACT MODELS
Stochastic Deterministic
Contains one or more random variables Does not contain a random variable
Examples: Examples:
• Simulation
• Stochastic programming
• LP, MIP and DP
• Simulation
ABSTRACT MODELS
Static Dynamic
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
ABSTRACT MODELS
Discrete Continuous
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
CHARACTERISTICS OF SIMULATION
• Abstract
• Numerical
• Descriptive
• Deterministic/Stochastic
• Static/Dynamic
• Discrete/Continuous
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
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
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)
STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
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
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
CONCEPTUAL MODEL
• Questions to be answered
• Scope (Level of detail)
• Performance measures
• Events, entities, attribute, exogenous variables, endogenous variables, & their relationships
• Data requirements
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
SCOPE
Modeller
Novice Modeller Experienced Modeller
Tends toward too much detail Tends toward greater detail
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
LOGICAL (FLOWCHART) MODEL
• Shows the logical relationships among the elements of the model
start
Read data
checkGenerate data
Set new event
CalculateStats
Print checkStop
SIMULATION (OPERATIONAL) MODEL
• The model that executes the logic contained in the flow-chart model
Coding
General Purpose Languages Special Purpose Languages & Environments
FORTRAN, C, PASCAL
Examples:
SIMAN, ARENA. AUTOSIM
Examples:
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:
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(); }
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
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.
VERIFICATION AND VALIDATION
Conceptual model
Logical model
Simulation model
Real World System
VERIFICATION
VALIDATION
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
ANALYSIS OF RESULTS
• Determine the simulation runs necessary to estimate the performance measures
• Statistical tests for significance and ranking
• Interpretation of results
DOCUMENTATION
• General model logic
• Key elements of the model
• Data structures
• Alternative scenarios
• Performance measures or criteria used
• Results of experiments
• Recommendations
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