system modeling group 7

8/8/2019 System Modeling Group 7

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Lecturer:

Assoc. Prof. Datin Dr Napsiah Ismail

System Modeling

28 Sep 201028 Sep 2010

Presented by Group 7Presented by Group 7HamidrezaHamidreza SoltaniSoltani ( (GS26516)GS26516)MasoudMasoud PishdarPishdar (GS26514)(GS26514)AbdollahAbdollah Omer Ibrahim (GS28223)Omer Ibrahim (GS28223)

EMM 5706DESIGN OF MANUFACTURING SYSTEM


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Overview1. What is system?2. What is modeling and simulation?

3. What is simulation modeling and analysis?

4. What types of problems are suitable forsimulation?

5. How to select simulation software?

6. What are the benefits and pitfalls inmodeling and simulation?

7. References


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What is system?


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A broader definition of a system is, Any object which has some actionto perform and is dependent on number of objects called entities, is asystem .

For example a class room, a college, or a university is a system.University consists of number of colleges (which are entities of thesystem called university) and a college has class rooms,students, laboratories and lot many other objects, as entities . Eachentity has its own attributes or properties.

System

A lso system can be defined as(i ) Continuous: (Fluid flow in a pipe, motion of an aircraft or trajectory of aprojectile)(ii ) Discrete: (a factory where products are produced and marketed in lots)


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modeling

What is modeling and simulation?

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Model of a system is the replica of the system, physical or mathematical, which has all the properties and functions of thesystem, whereas simulation is the process which simulates in thelaboratory or on the computer.

In fact, a modeling is the general name whereas simulation is specific

name given to the computer modeling.

MODELING AND S IMULATION


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M odeling is the process of producing a model which :

Representation of the construction and working of some system of interest;

Similar to but simpler than the system it represents;Enable the analyst to predict the effect of changes to the system;

A close approximation to the real system and incorporate most of itssalient features; and

Not so complex that it is impossible to understand and experiment with

it.A good model is a judicious trade off between realism and simplicity.

Simulation practitioners recommend increasing the complexity of amodel iteratively.


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Whil e bu ilding a mo d e l c ert a in ba s ic p r in c ip les a re to b e f o llowe d. Whil e m ak ing a mo d e l o n e s h o u ld kee p in m ind f ive ba s ic ste p s .

Block building R elevance Accuracy Aggregation

ValidationModels can be put under three categories, physical models , mathematical models and computer models . A ll of these types are further defined as static and dynamic

models.

F ive ba s ic ste p s


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Diff ere n t ty p es o f mo d e ls


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PHY S ICAL MODEL S

P h ys ica l mo d e ls a re o f two ty p es , st a tic a nd d yn a m ic .

St a tic p h ys ica l model is a scaled down model of a systemwhich does not change with time. A n architect beforeconstructing a building, makes a scaled down model of thebuilding, which reflects all it rooms, outer design and other important features.

Dyn a m ic p h ys ica l models are ones which change with time or which are function of time. In wind tunnel, small aircraft models(static models) are kept and air is blown over them withdifferent velocities and pressure profiles are measured with thehelp of transducers embedded in the model.


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MATHEMATICAL MODEL S

Most of the systems can in general be transformed intomathematical equations. These equations are called themathematical model of that system. Since beginning, scientistshave been trying to solve the mysteries of nature by observationsand also with the help of Mathematics.

Equations of fluid flow represent fluid model which is dynamic.

A static model gives relationships between the system attributeswhen the system is in equilibrium.


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COM P UTER MODEL S

W ith the advent of computers, modeling and simulation conceptshave totally been changed. Now all types of stochastic as well ascontinuous mathematical models can be numerically evaluated withthe help of numerical methods using computers. Solution of theproblem with these techniques is called computer modeling.

wh a t is th e di ff ere n c e b etwee n m a th em a tica lly o b ta in e d so lu tio n o f a p ro b lem a nd simulation .

Literal meaning of simulation is to simulate or copy the behavior of asystem or phenomenon under study. Simulation in fact is a computer model, which may involve mathematical computation, computer graphicsand even discrete modeling.


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S IMULATION

Na ylor , defines the simulation as follows:S imulation is a numerical technique for conducting experimentson a digital computer , which involves certain types of mathematical and logical models over extended period of real time.

We thus define system simulation as the technique of solving problems by the observation of the performance , over time , of adynamic model of the system .In other words, we can define simulation as an experiment of

physical scenario on the computer.

an analysis tool for understanding the system.the operation of a model of the system.


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S h a nn o n [1975] defines simulation as an experimentaland applied methodology which seeks to:

i. describe theories or the behavior of systems;.ii. construct hypotheses that account for the

observed behavior;iii. use these theories to predict future behavior,

that is, the effects that will be produced bychanges in the system or in its method of operation.


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Simulation is used before an existing system isaltered or a new system built.

WHY?

To reduce the chances of failure to meet specifications

To eliminate unforeseenbottlenecks

To prevent under or over-utilization of resources

To optimize system performance










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Strengths of SimulationTime compression the potential to simulate years of realsystem operation in a few minutes or seconds.Component integration the ability to integrate system

components to study interactionsRisk avoidance hypothetical or potentially dangerous systemscan be studied without the financial or physical risks that may beinvolved in building and studying a real systemPhysical scaling the ability to study much larger or smallerversions of a systemRepeatability the ability to study different systems in identicalenvironments or the same system in different environmentsControl everything in a simulation can be precisely monitoredand exactly controlled

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What is simulation modeling and analysis?


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Simulation M odelling

Simulation is a modeling and analysis tool used forthe purpose of designing planning and control of manufacturing systems.Simulation may be defined as a concise frameworkfor the analysis and understanding of a system.It is an abstract framework of a system that facilitatesimitating the behavior of the system over a period of

time.In contrast to mathematical models, simulationmodels do not need explicit mathematical functionsto relate variables


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Therefore ,they are suitable for representing complexsystems to get a feeling of real system.One of the greatest advantage of a simulationmodels is that it can compress or expand time.Simulation models can also be used to observe aphenomenon that cannot be observed at very smallintervals of time.Simulation can also stops continuity of theexperiment.


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Simulation modeling techniques are powerful formanipulation of time system inputs, and logic.They are cost effective for modeling a complexsystem, and with visual animation capabilities they

provide an effective means of learning,experimenting, and analyzing real-life complexsystems such as F M S.Simulation are capable of taking care of stochastic

variable without much complexity.They enable the behavior of the system as a whole tobe predicted.


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Simulation M odelConsist of the following components:

o system entitieso input variableso performance measureso functional relationships

Almost all simulation software packagesprovides constructs to model each of theabove components


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Classification of simulation models S tatic vs. dynamic Deterministic vs. stochastic Continuous vs. discrete

M ost operational models are dynamic,stochastic, and discrete will be calleddiscrete-event simulation models

Simulation Model


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D ISCRETE-EVENT SIMUL AT IONDiscrete-event simulation: Modeling of a system as it evolves overtime by a representation where the state variables changeinstantaneously at separated points in time

o More precisely, state can change at only a countable number of points in time

o These points in time are when events occur Event: Instantaneous occurrence that may change the state of thesystem

o Sometimes get creative about what an event is e.g., end of simulation, make a decision about a system s operationCan in principle be done by hand, but usually done on

computer


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D ISCRETE-EVENT SIMUL AT IONExample: Single-server queue

Estimate expected average delay in queue (line, not service)

State variablesStatus of server (idle, busy) needed to decide what to do with anarrivalCurrent length of the queue to know where to store an arrivalthat must wait in lineT ime of arrival of each customer now in queue needed tocompute time in queue when service startsEventsArrival of a new customerService completion (and departure) of a customer


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What types of problems are suitable for

simulation?


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W HEN SIMULATION IS APPROPRIATE?

Simulation enables the study of, and

experimentation with, the internal interactions of acomplex system, or of a subsystem within a complexsystem.

Informational, organizational, and environmental

changes can be simulated, and the effect of thesealterations on the model s behavior can be observed.


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The knowledge gained in designing a simulationmodel may be of great value toward suggestingimprovement in the system under investigation.

By changing simulation inputs and observing theresulting outputs, valuable insight may be obtainedinto which variables are most important and howvariables interact


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Simulation can be used as a pedagogical device to reinforceanalytic solution methodologies.Simulation can be used to experiment with new designs orpolicies prior to implementation, so as to prepare for whatmay happen.Simulation can be used to verify analytic solutions.By simulating different capabilities for a machine,requirements can be determined.Simulation models designed for training allow learning

without the cost and disruption of on-the-job learning.Animation shows a system in simulated operation so that heplan can be visualized.


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W HEN SIMULATION IS NOT APPROPRIATE?

The Problem is solved by common sense.The Problem is solved by analytical means.It is easier to perform direct experimentationThe resources are not availableThe cost exceeds savingsThe time is not available

No enough time and personal are not availableU n-reasonable expectationsThe behavior of the system is too complex to define


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Stages in Simulation

Step 1 -

Identify theproblem.

Step 2 -Formulate theproblem.

Step 3 -

Collect and processreal system data.

Step 4 -

Formulate anddevelop a model.

Step 5 -

Validate the model.

Step 6 -

D ocument model forfuture use.

Step 7 -

Select appropriateexperimentaldesign.

Step 8 -Establishexperimentalconditions for runs.

Step 9 -Perform simulationruns.

Step 10 -

Interpret andpresent results.

Step 11 -

Recommend furthercourse of action


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Simulation M odelSteps Involved:1- Identify the problem

Every study should begin with a statement of the problem. If the

statement is provided by the policy makers, or those that have the

problem, the analyst must ensure that the problem being described is

clearly understood. If the problem is being developed by the analyst, it isimportant that the policy makers understand and agree with the

formulation


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2 - F ormulate the problemT he objective indicates the questions to be answered by simulation. At

this point a determination should be made concerning whether

simulation is the appropriate methodology for the problem as

formulated and objectives as state. Assuming it is decided that

simulation is appropriate; the overall project plan should include a

statement of the alternative systems to be considered, and a method for

evaluating the effectiveness of these alternatives. It should also include

the plan for the study in terms of the number of people involve, the cost

of the study, and the number of days required to accomplish each phase

of work with the anticipated results at the end of each stage .


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3 - C ollect the process real system dataT he construction of a model of the system is problem as much

art as science. T he art of modeling is enhanced by an ability to

abstract the essential features of a problem, to select and modify

basic assumptions that characterize the system, and then to

enrich and elaborate the model until a useful approximation

results. T hus it is best to start with a simple model and build

toward greater complexity. However, the model complexity

need not exceed that required to accomplish the purposes for

which the model is intended. It is not necessary to have a one-

to-one mapping between the model and the real system.


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4 -F ormulate & develop a modelT here is a constant interplay between the construction of the model and

the collection of the needed input data. As the complexity of the model

changes, the required data elements may also change. Also, since data

collection takes such a large portion of the total time required to

perform a simulation, it necessary to begin it as early as possible,

usually together with early stages of the model building.


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5 - V erification

Is the computer implementation of the conceptual model

correct?Procedures

S tructured programming

S elf-document

Peer-review

Consistency in input and output data

Use of IRC and animation


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6 - V alidation

Can the conceptual model be substituted, at least

approximately for the real system?Procedures

S tanding to criticism/Peer review ( T uring)

S ensitivity analysis

Extreme-condition testingValidation of Assumptions

Consistency checks


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V alidation - contd.

Validating Input-Output transformations

Validating using historical input data


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Ex perimentation and Output Analysis

Performance measures

S tatistical Confidence

Run Length

T erminating and non-terminating systems.

Warm-up period.


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S teps in S imulation - contd.

Production Runs and Analysis

Documentation/Reporting

Implementation


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Simulation ExperimentIt is a test or series of test, meaningful

changes are made to the input variablesWe can observe and identify the reasons of

change in the performance measures.

Steps Involved:


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7 - S elect appropriate e x perimental designT he alternatives that are to be simulated must be

determined. Often, the decision concerning whichalternatives to simulate may be a function of run that

have been completed and analyzed. For each system

design that is simulated, decision need to be made

concerning the length of the initialization period, the

length of simulation runs, and the number of

replications to be made of each run


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8 - E stablish e x perimental conditions for runsProduction runs, and their subsequent analysis, are used to

estimate measures of performance for the system designs that are

being simulating.

9-Perform simulation runs

Based on the analysis of the runs that have been

completed, the analyst determines if additional runs are

needed and what design those additional experiments

should follow


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10- Documentation and reporting:T here are two types of documentation:

Program documentation is necessary for numerous

reasons. If the program is going to be used again by the

same or different analysts, it may be necessary to

understand how the program operates. T his will build

confidence in the program, so the model users and

police makers can make decisions based on theanalysis. Also, if the program is to be modified by the

same or a different analyst, this can be greatly

facilitated by adequate documentation.


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11-R ecommend further course of action

Progress reports give a chronology of work done and

decisions made. T his can prove to be of great value in

keeping the project on course, also it help the

improvement of this simulation in the future.


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Procedure for Conducting a Simulation StudyP la n St u d y

De f in e System

Bu ild Mo d e l

Ru n Exp er ime n ts

An a lyze Ou tpu t

Re p ort Res u lts


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ManufacturingEnvironments

Manufacturing Issues Performance Measurementof Manufacturing System

New equipment and buildingsare required (called greenfields).New equipment is required inan old building.A new product will beproduced in all or part of anexisting building.Upgrading of existingequipment or its operation.Concerned with producing thesame product more efficiently.Changes may be in theequipment (e.g., introduction

of a robot) or in operationalprocedures (e.g., schedulingrule employed).

Number and type of machinesfor a particular objective.Location and size of inventorybuffers.Evaluation of a change inproduct mix (impact of newproducts).Evaluation of the effect of anew piece of equipment on anexisting manufacturing line.Evaluation of capitalinvestments.Manpower requirementsplanning.

Throughput analysis.Makespan analysis.Bottleneck analysis.Evaluation of operationalprocedures.Evaluation of policies forcomponent part or rawmaterial inventory levels.Evaluation of control strategies

Throughput (number of jobsproduced per unit of time).Time in system for jobs(makespan).Times jobs spend in queues.Time that jobs spend being

transported.Sizes of in-processinventories (WIP or queuesizes).Utilization of equipment andpersonnel (i.e., proportion of time busy).Proportion of time that a

machine is under fadum,blocked until and starved.Proportion of jobs producedwhich must be reworked orscrapped.Return on investment for anew or modifiedmanufacturing system.

U se of Simulation in M anufacturing


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Areas suitable for simulationApplications of simulation abound in the areas of :

government health care

defense ecology and environment

computer andcommunication systems

sociological andbehavioral studies

manufacturing biosciences

transportation (air trafficcontrol)

epidemiology

economics and businessanalysis

services (bank tellerscheduling)


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S imulation language

describes the operation of a simulation on a computer.

T here are three major types of simulation:1. D iscrete event simulation languages, viewing the

model as a sequence of random events eachcausing a change in state. For example Arena.

2. Continuous simulation languages, viewing the

model essentially as a set of differential equations.For example ACS L.3. Hybrid , and other. for example AnyLogic multi-

method simulation tool, which supports Systemdynamics .


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T ypes of simulation software

Simulation software is based on the process of imitating a real phenomenon with a set of mathematical formulas .

S imulation soft ware can be classified to :1. General simulation fall into two categories: discrete event

and continuous simulation .

2. Electronic simulation utilizes mathematical models to replicatethe behavior of an actual electronic device or circuit.

Examples of simulation software:

Open Source such as ASCEND and NS2.Commercial such as AM ESim and Arena .


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S IMULA T ION S O F TW AR E

1 st Category 2nd Category 3rd Category Webbasedsimulation

Channel

purposelanguage

Simulation

language

Simulation

Packages

FO RTRANC, C ++VB, VB+ + . . .. . . . . . . . . . . .. . . . . . .. . . . .

. . . . . .. . . . . .

. . . . .manyother orientedlanguages

GPSS(1965)SIMSCRIPT(1963)SIMULAGASP

(1961)ALG OLSLAM(1979)SIMANGPSS/4(1977)SLAM IIAWESIM(1995)GEMS

ARENA(1993)AutoM ODQUEST EXTEN D PROMOD EL

TaylorE D WITNESS. . . . .. . . . . .andmany more

JAVASIMWEB-BASE D SIMULATI ON. . .. . . . . . . .. . . .

. . . . . . .. . . . .

. . . . . .. . . . . .

. . . . .


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S imulators

Facilitates the development of models related to a

specific class of problems.

S hort development cycles.

Rapid model prototypes.

Gentle learning curve.

Lack flexibility to model outside of class.Do not handle unusual situations.

Built in assumptions can be problematic .


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Arena is a discrete event simulation software simulation andautomation software developed by S ystems Modeling and acquired

by Rockwell Automation in 2000 .In Arena, the user builds an experiment mode l by placing modu l e s

(boxes of different shapes) that represent processes or logic.Connector lines are used to join these modules together andspecifies the flow of entitie s .

Arena simulation software

Arena integrates very well toM icrosoft technologies. It includesVisual Basic for Applications somodels can be further automated if specific algorithms are needed.


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AR E NA

Process hierarchy.Integrates with Microsoft desktop toolsS preadsheet interfaceCrystal reportsFree runtime software.Fully graphical environment. No programming

required.VBA embedded.Optimization with Opt Quest for Arena.Builds reusable modules.$1,000 - $17,000 ($U S ). Various add-in modules

available


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Manufacturing S ystems modeling

Material Flow S ystems

Assembly lines and T ransfer lines

Flow shops and Job shops

Flexible Manufacturing S ystems and Group

T echnology

S upporting ComponentsS etup and sequencing

Handling systems

Warehousing


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G oals of Manufacturing Modeling

Manufacturing S ystems

Identify problem areas

Quantify system performance

S upporting S ystems

Effects of changes in order profiles

T ruck/trailer queueingEffectiveness of materials handling

Recovery from surges


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56

METHODOLOGY FOR SELECTION OF SIMULATION SOFTW

ARE

Nee d f or pu r c h a s ing s im u la tio n so f tw a re

Initial software survey

Eva lua tio n

Software selection

So f tw a re c o n tr ac t n e g ot ia tio n

So f tw a re pu r c h a se

St a g e 1

St a g e 2

St a g e 3

St a g e 4

St a g e 5

St a g e 6

Figure 3 : Stages of simulation software selection methodology


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57

Need for purchasingsimulationsoftware

Purposeof

simulation

Constraints

Modelsto be

simulated

Modeldevelope

rs

Education

Individual

preference

Quickand

dry -ind

D/C ind or

research

Time Discrete

Continuo.

Combined

disc/cont

Previousexper. in

simulation

Initialsoftwaresurvey

Continued in the next slide


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Initial softwaresurvey




Softwareselection

Softwarecontract

negotiation

Softwarepurchase

Contract acceptable

Le g e nd:

Stages

IntermediateR esults

Elements

Short list of softwarefor evaluation

R esults of Evaluation

Selection of software


Initialsoftwaresurvey


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ProModel

ProModel is offered by ProModel CorporationIt is a simulation and animation tool designed to modelmanufacturing systems.ProModel offers 2-D animation with an optional 3-D like

perspective view .


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61

PromodelS tate-of-the-art simulationengine

Graphical user interfaceDistribution-fitting.Output analysis moduleOptional optimizer.

Modules designed for: Manufacturing Healthcare S ervices

$17,000 ($U S )


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62

Case study

Machine A rea (m 2)M1

M2M3M4M5M6

M7M8M9M10

20 x 2 0

20 x 2 020 x 2 020 x 2 020 x 2 020 x 2 0

20 x 2 020 x 2 020 x 2 020 x 2 0

Tab le 1 : Mac hin e Are a I n f orm a tio n


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Part Type Job Sequence QuantityP 1P2

P3P4P 5P6P 7P8P 9

P 10

P 11P 12P 13P 14P 15P 16P 17

P 18

8-6-8- 10 -47-9-2

6-53-1-3

5-6-7-107-9-7-8

7-93-4- 1-6

2-72-7-9-5

10 -8-51-3-10

8-10 -5-69-2-7

6-8- 104-36-5

4-3- 1

160310

28 026 580

12536 024 017595

10023 028 531550

27526 0

150

Tab le 2 : P a rt J o b Seq u e n c e a nd Qua n tity In f orm a tio n


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65

Ce ll F orm a tio n

Cell 1 = 3 1 10 4Cell 2 = 8 6Cell 3 = 2 9 7 5

Here the initial solution for the above case study is obtained usinggenetic algorithm as below


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66(Ru n Ho u rs 231 .57 )


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67

from above table average process time in percentage of total scheduledhours = (3 9 .62+ 14. 97 +2 0 .04+ 11 .88+ 11 .16+2 1 .7+16.99 +22.8 9+23.8 9+2 0 .51 )/18= 11 .3 1% =0 .11 31

average process time = 0 .11 31*23 1 .57*60=157 2. 05


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68

Ru n h o u rs 352 The solution for the above case study using heuristic method is as follows

Ste p 1 : A rrange all machines randomly according to the given dimensions of machines. Here machine tomachine clearance of 1 m is also considered.


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Ste p 2 : From job sequence of parts, check the minimum sequence (2 machines)

common for all parts e.g. M 7 M9 , M5 M6, M4 M3, M8 M6, M8 M 10 and bringthose 2 machines closer or nearer to each other.

(Ru n Ho u rs 229 .37 )


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70

Ste p 3 : From job sequence, calculate number of times, all parts uses the samemachines.

M1-4M2-4M3-6M4-4M5-6M6-7

M7-8M8-6M9-5

M10 -6


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71

The least utilized machines are M 1 ,M2 and M4. these machines are kept away from remainingmachines or at periphery so that they will not obstruct other more utilized machines.( e.g. 3- 1 -3,1 -3- 10 , 3-4- 1 -6 i.e. 3 must be closer to 1 and 2- 7 , 2- 7 -9 -5, 9 -2-7 , i.e. 2 must be closer to 7 & 9).In this step, since the row distance is high, it will take more time for the vehicle to move from onemachine to another machine. So the row distance is reduced from 5 machines to 3 and 4machines.

(Ru n h o u rs 223 .24 )


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72

The least utilized machines are M 1 ,M2 and M4. these machines are kept away from remainingmachines or at periphery so that they will not obstruct other more utilized machines.( e.g. 3- 1 -3,1 -3- 10 , 3-4- 1 -6 i.e. 3 must be closer to 1 and 2- 7 , 2- 7 -9 -5, 9 -2-7 , i.e. 2 must be closer to 7 & 9).In this step, since the row distance is high, it will take more time for the vehicle to move from onemachine to another machine. So the row distance is reduced from 5 machines to 3 and 4machines.

(Ru n h o u rs 223 .24 )


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73

Ste p 5 : Here M 5 is accompanied M6, M 7 is accompanied byM9 , M3 is accompanied by M4. These machines are kept atminimum possible distance.

Ste p 6 : now considering maximum number of parts to beprocessed and their job sequence.P 7=36 0 , 7-9P2=3 10 , 7-9-2,P 14=3 15 , 9-2- 7So these machines are at minimum distance in straight linemanner ( 7-9-2)In next iteration next lower maximum parts are considered.


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74(Ru n h o u rs 213 )


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75

Ste p 7 : place remaining machines closer to respective machines accordingto job sequence.

average process time( % ) per part =(42. 98+ 16.24+2 1 .75 +12.88+ 12. 10 +23. 54+ 18.43+24.83+2 5 .92+22.2 5)/18 = 12.2 73%=0 .1273

average process time per part type =0

.1

27

3*2

13.4

5*6

0=1571 .84 min.


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76

average material handling time per part type = (82.26 *213.4 5*60 ) / ( 100*1 8)= 585 .2 7 min average process time( % ) per part =(42. 98+ 16.24+2 1 .75 +12.88+ 12. 10 +23. 54+ 18.43+24.83+2 5 .92+22.2 5)/18 =12.2 73%=0 .1273average process time per part type = 0 .1273*213.4 5*60 = 1571 .84 min.


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77

CELL F ORMATIONCell 1 2 9 7Cell 2 - 10 5 6

Cell 3- 4 3 8 1


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78

C ON C LU S ION S

the application for simulation to address manufacturing problems.

Developments in the area of simulation existing softwares for discrete

event simulation and conduction of simulation studies were reviewed.

T he necessity and importance of simulation for modeling and analyzing the

various classes of manufacturing problems was focused in this paper;

we hope this paper may encourage the extensive use of simulation in

manufacturing and development of simulation technology for addressing

the problems which need serious attention.


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References

Averill M . Law, W. D avid, Kelton,2000 Simulation M odeling and Analysis ,M cGraw-HillCharles Harrell, et al., 2000, Simulation U sing Pro M odel , M cGraw-HillRamsey Suliman, et al.,2000 Tools and Techniques for Social ScienceSimulation , Physica VerlagM ichael Pidd, 1998, Computer Simulation in M anagement Science , JohnWiley & SonsM ichael Prietula, et al., 1998, Simulating Organizations: ComputationalM odels of Institutions and Groups , M it. PressD avid Profozich,1997, M anaging Change with Business ProcessSimulation , Pearson Ptr.Paul A. Fishwick, Richard B. M odjeski, 1991, Knowledge-BasedSimulation ,Springer-VerlagKlaus G. Troitzsch, et al., 1996, Social Science M icrosimulation , SpringerVerlagHarry A. Pappo, 1998, Simulations for Skills Training , EducationalTechnology Publications


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T he end

Thank you

system modeling group 7

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