IE 324 SIMULATION INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? To feign, to obtain the essence of, without reality. [Webster’s Collegiate Dictionary]

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)]

• 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

MODEL

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

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)

SIMULATION APPLICATIONS

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

MODEL DEVELOPMENT

Conceptual model

Logical model

Simulation model

Real World System

CONCEPTUAL MODEL

Subsystem of interest

Conceptual model

Real World System

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

Accuracy of the model

Scope & level of detail

Scope & level of detail

Cost of model

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:

ARENA MODEL

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

IMPLEMENTATION