Record

CHAPTER-1

SIMULATION MODELLING

1.1 INTRODUCTION

Simulation modeling is a common paradigm for analyzing complex systems. In a

nutshell, this paradigm creates a simplified representation of a system under study.

The paradigm then proceeds to experiment with the system, guided by a prescribed set

of goals, such as improved system design, cost–benefit analysis, sensitivity to design

parameters, and so on. This book is concerned with simulation modeling of industrial

systems. such as ,

1 -manufacturing systems (e.g., production lines, inventory systems, job

shops, etc.),

2 -supply chains, computer and communications systems (e.g.,client-server

system ,computer network system.

3-transportation systems (e.g., seaports, airports, etc.).

1.2 SYSTEMS AND MODELS.

Modeling is the enterprise of devising a simplified representation of a complex system

with the goal of providing predictions of the system's performance measures

(metrics) of interest. Such a simplified representation is called a model. A model is

designed to capture certain behavioral aspects of the modeled system—those that are

of interest to the analyst/modeler—in order to gain knowledge and insight into the

system's behavior .

1.3 ANALYTICAL VERSUS SIMULATION MODELING

A simulation model is implemented in a computer program. It is generally a

relatively inexpensive modeling approach, commonly used as an alternative to

analytical modeling. The tradeoff between analytical and simulation modeling lies in

the nature of their “solutions,” that is, the computation of their performance measures

as follows:

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1. An analytical model calls for the solution of a mathematical problem, and the

derivation of mathematical formulas, or more generally, algorithmic procedures.The

solution is then used to obtain performance measures of interest.

2. A simulation model calls for running (executing) a simulation program to produce

sample histories. A set of statistics computed from these histories is then used to

form performance measures of interest.

To compare and contrast both approaches, suppose that a production line is

conceptually modeled as a queuing system. The analytical approach would create an

analytical queuing system (represented by a set of equations) and proceed to solve

them. The simulation approach would create a computer representation of the queuing

system and run it to produce a sufficient number of sample histories. Performance

measures, such as average work in the system, distribution of waiting times, and so

on, would be constructed from the corresponding “solutions” as mathematical or

simulation statistics, respectively.

The choice of an analytical approach versus simulation is governed by general

tradeoffs. For instance, an analytical model is preferable to a simulation model when

it has a solution, since its computation is normally much faster than that of its

simulation- model counterpart. Unfortunately, complex systems rarely lend

themselves to modeling via sufficiently detailed analytical models. Occasionally,

though rarely, the numerical computation of an analytical solution is actually slower

than a corresponding simulation. In the majority of cases, an analytical model with a

tractable solution is unknown, and the modeler resorts to simulation.

When the underlying system is complex, a simulation model is normally preferable,

for several reasons. First, in the unlikely event that an analytical model can be found,

the modeler's time spent in deriving a solution may be excessive. Second, the modeler

may judge that an attempt at an analytical solution is a poor bet, due to the apparent

mathematical difficulties. Finally, the modeler may not even be able to formulate an

analytical model with sufficient power to capture the system's behavioral aspects of

interest. In contrast, simulation modeling can capture virtually any system, subject to

any set of assumptions. It also enjoys the advantage of dispensing with the labor

attendant to finding analytical solutions, since the modeler merely needs to construct

and run a simulation program. Occasionally, however, the effort involved in

constructing an elaborate simulation model is prohibitive in terms of human effort, or

running the resultant program is prohibitive in terms of computer resources (CPU

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time and memory). In such cases, the modeler must settle for a simpler simulation

model, or even an inferior analytical model.

Another way to contrast analytical and simulation models is via the classification of

models into descriptive or prescriptive models. Descriptive models produce estimates

for a set of performance measures corresponding to a specific set of input data.

Simulation models are clearly descriptive and in this sense serve as performance

analysis models. Prescriptive models are naturally geared toward design or

optimization (seeking the optimal argument values of a prescribed objective function,

subject to a set of constraints). Analytical models are prescriptive, whereas simulation

is not. More specifically, analytical methods can serve as effective optimization tools,

whereas simulation-based optimization usually calls for an exhaustive search for the

optimum.

Overall, the versatility of simulation models and the feasibility of their solutions far

outstrip those of analytical models. This ability to serve as an in vitro lab, in which

competing system designs may be compared and contrasted and extreme-scenario

performance may be safely evaluated, renders simulation modeling a highly practical

tool that is widely employed by engineers in a broad range of application areas .In

particular, the complexity of industrial and service systems often forces the issue of

selecting simulation as the modeling methodology of choice..

1.4 SIMULATION MODELING AND ANALYSIS

The advent of computers has greatly extended the applicability of practical

simulation modeling. Since World War II, simulation has become an indispensable

tool in many system-related activities. Simulation modeling has been applied to

estimate performance metrics, to answer “what if” questions, and more recently, to

train workers in the use of new systems. Examples follow.

Estimating a set of productivity measures in production systems, inventory

systems,

manufacturing processes, materials handling, and logistics operations

Designing and planning the capacity of computer systems and communication

networks

so as to minimize response times

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Conducting war games to train military personnel or to evaluate the efficacy of

proposed military operations

Evaluating and improving maritime port operations, such as container ports or

bulk material marine terminals (coal, oil, or minerals), aimed at finding ways

of reducing

vessel port times

Improving health care operations, financialImproving health care operations,

financial and banking operations, and transportation systems and airports,

among many others

1.5 SIMULATION WORLDVIEWS

A worldview is a philosophy or paradigm. Every computer tool has two associated

Worldviews.

Developer worldview

User world view.

The first worldview pertains to the philosophy adopted by the creators of the

simulation software tool (in our case, software designers and engineers). The second

worldview pertains to the way the system is employed as a tool by end-users (in our

case, analysts who create simulation models as code written in some simulation

language). A system worldview may or may not coincide with an end-user worldview,

but the latter includes the former.

1.6 MODEL BUILDING

Modeling, including simulation modeling, is a complicated activity that

combines art and science. Nevertheless, from a high-level standpoint, one can

distinguish the following major steps:

1. Problem analysis and information collection. The first step in building a simulation

model is to analyze the problem itself. Note that system modeling is rarely undertaken

for its own sake. Rather, modeling is prompted by some systemoriented problem

whose solution is the mission of the underlying project. In order to facilitate a

solution, the analyst first gathers structural information that bears on the problem, and

represents it conveniently. This activity includes the identification of input

parameters, performance measures of interest, relationships among parameters and

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variables, rules governing the operation of system components, and so on. The

information is then represented as logic flow diagrams, hierarchy trees, narrative, or

any other convenient means of representation. Once sufficient information on the

underlying system is gathered, the problem can be analyzed and a solution mapped

out.

2. Data collection. Data collection is needed for estimating model input parameters.

The analyst can formulate assumptions on the distributions of random variables in the

model. When data are lacking, it may still be possible to designate parameter ranges,

and simulate the model for all or some input parameters in those ranges.

3. Model construction. Once the problem is fully studied and the requisite data

collected, the analyst can proceed to construct a model and implement it as a

computer program. The computer language employed may be a general-purpose

language (e.g., C++, Visual Basic, FORTRAN) or a special-purpose simulation

language or environment (e.g., Arena, Promodel, GPSS).

4. Model verification. The purpose of model verification is to make sure that the

model is correctly constructed. Differently stated, verification makes sure that the

model conforms to its specification and does what it is supposed to do. Model

verification is conducted largely by inspection, and consists of comparing model code

to model specification. Any discrepancies found are reconciled by modifying either

the code or the specification.

5. Model validation. Every model should be initially viewed as a mere proposal,

subject to validation. Model validation examines the fit of the model to empirical data

(measurements of the real-life system to be modeled). A good model fit means here

that a set of important performance measures, predicted by the model, match or agree

reasonably with their observed counterparts in the real-life system. Of course, this

kind of validation is only possible if the real-life system or emulation thereof exists,

and if the requisite measurements can actually be acquired. Any significant

discrepancies would suggest that the proposed model is inadequate for project

purposes, and that modifications are called for. In practice, it is common to go through

multiple cycles of model construction, verification, validation, and modification.

6. Designing and conducting simulation experiments. Once the analyst judges a model

to be valid, he or she may proceed to design a set of simulation experiments (runs) to

estimate model performance and aid in solving the project's problem (often the

problem is making system design decisions). The analyst selects a number of

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scenarios and runs the simulation to glean insights into its workings. To attain

sufficient statistical reliability of scenario-related performance measures, each

scenario is replicated (run multiple times, subject to different sequences of random

numbers), and the results averaged to reduce statistical variability.

7. Output analysis. The estimated performance measures are subjected to a thorough

logical and statistical analysis. A typical problem is one of identifying the best design

among a number of competing alternatives. A statistical analysis would run statistical

inference tests to determine whether one of the alternative designs enjoys superior

performance measures, and so should be selected as the apparent best design.

8. Final recommendations. Finally, the analyst uses the output analysis to formulate

the final recommendations for the underlying systems problem. This is usually part of

a written report.

1.7 SIMULATION COSTS AND RISKS

Simulation modeling, while generally highly effective, is not free. The main costs

incurred in simulation modeling, and the risks attendant to it, are listed here.

Modeling cost. Like any other modeling paradigm, good simulation modeling

is a prerequisite to efficacious solutions. However, modeling is frequently

more art than science, and the acquisition of good modeling skills requires a

great deal of practice and experience. Consequently, simulation modeling can

be a lengthy and costly process. This cost element is, however, a facet of any

type of modeling. As in any modeling enterprise, the analyst runs the risk of

postulating an inaccurate or patently wrong model, whose invalidity failed to

manifest itself at the validation stage. Another pitfall is a model that

incorporates excessive detail. The right level of detail depends on the

underlying problem. The art of modeling involves the construction of the

least-detailed model that can do the job (producing adequate answers to

questions of interest).

Coding cost. Simulation modeling requires writing software. This activity can

be errorprone and costly in terms of time and human labor (complex software

projects are notorious for frequently failing to complete on time and within

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budget). In addition, the ever-present danger of incorrect coding calls for

meticulous and costly verification.

Simulation runs. Simulation modeling makes extensive use of statistics. The

analyst should be careful to design the simulation experiments, so as to

achieve adequate statistical reliability. This means that both the number of

simulation runs (replications) and their length should be of adequate

magnitude. Failing to do so is to risk the statistical reliability of the estimated

performance measures. On the other hand, some simulation models may

require enormous computing resources (memory space and CPU time). The

modeler should be careful not to come up with a simulation model that

requires prohibitive computing resources (clever modeling and clever code

writing can help here).

Output analysis. Simulation output must be analyzed and properly interpreted.

Incorrect predictions, based on faulty statistical analysis, and improper

understanding of system behavior are ever-present risks.

CHAPTER-2

DISCRETE EVENT SIMULATION

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The majority of modern computer simulation tools (simulators) implement a

paradigm, called discrete-event simulation (DES). This paradigm is so general and

powerful that it provides an implementation framework for most simulation

languages, regardless of the user worldview supported by them. Because this

paradigm is so pervasive, we will review and explain in this chapter its working in

some detail.

2.1 ELEMENTS OF DISCRETE EVENT SIMULATION

In the DES paradigm, the simulation model possesses a state S (possibly

vectorvalued) at any point in time. A system state is a set of data that captures the

salient variables of the system and allows us to describe system evolution over time.

TFig: - frame’s of discrete event simulation

2.2 EXAMPLES OF DES MODELS.

In this section the power and generality of DES models are illustrated through several

examples of elementary systems. The examples illustrate how progressively complex

DES models can be constructed from simpler ones, either by introducing new

modeling wrinkles that increase component complexity, or by adding components to

create larger DES models.

2.2.1 SINGLE MACHINE

Consider a failure-proof single machine on the shop floor, fed by a buffer. Arriving

jobs that find the machine busy (processing another job) must await their turn in the

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buffer, and eventually are processed in their order of arrival. Such a service discipline

is called FIFO (first in first out) or FCFS (first come first served), and the resulting

system is called a queue or queueing system.

To represent this system as a DES, define the state S(t) to be the number of

jobs in the system at time t. Thus, S(t) = 5 means that at time t, the machine is busy

processing the first job and 4 more jobs are waiting in the buffer. There are two types

of events: arrivals and process completions. Suppose that an arrival took place at time

t, when there were S(t) = n jobs in the system. Then the value of S jumps at time t

from n to n + 1, and this transition is denoted by . Similarly, a process

completion is described by the transition Both transitions are

implemented in the simulation program as part of the corresponding event processing.

Fig :-FIFO buffer job system

2.2.2 SINGLE MACHINE WITH FAILURES

Consider the previous single machine on the shop floor, now subject to failures. In

addition to arrival and service processes, we now also need to describe times to failure

as well as repair times. We assume that the machine fails only while processing a job,

and that on repair completion, the job has to be reprocessed from scratch .

The state S(t) is a pair of variables, S(t) = (N(t), V(t) ), where N(t) is the

number of jobs in the buffer, and V(t) is the process status (idle, busy, or down), all at

time t. In a simulation program, V(t) is coded, say by integers, as follows: 0=idle,

1=busy, and 2= down. Note that one job must reside at the machine, whenever its

status is busy or down.

The events are arrivals, process completions, machine failures, and machine

repairs. The corresponding state transitions follow:

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2.2.3 SINGLE MACHINE WITH AN INSPECTION STATION AND ASSOCIATED INVENTORY

Consider the single machine on a shop floor, without failures. Jobs that finish

processing go to an inspection station with its own buffer, where finished jobs are

checked for defects. Jobs that pass inspection are stored in a finished inventory

warehouse. However, jobs that fail inspection are routed back to the tail end of the

machine's buffer for reprocessing. In addition to interarrival times and processing

times, we need here a description of the inspection time as well as the inspection

decision (pass/fail) mechanism (e.g., jobs fail with some probability, independently of

each other).

Fig:- FIFO job arrival system

The state S(t) is a triplet of variables, S(t) = (N(t), I (t), K(t) ) where N(t) is the

number of items in the machine and its buffer, I(t) is the number of items at the

inspection station, and K(t) is the storage content, all at time t. Events consist of

arrivals, process completions, inspection failure (followed by routing to the tail end of

the machine's buffer), and inspection passing (followed by storage in the warehouse).

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CHAPTER -3

ELEMENTS OF PROBABILITY AND STATISTICS

3.1 INTRODUCTIONS

Many real-life systems exhibit behavior with random elements. Such systems

encompass a vast array of application areas, such as the following:

1. Manufacturing

Random demand for product held in an inventory system

Random product processing time or transfer time

Random machine failures and repairs

2. Transportation

Random congestion on a highway

Random weather patterns

Random travel times between pairs of origination and destination points

3. Telecommunications

Random traffic arriving at a telecommunications network

Random transmission time (depending on available resources, such as buffer

space and CPU)

Indeed, simulation modeling with random elements is often referred to as Monte

Carlo simulation, presumably after its namesake casino at Monte Carlo on the

Mediterranean. This apt term commemorates the link between randomness and

gambling, going back to the French scientist Blaise Pascal in the 17th century.

Formally, modeling a random system as a discrete-event simulation simply means that

randomness is introduced into events in two basic ways:

Event occurrence times may be random..

Event state transitions may be random.

For instance, random interarrival times at a manufacturing station exemplify the first

case, while random destinations of product units emerging from an inspection station

(possibly needing re-work with some probability) exemplify the second. Either way,

probability and statistics are fundamental to simulation models and to understanding

the underlying random phenomena in a real-life system under study. In particular,

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they play a key role in simulation-related input analysis and output analysis. Recall

that input analysis models random components by fitting a probabilistic model to

empirical data generated by the system under study, or by postulating a model when

empirical data is lacking or insufficient. Once input analysis is complete and

simulation runs (replications) are generated, output analysis is then employed to

verify and validate the simulation model, and to generate statistical predictions for

performance measures of interest.

3.2 PROBABILITY MASS FUNCTIONS

Every discrete random variable X has an associated probability mass function

(pmf ),

pX(x),definedby

Note that the notation {X = x} above is a shorthand notation for the event

It should be pointed out that the technical definition of a random

variable ensures that this set is actually an event (i.e., belongs to the underlying event

set E). Thus, the pmf is always guaranteed to exist, and has the following properties .

3.3 CUMULATIVE DISTRIBUTION FUNCTIONS

Every real-valued random variable X (discrete or continuous) has an

associated cumulative distribution function (cdf), FX (x), defined by

Note that the notation {X x} is a shorthand notation for the event {ᵚ: X(ᵚ)

x}. It should be pointed out that the technical definition of a random variable ensures

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that this set is actually an event (i.e., belongs to the underlying event set E). Thus, the

cdf is always guaranteed to exist.

The cdf has the following properties.

In words, since FX (x) may not be strictly increasing in x, is defined as the

smallest value x, such that FX (x) = y. The inverse distribution function is extensively

used to generate realizations of random variables.

3.4 PROBABILITY DENSITY FUNCTIONS

If FX (x) is continuous and differentiable in x, then the associated probability

density function (pdf), fX (x), is the derivative function .

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For a discrete random variable X, the associated pmf is sometimes referred to as a pdf

as well. This identification is justified by the fact that a mathematical abstraction

allows us, in fact, to define differencing as the discrete analog of differentiation.

Indeed, for a discrete real-valued random variable X, we can write

3.5 JOINT DISTRIBUTIONS

Let X1, X2, . . . , Xn be n real-valued random variables over a common

probability space. The joint cdf of X1, X2, . . . , Xn is the function .

Similarly, the joint pdf, when it exists, is obtained by multiple partial differentiation,

In this context, each cdf FXi (x) and pdf fXi (x) are commonly referred to as a

marginal distribution and marginal density, respectively. The random variables X1,

X2, . . . , Xn are mutually independent, if

provided that the densities exist. In other words, mutual independence is exhibited

when joint distributions or densities factor out into their marginal components. A set

of random variables, X1, X2, . . . , Xn, are said to be iid (independently, identically

distributed), if they are mutually independent and each of them have the same

marginal distribution.

3.6 EXPECTATIONS

and for a continuous random variable with pdf fX (x), we define

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Let X and Y be random variables, whose expectations exist, and let a and b be real

numbers. Then,

3.7 MOMENTS

3.8 CORRELATIONS

Let X and Y be two real-valued random variables over a common probability

space.It is sometimes necessary to obtain information on the nature of the association

(probabilistic relation) between X and Y, beyond dependence or independence. A

useful measure of statistical association between X and Y is their correlation

coefficient (often abbreviated to just correlation), defined by

The correlation coefficient has the following properties:

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2. If X and Y are independent random variables, then X and Y are uncorrelated, that

is r(X, Y) = 0 However, the converse is false, namely, X and Y may be

uncorrelated and dependent, simultaneously.

3. If Y is a (deterministic) linear function of X, that is, Y = aX þ b, then

3.9 COMMON DISCRETE DISTRIBUTIONS

3.10 GENERIC DISCRETE DISTRIBUTION

where [x] is the integral part of x.

The generic discrete distribution may be used to model a variety of situations,

characterized by a discrete outcome. In fact, all other discrete distributions are simply

useful specializations of the generic case.

3.10.1 BERNOULLI DISTRIBUTION

and the corresponding mean and variance are given by the formulas:

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A Bernoulli random variable may be used to model whether a job departing from a

machine is defective (failure) or not (success).

3.10.2 BINOMIAL DISTRIBUTION

The corresponding mean and variance are given by the formulas.

A binomial random variable may be used to model the total number of defective items

in a given batch. Such a binomial trial can be a much faster procedure than conducting

multiple Bernoulli trials.

3.10.3 GEOMETRIC DISTRIBUTION

and the corresponding mean and variance are given by the formulas,

3.10.4 POISSON DISTRIBUTION

and the corresponding mean and variance are given by

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3.11 COMMON CONTINUOUS DISTRIBUTIONS

This section reviews the most commonly used continuous distributions and the

underlying random experiment, and discusses their use in simulation modeling.

3.11.1 UNIFORM DISTRIBUTION

and the cdf is

The corresponding mean and variance are given by the formulas.

A uniform random variable is commonly employed in the absence of information on

the underlying distribution being modeled.

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3.11.2 STEP DISTRIBUTION

A step or histogram random variable, X, generalizes the uniform distribution

in that it constitutes a probabilistic mixture of uniform random variables. The step

distribution is denoted by Cont({(pj, lj, rj): j = 1, 2, . . . , J}), where the parameters

have the following interpretation: with probability p j = 1, 2, . . . ,

J. Thus, the state space of X is the union of intervals,

Thus, the resulting pdf is a step function (mixture of uniform densities) as illustrated

in by Figure and the corresponding cdf is given by

The corresponding mean and variance are given by the formulas

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Density function of the Cont({(0.3, 0, 3), (0.2, 3, 4), (0.5, 4, 8)}) distribution

3.11.3 TRIANGULAR DISTRIBUTION


Density function of the Tria(5, 7, 10) distribution.

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3.11.3 EXPONENTIAL DISTRIBUTION

and the cdf is


3.11.4 NORMAL DISTRIBUTION


Density function of the Norm(0,1) distribution.

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3.11.5 LOGNORMAL DISTRIBUTION

3.11.6 GAMMA DISTRIBUTION

Mean and variance are

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Density functions of the Gamm(1,1), Gamm(2,1), and Gamm(3,1) distributions.

3.11.7 STUDENT’S t DISTRIBUTION

Density function of the t(10) distribution.

3.11.8 F DISTRIBUTION

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Density function of the F(1, 1) distribution.

3.11.9 BETA DISTRIBUTION

Where

Density functions of the Beta(1.5, ), Beta(5, 5), and Beta(5, 1.5) distributions.

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3.11.10 WEIBULL DISTRIBUTION

Density functions of the Weib(1,1), Weib(2,1), and Weib(3,1) distributions.

STOCHASTIC PROCESSES

The auto correlation function of a stochastic process is the correlation

coefficient of its lagged random variables,

3.12 VARIATE GENERATION USING THE INVERSE TRANSFORM METHOD

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The Inverse Transform method.

3.12.1 GENERATION OF UNIFORM VARIATES

3.12.2 GENERATION OF EXPONENTIAL VARIATES

where u is given and x is unknown. Solving the above for x readily yields the formula

It can be simplified into the equivalent formula

3.12.3 GENERATION OF DISCRETE VARIATES

or equivalently,

The Inverse Transform method for generating a discrete variate.

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3.12.4 GENERATION OF STEP VARIATES FROM HISTOGRAMS

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CHAPTER-4

FREQUENTLY USED ARENA MODULES

Following is a subset of frequently used Arena modules, the associated

template panel, and a brief explanation of module function and operation. The term

parameter stands for the contents of the corresponding field in the module dialog box.

1 .ACCESS MODULE (ADVANCED TRANSFER)

Function: Used to allocate one or more cells of a conveyor to an entity for

movement from one station to another.

Operation: When an entity arrives at this module, it waits until the

appropriate number of contiguous cells on the conveyor become empty and align with

the entity’s station location. Once this condition is satisfied and the entity gains

control of the requisite cells on the conveyor, it may be conveyed to the next station.

Access

2 .ASSIGN MODULE (BASIC PROCESS)

Function: Used to assign values to variables, entity attributes, entity types,

entity pictures, and other system variables.

Operation: Whenever an entity enters this module, one or more assignments

are executed. An assignment can be made to entity attributes, entity type or entity

picture and/or to global variables or other system variables. After new values are

assigned, all entities exit the module from a single exit point. Assignments are added

by filling out the sub-form Assignments, which pops up on clicking the Add button on

the module form.

Assign

3. BATCH MODULE (BASIC PROCESS)

Function: Used to group entities into batches.

Operation: Entities arriving at the Batch module are placed in a queue until

the required number of entities has accumulated. Once accumulated, the entities are

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grouped and replaced by a new representative entity, which inherits its attributes from

batch members according to a rule specified in the Save Criterion parameter. The

representative batch exits the module from a single exit point. Batches can be

permanent or temporary.

Batch

4 .CREATE MODULE (BASIC PROCESS)

Function: Used as a source to generates new entities, and release them into

the model.

Operation: Entities are created using a schedule or based on inter-arrival

times. Once created, the entities leave the module.

Create

5 .DECIDE MODULE (BASIC PROCESS)

Function: Used as a decision point in the model.

Operation: When an entity arrives at this module, a decision is made based on

one or more conditions (deterministic outcome) or by chance (random outcome). The

entity then leaves the module at an exit point, which is determined by the outcome.

Conditions are based either on attribute values, or variable values, or expressions, or

the entity type. When the value of parameter Type is 2-way by Chance or 2-way by

Condition, the model has two exit points: one for true outcomes (located at the right

side of the module) and one for false outcomes (located at the bottom of the module).

When the value of parameter Type is N-way by Chance or N-way by Condition, there

is an exit point for each outcome. An entity leaves the module from the computed exit

point.

Decide

6 .DELAY MODULE (ADVANCED PROCESS)

Function: Used to delay an entity by a specified amount of time.

Operation: When an entity arrives at this module, the time expression defined

in the Delay Time parameter is evaluated and the entity remains in the module for that

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time period. The time is then allocated to the entity,s value added, non-value

added,transfer, wait or other time as specified in the Allocation parameter.

Delay

7 .DISPOSE MODULE (BASIC PROCESS)Function: Used as the exit point of entities from a simulation model.

Operation: Entities arriving at this module are disposed of and removed from

the model. Entity statistics may be recorded before the entity is disposed of by

checking the Record Entity Statistics checkbox.

Dispose

8 .DROPOFF MODULE (ADVANCED PROCESS)

Function: Used to remove a specified number of entities from an entity’s

group and to send them to the next module in the model.

Operation: When an entity group arrives at this module, the specified number

of the entities in the group, starting form the rank defined in the Starting Rank

parameter, are removed from the group and sent to the module specified by model

connections. The value of the user-defined group attributes and internal attributes of

the representative entity of the group (designated at group formation time) may be

copied to the dropped off entities based on a rule specified in the

Member Attributes parameter. There are two exit points from this module. The

original group of entities exit to the right of the module, while the dropped off entities

exit at the bottom of the module.

Dropoff

9 .FREE MODULE (ADVANCED TRANSFER)Function: Used to release the entity’s most recently allocated transporter unit.

Operation: When the entity enters this module, it releases its most recently

allocated transporter unit. If another entity is waiting in a queue to request or allocate

the transporter, that transporter will be allocated to that entity. If there are no waiting

entities at the time the transporter unit is freed, the transporter will wait idle at the

freeing entity’s station location, unless otherwise specified in the Transporter module.

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Free

10 .HALT MODULE (ADVANCED TRANSFER)Function: Used to change the status of a transporter unit to inactive.

Operation: When an entity enters this module it tries to halt the requisite

transporter unit. If that unit is idle at the time, then its status is set immediately to

inactive. If, however, that unit is busy at the time, then its status changes immediately

to busy and inactive. If later on the entity that controls the halted unit proceeds to free

it, then its status changes to inactive only at that point in time. Once a transporter unit

has been halted, no entities can gain control of that unit until it is activated

Halt

11. HOLD MODULE (ADVANCED PROCESS)

Function: Used to hold an entity in a queue to either wait for a signal, wait for

a specified condition to become true, or to be held indefinitely.

Operation: When an entity arrives at this module and the value of the Type

attribute is Wait for Signal, then a Signal module must be used to send the requisite

signal that allows the entity to move on to the next module. If the value of the Type

attribute is Scan for Condition, then the entity will remain at the module until the

condition(s) defined in the Condition parameter become(s) true. On the other hand, if

the value is Infinite Hold, then the hold period is indefinite, unless a Remove module

is used to allow the entity to continue processing. The waiting queue for the entities

can be specified in the Queue Type attribute as the module s internal queue or another

queue.

,

Hold

12 .MATCH MODULE (ADVANCED PROCESS)

Function: Used to bring together (synchronize) a specified number of entities

waiting in different queues at this module.

Operation: An entity arriving at this module is placed in one of up to five

associated queues, based on its entry point, and remains in its queue until a match

materializes (a match may be accomplished when there is at least one entity in each

32

queue). At that point in time, one matching entity from each queue is removed, and all

these entities exit the module simultaneously via their respective exit point. All exit

points must be connected to some modules.

Match

13. PICKSTATION MODULE (ADVANCED TRANSFER)

Function: Used to select a particular station.

Operation: When an entity arrives at this module, a station is selected from a

station group, based on the selection logic specified in the Selection Based On . . .

section. The entity may then route, transport, convey, or connect to the selected

station depending on the value of the Transfer Type parameter. The station selection

process is based on the minimum or maximum value of a variety of system variables

and expressions depending on the value of the Test Condition parameter.

PickStation

14. PICKUP MODULE (ADVANCED PROCESS)

Function: Used to remove a number of consecutive entities from a given

queue.

Operation: When an entity group arrives at this module, it removes a

specified number of entities from a specified queue starting at a specified rank in the

queue. The picked up entities are added to the end of the incoming entity group.

Pickup

15. PROCESS MODULE (BASIC PROCESS)Function: Used as the main processing method for various functions such as

delaying, seizing, and releasing resources and queuing

Operation: Entities arriving at this module are processed differently,

depending on the specified value for the Action parameter. Additionally, the user can

choose the sub model option as the Type parameter, and specify a hierarchy of user-

defined sub models and their logic. Process times and associated costs are allocated to

incoming entities using the Allocation parameter, including Value Added, Non-Value

33

Added, Transfer, Wait, and Other. All entities exit this module from a single exit

point.

Process

16 .READWRITE MODULE (ADVANCED PROCESS)

Function: Used to read or write data from/to a specified source.

Operation: When an entity arrives at this module, data is read from an input

file or the keyboard, or data values are assigned to a list of variables, attributes, or

other expressions. The data can also be written to an output device, such as the screen

or a file. When reading from or writing to a file, the Read Write logic varies according

to the Type parameter for the Arena File Name parameter.

ReadWrite

17. RECORD MODULE (BASIC PROCESS)

Function: Used to collect statistics in a particular location in the model.

Operation: When an entity arrives at this module, a single user-specified

statistic (count or tally) is collected. The statistic type is selected in the Type

parameter. Once the requested statistic is collected, the entity exits from a single exit

point of the module.

Record

18 .RELEASE MODULE (ADVANCED PROCESS)

Function: Used to release units of a resource previously seized by an entity.

Operation: When an entity arrives at this module, it gives up control of resource

unit(s) from a specified resource. Any entities waiting in queues for those resources

will then contend for control of the released units.

Release

34

19. REMOVE MODULE (ADVANCED PROCESS)

Function: Used to remove a single entity from a specified position in a queue,

and to send it to a designated module.

Operation: When an entity arrives at this module, it removes a specified

entity from a specified queue and sends the removed entity to the next module. The

removed entity is selected based on the entity’s rank (position in the queue). The

removed entity exits the module at the exit point labeled Removed Entity on the

module icon, while the removing entity exits the module at the exit point labeled

Original on the module icon. The removing entity is processed before the removed

entity.

Remove

20 .REQUEST MODULE (ADVANCED TRANSFER)

Function: Used to assign a transporter unit to an entity and then to move the unit to

the entity’s location (in order to transport that entity).

Operation: When an entity arrives at this module, it is allocated a transporter unit (if

none is available, the entity waits in this module until one becomes available). Once a

transporter unit is allocated to the entity, that entity waits in this module until the

transporter unit reaches the entity’s location (specified in its Station attribute), and

then the entity exits the module. A specific transporter unit may be defined using the

Transporter Name parameter, or the selection may occur based on a rule in the

Selection Rule parameter.

Request

21 .ROUTE MODULE (ADVANCED TRANSFER

Function: Used to transfer an entity to a specific station or the next station in

the station sequence defined for that entity.

Operation: When an entity arrives at this module, its Station attribute is set by

this module to a destination station. The entity is then sent to this destination station,

and will arrive there after the time period specified in the Route Time parameter. If

the value of the Destination Type parameter is Sequential, then the next station is

determined by the entity, s sequence and step within the sequence.

35

Route

22. SEARCH MODULE (ADVANCED PROCESS)

Function: Used to search over entities in a queue or a batch, or an expression

over a range of indices, and to return in the global variable J the first index for which

the specified condition is true. In the first case, J returns the entity rank (in the queue

or batch), while in the second case, J returns the first index for which the specified

expression evaluated to true.

Operation: When an entity arrives at this module, the global variable J is set

to a starting index and the search condition is then evaluated. If the search condition is

satisfied, the search ends and the current value of J is retained. Otherwise, the value of

J is incremented (or decremented) and the condition is re-evaluated. This process

repeats until either the search condition is satisfied or the ending value is reached, in

which case J is set to 0.

Search

23. SEIZE MODULE (ADVANCED PROCESS)

Function: Used to allocate units of one or more resources to an entity.

Operation: When an entity enters this module, it waits in a queue until all

specified resources are available simultaneously. The entity can seize units of a

particular resource or units of a member of a resource set.

Seize

24. SEPARATE MODULE (BASIC PROCESS)

Function: Used to separate and recover the original members of a temporary

batch of entities previously grouped in a Batch module. Also used to duplicate

entities.

Operation: When a temporary batch entity enters this module, batch members

are recovered and depart sequentially, whereas the temporary batch entity is disposed

of. The simulation clock is not advanced while batch members depart from this

module. When used for entity duplication purposes, all entities inherit the incoming

entity’s attributes and leave the module before it.

36

Separate

25 .SIGNAL MODULE (ADVANCED PROCESS)

Function: Used to send a signal to each Hold module in the model where the

value of the Type parameter is Wait for Signal, in order to release the maximum

specified number of entities.

Operation: When an entity arrives at this module, the Signal Value parameter

of the module is evaluated as a signal code, which is then sent to each Hold module in

the model in which the value of the Type parameter is Wait for Signal. On receipt of

the signal, entities at Hold modules that are waiting for that signal are removed from

their queues. The entity sending the signal then exits the module.

Signal

26. STATION MODULE (ADVANCED TRANSFER)Function: Used to define a station or a set of stations corresponding to a

physical or logical location where processing occurs.

Operation: An entity arrives at this module directly from any of the modules

where the entity transfer is initiated, even if the latter modules are not connected to

the Station module. The entity may trigger statistics collection before exiting the

module.

Station

27 .STORE MODULE (ADVANCED PROCESS)

Function: Used to add an entity to storage.

Operation: When an entity arrives at this module, the storage level is

incremented, and the entity immediately moves to the next module in the model. The

Unstore module may then be used to remove the entity from the storage.

Store

28 .TRANSPORT MODULE (ADVANCED TRANSFER)

Function: Used to transfer an entity controlling a transporter unit to a

destination

37

station.

Operation: When an entity arrives at this module, its Station attribute is set to

the entity’s destination station. The entity is then transported on a specified transporter

unit to a destination station. After the time delay required for the transport elapses, the

entity reappears in the model at the destination Station module.

Transport

29. UNSTORE MODULE (ADVANCED PROCESS)Function: Used to remove an entity from storage. Operation: When an entity

arrives at this module, the specified storage level is decremented and the entity

immediately moves to the next module in the model.

Unstore

30 .VBA BLOCK (BLOCKS)

Function: Used to insert VBA (Visual Basic for Applications) procedural user

code into the model. The code is entered via the Visual Basic Editor.

Operation: For a VBA block with ID number N, the user provides VBA code

for the corresponding VBA Block N Fire event. When an entity enters a VBA block,

Arena fires the corresponding event to execute the user-provided VBA code.

38

EXPERIMENT NO 1

Analysis of a simple serial two process system

Develop the model of a single serial two process system, items arrived at the

system with mean time between arrivals of 10 minutes, with the first arrival at time

zero. They are immediately send to process 1, which has a single resource with a

mean time of 9 minutes. Upon completion they are send to process 2 which is

identical to but independent of process 1. The items depart from the system upon

completion of process 2. Performance measures of interest are the average number in

queue at each process and the total time in system of items. Use replication length of

10000 minutes and 3 replications. Compare the results for the following distributions

(a) Expo inter arrival times and exponential service time

(b) Constant inter arrival time and exponential service time

(c) Exponential inter arrival time and constant service time

(d) Constant inter arrival time and constant service time. consider first 500

minutes as warm up period .show the results graphically

39

AIM

To develop a simple serial two process system and to find average number in queue

at each process and total time in system of items.

DATA GIVEN

Inter arrival time (IAT) = 10 min

Processing time of first process = 9 min

Processing time of second process = 9 min

Replication Length = 10000min

Number of replication = 3

Warm up period = 500 min

BASIC MODULE

Create, assign, process, record and dispose

SPREADSHEET MODULE

NIL

PROCEDURE

1Drag and drop create module

1 Double click on create module, make the following changes in the dialogue

box.

Name: item arrival

Type: random (expo), value 10

Units: min, entities per arrival: 1

Click ok

2 Drag and drop assign module.

3 Double click on assign module and make the following changes in the

dialogue box.

Name: assign for total time

Add: attribute

Attribute name: arrival time

Value: tnow

Click ok.

4 Drag and drop process module

5 Double click on process module and make the following changes in the

dialogue box.

40

Name: process 1

Action: seize, delay release

Priority: medium

Add: resource, resource 1

Delay type: expression Unit: min

Expression: expo (9)

Click ok

6 Drag and drop process2 module and make the changes.

Name: process 2

Action: seize, delay, release

Add: resource, resource1

Delay type: expression

Unit: minute

Expression: expo (9)

Click ok

7 Drag and drop record module and make the following changes.

Name: total time

Type: time interval


Click ok

8 Drag and drop dispose module and make the changes.

Name: item dispose

Click ok

9 Save the model and run setup

Click run – menu – check model

Do make corrections if errors occur

10 Click run – menu – go

Run setup – menu

No: of replications: 3

Warm up period: 500 mins

Replication length: 10000 min

Base time units: minutes

Click ok.

11 Repeat the same procedure to b, c, d options.

41

MODEL DISCRIPTION

EXPERIMENT MODEL -1.1

In this simulation , take inter arrival time as expo(10) minute. The processing

time for process 1 and process 2 are expo(9) minute. select replication length

as 10000 minutes and run by 3 replication,warm up period is 500 minutes.

Then the curresponding simulation model as shown below.

Fig 1.1- simple serial two process system with IAT expo (10) and

PT expo (9)


In this simulation , take inter arrival time as const(10) minute. The

processing time for process 1 and process 2 are expo(9) minute. select

replication length as 10000 minutes and run by 3 replication,warm up period is

500 minutes. Then the curresponding simulation model as shown below.

Fig 1.2- simple serial two process system with IAT const (10) and PT expo

(9).

42


In this simulation , take inter arrival time as expo(10) minute. The processing

time for process 1 and process 2 are const(9) minute. select replication length as

10000 minutes and run by 3 replication,warm up period is 500 minutes. Then the

curresponding simulation model as shown below.

Fig 1.3- simple serial two process system with IAT expo (10) and PT const

(9).


In this simulation , take inter arrival time as const(10) minute. The

processing time for process 1 and process 2 are const(9) minute. select

replication length as 10000 minutes and run by 3 replication,warm up period is

500 minutes. Then the curresponding simulation model as shown below.

Fig 1.4- simple serial two process system with IAT const (10) and PT

const (9).

43

RESULTS & DISCUSSION

EXPERIMENT 1.1

After simulating the model for a replication length 10000 minutes , the

following results were obtained as shown in table below:

Average No In Queue Total Time In

System (min)Process 1

(nos)

Process 2

(nos)

Replication 1 5.12 4.5643 111.75

Replication 2 5.2422 2.9566 103.42

Replication 3 4.3774 6.2512 124.19

Average 4.9132 4.5907 113.12

Table 1.1 Avg no in queue and total time in system for model 1.1

From this simulation we get the average number in queue for first process as

4.9132 ,the average number in queue for 2nd process as 4.5907 and also the

total time for the entire system is 113.12 minutes.

EXPERIMENT 1.2





(nos)

Process 2

(nos)

Replication 1 2.6403 3.5889 79.98

Replication 2 2.3885 4.5907 87.863

Replication 3 2.9010 4.4385 91.204

Average 2.643 4.206 86.349


44


2.643 ,the average number in queue for 2nd process as 4.206 and also the total

time for the entire system is 86.349 minutes.

EXPERIMENT 1.3

After simulating the model for a replication length 10000 minutes , the following results were obtained as shown in table below:



(nos)

Process 2

(nos)

Replication 1 3.0241 0 47.885

Replication 2 3.8485 0 55.785

Replication 3 5.3293 0 69.265

Average 4.0673 0 57.645




time for the entire system is 57.645 minutes.

EXPERIMENT 1.4





(nos)

Process 2

(nos)

Replication 1

0 0 18

Replication 2

0 0 18

Replication 3 0 0 18

Average 0 0 18


45



time for the entire system is 18 minutes.

From the experiment it is seen that model 1.4 is purely deterministic model whereas model 1.1 is purely probabilistic model. Models 1.2 and 1.3 are randomly probabilistic models. The table 5 below shows the variation in average number in queue and total system time when we change the system from a deterministic one to a probabilistic one.

Average no in queue (nos) Total time in

system (min)process 1 process 2

Model 1.4 0 0 18

Model 1.3 4.067 0 57.645

Model 1.2 2.645 4.206 86.349

Model 1.4 4.913 4.597 113.12

Table 1.5 average no in queue and total time in system

GRAPHGraph is obtained from above information

model 1.4 model 1.3 model1.2 model 1.10

1

2

3

4

5

6

process 1process 2

models

avg no in queue

Graph 1.1:-average no in queue vs model

During constant inter arrival time constant processing time , average no in queue is zero.

46

model 1.4

model 1.3

model 1.2

model 1.1

0

20

40

60

80

100

120

Total time in systemSeries2

Model

Total time in system

Graph 1.2:-model vs total timeDuring constant inter arrival time and constant processing time, total time taken by the system is less.

INFERENCE

It is seen that from the above experiment, as uncertainty in the system

increases the number in queue and total time increases and vice – versa.

47

EXPERIMENT NO.2

Analysis of a production system with 5 serial automatic work stations and part reprocessing

A proposed production system consists of five serial automatic workstations.

The processing times at workstations are constant:11,10,11,11, and 12(all times given

in this problem are in minutes).The part interval times are UNIF(13,15)minutes. There

is an unlimited buffer in front of all workstations, and we will assume that all transfer

times are negligible or zero. The unique aspect of this system is that at workstations 2

through 5 there is a chance that the part will need to be reprocessed by the

workstations that precedes it. For example, after completion at workstation 2,the part

can be sent back to the queue in front of workstation 1,The probability of revisiting a

workstation is independent in that the same part could be send back many times with

no change in the probability. At present, it is estimated that this probability, the same

for all workstations, will be between 5% and 10%.Develop the simulation model and

make six runs of 10,000 minutes each for probabilities of 5,6,7,8,9, and 10%.Consider

first 500 minutes as warm-up period. Using the results construct a plot of the average

cycle time(system time) against the probability of a revisit. Also include the

maximum cycle time for each run on your plot. Run the model for 3 replications and

compare the results.

A1M

48

To develop a simple serial five process system and to find average cycle time

of process and total time in system . Using the results construct a plot of the average

cycle time (system time) against the probability of a revisit

DATA GIVEN:-

Inter arrival time (IAT) = UNIF (13, 15) minutes

Process time (PT) = CONST (11, 10, 11, 11, 12) minutes

No of replication = 3

Replication length= 10000 minutes

BASIC MODULE:-

Create, Process, Assign, Decide, Record, Dispose

SPREAD SHEET MODULE:-

Nil

PROCEDURE:-

1 Drag and drop create module to model area

2 Double click on create and enter the details

Name: path arrived

Time between arrivals

Type: Expression

Expression: UNIF (13, 15) minutes

Units: min

Click OK

3 Drag and drop assign module

4 Double click on it ,change the details

Name: arrived time

Add: attribute named arrival time

Value: tnow

5 Drag and drop process module ,double click on it enter data

Name: workstation1

Action: seize delay release

Add Resource: Resource1.1

Delay type: CONST

49

Unit: minutes

Value: 11

Click OK

6 Drag and drop 2nd process module ,double click on it enter data

Name: workstation2



Delay type: CONST

Unit: minutes

Value: 10

Click OK

7 Drag and drop decide module ,double click on it enter data

Name: Rework at workstation 2

Type: two way by chance

If true: workstation 3 and if false workstation 1

8 Drag and drop 3rd process module ,double click on it enter data

Name: workstation3



Delay type: CONST

Unit: minutes

Value: 11

Click OK





10 Drag and drop 4th process module ,double click on it enter data

Name: workstation4



Delay type: CONST

Unit: minutes

50

Value: 11

Click OK





12 Drag and drop 5th process module ,double click on it enter data

Name: workstation 5



Delay type: CONST

Unit: minutes

Value: 12

Click OK




If true: move to record and if false workstation 4

14 Drag and drop record module ,double click on it enter data

Name : record time

Type: time interval


Click OK

15 Drag and drop dispose module ,double click on it enter data

Name : dispose

Click OK

16 Click RUN go to SETUP change the following parameters

No. of replication= 3

Replication length = 10000

Warm up time = 500

Basic unit minutes

17 Then change the rework probability of

51

1st time set as 5% then 6,7,8,9,10 and check the average cycle time of

each case

18 Run check the model

19 Run and check the average cycle time of each cases and plot the graph

MODEL DESCRIPTION

Case 1

For Analysis of a production system with 5 serial automatic work stations and part

re processing with probability of re-visit at 5%, uniform inter arrival time and

processing time for work station-1 is 11 minutes, for work station-2 it is 10

minutes , for work station-3 is 11 minutes , for work station- 4 it is again 11

minutes and finally for work station-5 it is 12 minutes.

Fig.2.1 Model with probability of revisit at 5 %

Case2






52


Case 3







Case 4

For Analysis of a production system with 5 serial automatic work stations and part re

processing with probability of re-visit at 5%, uniform inter arrival time and processing

time for work station-1 is 11 minutes, for work station-2 it is 10 minutes , for work

station-3 is 11 minutes ,for work station- 4 it is again 11 minutes and finally for work

station-5 it is 12 minutes.

53


Case 5






Fig.2.5 Model with probability of revisit at 9%

54

Case 6







RESULT AND DISCUSSIONS

Case 1

When probability of rework is 5%, processing time for first work station is

11 minutes, for second work station it is 10 minutes, for third and fourth it is

11minutes,and for final work station it is12 minutes and inter arrival time is

Unif (13 ,15) minutes respectively. No of replication is 3.

No Of

Replication

Total Time

(minutes)

1 73.01

2 71.89

3 72.11

Table 2.1 Probability of rework at 5%

55

For first replication total time is 73.01 minutes, for second replication total

time is 71.89 minutes and for third replication total time is 72.11 minutes and Average

Total cycle time =72.785 minutes.

Case 2

When probability of rework is 6%, processing time for first work station is 11

minutes, for second work station it is 10 minutes, for third and fourth it is


Unif (13, 15) minutes respectively. No of replication is 3.

No Of

Replication

Total Time

(minutes)

1 78.11

2 78.89

3 78.11


For first replication total time is 78.11 minutes, for second replication total time is

78.89 minutes and for third replication total time is 78.11 minutes and Average Total

cycle time =78.43minutes.

Case 3




Unif (13 ,15) minutes respectively. No of replication is 3.

56

No Of

Replication

Total Time

(minutes)

1 87.01

2 88.01

3 86.77

Table2.3 Probability of rework at 7%


88.01 minutes and for third replication total time is 86.77 minutes and Average Total

cycle time = 87.76 minutes.

Case 4




Unif ( 13, 15) minutes respectively. No of replication is 3.

No Of

Replication

Total Time

(minutes)

1 102.01

2 102.89

3 102.23



102.89 minutes and for third replication total time is 102.23 minutes and Average

Total cycle time=102.107 minutes.

57

Case 5


minutes, for second work station it is 10 minutes,for third and fourth it is


Unif (13 ,15 )minutes respectively. No of replication is 3.

No Of

Replication

Total Time

(minutes)

1 119.11

2 118.89

3 117.56




Total cycle time=118.76 minutes.

Case 6

When probability of rework is 10%, processing time for first work station is

11 minutes, for second work station it is 10 minutes, for third and fourth it is

11 minutes, and for final work station it is12 minutes and inter arrival time is

Unif (13, 15) minutes respectively. No of replication is 3.

No Of

Replication

Total Time

(minutes)

1 168.01

2 168.89

3 169.11

58




Total cycle time=168.77minutes.

GRAPH

By analysis of above table following graph is obtained.

1 2 3 4 5 60

20

40

60

80

100

120

140

160

180

Rework %

Cycle Time

cycle time

Rework %

Graph 2.1:- rework vs. cycle time

From graph we can understand that probability of revisiting work station increases,

cycle time also increases.

INFERENCE

Production system with 5 serial automatic work stations and part re processing

is analyzed, when probability of revisiting work station changes between 5-10% the

cycle time seems to be increasing.

59

EXPERIMENT NO 3

Analysis of a production system with 4 serial automatic workstations including minor and major failures

A production system consists of four serial automatic workstations. Jobs arrive

at the first workstation as exponential with mean 8. All transfers times are assumed to

be zero and all processing times are constant. There are two types of failures 1) major

failures and 2) jams. The data for this system is given in the table below (all times are

in minutes). Use exponential distributions for the uptimes and uniform distributions

for the repair times (for instance the repairing jams at workstations 3 is UNIF (2.8,

4.2)minutes. Run your simulation for 1000 minutes to determine the percent of time

each resource spends in the failure state and the ending status of each work station

queue. Consider first 500 minutes as warm up period .Run the model for 3

replications and show graphically the results for single replications and 3 replications

Workstation

Number

Process

time

Major Failure

Means(minutes)

Jam Means

(minutes)

Uptimes Repair Uptimes Repair

1 8.5 475 20, 30 47.5 2, 3

2 8.3 570 24, 36 57.0 2.4, 3.6

3 8.6 665 28, 42 66.5 2.8, 4.2

4 8.6 475 20, 30 47.5 2, 3

All times are in minutes

60

AIM:

To analysis a production system with minor and major failures, and to find percentage

time of each resource spent in failure state and number in each resource queue.

DATA GIVEN:

Inter arrival time (IAT) = EXPO (8) min

Replication Length = 10000min

Warm up time = 500min

Number of Replication = 3

Workstation

Number

Process

time

Major Failure

Means

Jam Means

Uptimes Repair Uptimes Repair

1 8.5 475 20, 30 47.5 2, 3

2 8.3 570 24, 36 57.0 2.4, 3.6

3 8.6 665 28, 42 66.5 2.8, 4.2

4 8.6 475 20, 30 47.5 2, 3

Table 3.1 major and minor failure rates with different process time

All times are in minutes

BASIC MODULE:

Create, Assign, Process, Record, Dispose

SPREAD SHEET MODULE:

Resource, State Set, Failure

PROCEDURE:

1 Drag and drop, create module from basic process

Type: Random [Expo8]

2 Double click on this module and make change in dialogue box

Name: arrival

Type: Expo (8)min

Click ok

3 Drag and drop assign module to the area double click assign and make

following updates

Name: system time

61

Value= tnow

4 Drag and drop the process boxes, double click and make the following

changes

Name: workstation 1,2,3,4 respectively

Action: Seize- Delay- Release

Delay type= Constant (min) 8.5, 8.3, 8.6, 8.6 respectively

5 Drag and drop record module, double click and make the following

changes on the dialogue box

Name: Total Time

Type: Time Interval

Attribute name: System Time

Click ok

6 Delay and drop dispose module from basic process

7 Change run setup to

No of replication=3

Warm up period= 500min

Replication length=1000min

8 Select Resource module

Enter work station name, State set name, failures for each work station.

Enter two failure name and two failure rules for each work station

Failure names are major failure and jam

Failure rules are preempt and wait.

9 Select state set module

Enter four different states for each work station.

State names are idle, busy, failure, jam

10 Select failure module

Enter up time and down time for both failure and jam of all work stations

MODEL DISCRIPTION

In this simulation , take inter arrival time as expo(8)minutes. The processing

time for work stations 1 ,2,3,4 are 8.5 minute ,8.3minutes,8.6 minutes,8.6 minutes

respectivly .select replication length as 10000 minutes and run by 3 replication,warm

up period is 500 minutes. Then the curresponding simulation model as shown below.

62

FIG .3.1.Model for analysis of a production system with 4 serial automatic

workstations

RESULTS & DISCUSSION

After simulating the model with inter arrival time expo (8) min, replication length

10000 minutes and number of replications are 3, the following results are obtained.

Failure StateWork Station

1Work Station 2 Work Station 3 Work Station 4

% Idle 0.066 2.36 0.833 1.13

% Busy 89.88 87.69 90.153 88.963

% Major

Failure5.43 5.033 4.373 5.46

% Jam 4.62 4.923 4.66 4.446

Number in

queue90.009 3.9713 6.8476 8.4332

Table 3.2.Production system with 4 serial automatic workstation including minor and

major failures

From this simulation, we get the percentages of idle , busy, major failure and jam for

work station 1 are0.066 ,89.88,5.43,and 4.62 respectively . The percentages of idle,

busy, major failure and jam for work station 2 are 2.36, 87.69, 5.033, and 4.923

respectively. The percentages of idle, busy, major failure and jam for work station 3

are 0.833, 90.153, 4.373, and 4.66 respectively. The percentages of idle, busy, major

failure and jam for work station 4 are 1.33, 88.963, 5.46, and 4.446 respectively. Also

got the number in queue for four work stations are 90.009, 3.9713, 6.8476, 8.4332.

63

GRAPHS:

From the above Table 3.2, we can represent the results in graphically.

1 2 3 40

1

2

3

4

5

6

1) WORK STATION VS FAILURE STATE

% idle

% m failure

% jam

Work Station

% F

ailu

re S

tate

Graph 3.1:-work station vs failure state

From this graph we can understood that percentage of idle for work station 1 is zero

and maximum at work station 2 .The variations in the percentage of jam for all work

stations are very less. Failure rate is very less at work station 3.

1 2 3 40

102030405060708090

100

2) QUEUE VS NUMBER IN QUEUE

no in queue

Queue

Nu

mb

er in

Qu

eue

Graph 3.2:-queue vs no in queue

64

From this graph we can understand that the number in queue is high for the first

queue ,after that the number in queue decreases for the second queue, after the second

queue the number in the queue gradually increases for the third and fourth queue.

INFERENCE

From the above two graphs we get an idea about the relationships between the

various failure rate and work stations .The rate of jam is almost same for all work

station, ie the difference for percentage of jam is very less. For ws1 and ws 2, we can

say that the percentages of idle are between two extremes. For queue 2, queue3, queue

4, the number in queue is very less compared to queue 1.

65

EXPERIMENT NO: 4

Model of an automobile license plate dispensing office with 3

independent arrival streams based on customer types

The office that dispenses automobile licenses plates have divided its

customer in two categories to level the work load. Customers arrive and enter one of

3 times based on their resident location. Model this arrival activity as three

independent arrival screens using an exponential inter arrival distribution with mean

10 minutes for each stream and an arrival at time zero for each stream. Each customer

type is assigned a single separate clerk to process, the application falls and accept

payment with a separate clerk to process the application falls and accept payment with

a separate queue for each. The service is UNIF(8,10) minutes for all customer types

after completion of this step all customers are sent to a single, second clerk who

checks the forms and issues the plates(this clerk serve all 3 customer type, who

merged in to a single first come, first serve queue for this clerk. The service time for

this activity is UNIF(2.66,3.33) minutes for all customer types.

Develop the model of the system and run for 50000 minutes. Observe the

average and maximum time in minutes. Observe the average and maximum time in

system for all customer types combined. Also observe the utilisation of each clerk .

The average waiting time in each queue and total throughput. Run model for three

replication. Show result in application.

The consultant has recommended that there is no need to differentiate

customer at the first stage and use a single line with clerks who can process any

customer type. Develop this model and run in for 5000 minutes and compare results

from those in first model.

66

AIM:

Develop a model of automatic license plate dispense office, where 3

independent arrival schema are present. Observe the average and maximum time in

system for all customer types combined. And also the same model with a single line

for 3 clerks and compare the two models.

DATA GIVEN:

Inter arrival time (IAT)=expo (10) minute

Process time(PT)=UNIF(8,10) minute for clerks 1,2,3

Process Time(PT) For clerk 4 = UNIF (2.66, 3.33)minute

BASIC MODULE:

Create, Assign, Record and Dispose

SPREADSHEET MODULE

Nil

PROCEDURE:

Case 1: Three independent arrival streams and three clerks.

1. Drag and drop 3 arrival modules.

Type: Random expo (10)

Entity type: Entity A, B, C for each arrival.

2. Drag and drop 3 assign variables.

Name: arrival time a, b, c

Add: attribute

Name: system time 1, 2, 3 respectively

New value: tnow

3. Drag and drop 3 process modules corresponding to each arrival and assign.

Name: Clerk 1, 2, 3 Delay type: uniform

Type: Standard unit: minutes

Action: Seize, delay, release minimum: 8

Resource type: resource maximum: 10

Resource name: c1, c2, c3

67

Quantity: 1

Click ok.

4. Drag and drop 4th process module

Name: clerk 4


Resource: c4

Delay type: UNIF (2.66, 3.33)

Value: minimum

5. Drag and drop record module

Name: total system time

Type: time interval

Attribute name: system name 1

6. Drag and drop dispose module and make changes

Name: dispose

Click ok

7. Save the model and run the setup.

Cick run – menu – check model

Do make changes if any error occur.

8. Click run – menu – go

Run set up menu

No of replications: 3

Warm up period: 5000

Replication length: 1000 min

Click ok.

Case 2: Single line model with clerk who can process any customer type.

1. Drag and drop create module.

Type: Random expo (10)

Entity type: Entity 1

68

2 Drag and drop assign variable.

Name: assign time a

Add: attribute

Name: attribute 1

3 Drag and drop process modules corresponding to each arrival and assign.

Name: For clerks Delay type: uniform

Type: Standard unit: minutes

Action: Seize, delay, release minimum: 8

Resource type: resource maximum: 10

Resource name: resource 1,resource 2, resource 3

Quantity: 1

4 Drag and drop 4th process module

Name: clerk 4


Resource: c4

Delay type: UNIF (2.66, 3.33)

Value: minimum

5. Drag and drop record module

Name: total system time

Type: time interval

Attribute name: system name

6. Drag and drop dispose module and make changes

Name: dispose

Click ok

7. Save the model and run the setup.

Cick run – menu – check model

Do make changes if any error occur.

8. Click run – menu – go

Run set up menu

No: of replications: 3

Warm up period: 5000

Replication length: 1000 mi

69

MODEL

In this simulation , take inter arrival time as expo(10). The processing time for

clerk 1 ,2,3, are UNIF(8,10) min and processing time for clerk 4 is UNIF( 2.66,3.33 )

min .select replication length as 10000 minutes and run by 3 replication,warm up

period is 500 minutes. Then the curresponding simulation model as shown below.

EXP 4.2

In this simulation , take inter arrival time as expo(10). The clerk 1 ,2,3, are set

sa a single clerk and processing time UNIF(8,10) min and processing time for clerk 4

is UNIF( 2.66,3.33 ) min .select replication length as 10000 minutes and run by 3

replication,warm up period is 500 minutes. Then the curresponding simulation model

as shown below.

RESULT and DISCUSSION

Experiment 4.1

After simulating the model with inter arrival time expo (10) minute, The

processing time UNIF(8,10) minute for both clerk 1 , 2,and 3rd and processing time for

clerk 4 is UNIF( 2.66,3.33 ) min,replication length 10000 minutes and number of

replications are 3, the following results are obtained.

70

Observed time in system

No Of

Replication

Total Time

1 1870

2 1862.13

3 1809.29

average 1847.13

Customers arrive and enter one of 3 times based on their resident location. Each

customer type is assigned a single separate clerk to process, and accept payment with

a separate clerk. The average observed time in system is 1847.13 The results of the

three replications are:

Experiment 4.2

After simulating the model with inter arrival time expo (10) minute, The

processing time UNIF(8,10) minute for the comman clerk and processing time for

clerk 4 is UNIF( 2.66,3.33 ) min,replication length 10000 minutes and number of

replications are 3, the following results are obtained.

Observed time in system

No Of

Replication

Total Time

1 48.121

2 34.447

3 33.551

average 38.706

Used a single line with clerks who can process any customer type, and accept

payment with a separate clerk. And The average observed time in system is: 38.7063

71

GRAPH

The graph is drawn from above information

1 2 317401760178018001820184018601880190019201940

Replication

Tim

e

Fig4.1 system time vs replication

The graph shows that two line clerks are sufficient to complete the work.

INFERENCE

From the above graphs we got an idea about the performance of the multiple

clerk line and single clerk line. The single clerk is performed very well so

Recommendation of the consultant can be implemented.

72

EXPERIMENT NO: 5

Analysis of an inventory packing system with schedule and four shipping agents and the system works for three 8 hours shifts for 4

weeks

Items arrive from an inventory picking system according to an exponential

inter arrival time, distribution with mean 1.1 minute. With the first arrival time

‘0’.Upon arrival the item are packed by one of four identical packers with single

queue feeding all four packers. The packing time is TRIA (2.75,3.3,4.0)

(min:2.75,most likely:3.3, max 4.0)min.The packed boxes are then separated by types

(20% international and 80% domestic) and send to shipping.

There is a single shipper (shipping agent) for international packages and two

agents for domestic packages with a single queue feeding the two domestic agents.

The international shipping agent time is TRIA (2.3,3.3, 4.8)min and domestic

shipping agent time is TRIA(1.7,2.0,2.7)min.

The packing system works three 8 hrs shifts, five days a week. All the packers

and shipping agents are given 15 min break 2 hrs into their shift. Run the simulation

for 4 weeks. Consider the first day as warm up period. Run the model 3 replication

and find out the throughput, percentage utilization of all resource and the average

number in each queue. Show the results graphically.

73

AIM

Model an inventory packing system with schedule and find out the throughput

time, percentage utilization of all resource and the average number in each queue.

Also show the results graphically.

DATA GIVEN

Inter Arrival Time (IAT): Expo (1.1) min

The processing time required for Packing: TRIA (2.75, 3.3, and 4.0) min

The international shipping agent processing time: TRIA (2.3, 3.3, 4.8) min

The Domestic shipping agent processing time: TRIA (1.7, 2.0, 2.7) min

The number of Replication: 3

The Replication length: 20 days

The Warm up period: 1 day

BASIC MODULES

Create, Assign, Process, Decision, Record, Dispose

SPREAD SHEET MODULE

Schedule

PROCEDURE

1.0 Drag and drop create module.

Name : Inventory picking station

Entity:1

Type: Random (Expo)

Value:1.1

Units: Minute

Entity per Arrival: 1

2.0 Drag and drop Assign module

Name: Assign time

Assignments: Attribute ,time, TNOW

74

OK

3.0 Drag and drop Process module

Name: Packing station

Logic: Seize Delay Release

Delay Type: Triangular

Units: Minutes


Units: Minutes

Value: Min:2.75, Most likely:3.3,Max:4

OK

4.0 Drag and drop Decide Module

Name: Separation

Type: 2 way by chance

Percent True:80%

OK

5.0 Drag and drop Process module

Name: Domestic

Action: S D R


Units: Minutes 1.7,2.0,2.7

OK

6.0 Drag and drop Record module

Name: Domestic rec

Type: Time Interval

Attribute Name: time

Tally Name: Domestic rec

OK

7.0 Drag and drop process module

Name: international

Action: S D R

Resource: agent 6


Unit: Min

75

Value: 2.3,3.3,4.8

OK

8.0 Drag and drop Record module

Name: international rec

Type: Time Interval

Attribute Name: time

Tally Name: International rec

OK

9.0 Drag and drop Dispose module

Name: disposed

10 Take the spread sheet module schedule from basic process and make the following

changes

Name: schedule 1

Type: capacity

Time units: quarter hours

Scale factor: 1

The schedule is assigned as three 8 hours shift per day for 20 days and 15 min break is

given in 2 hours

MODEL DESCRIPTION

The model for the inventory packing system with four shipping agents which

works on three 8 hours shift for 20 days and with inter arrival time is expo(1,1) is

given below. The model is run for 3 replication and first day is considered as

warmup period.

Fig.5.1 Model of an inventory packing system with 4 shipping agents

76

RESULT AND DISCUSSIONS

The experiment is run for 20 days and the number of replication is given as 3.The first

day is considered as warm up period

77

Replica

tion

Through

put time

% Utilization Average no in queue

Agnt

1

Agnt

2

Agnt

3

Agnt

4

Agnt 5 Agnt 6 Agnt

7

Domestic Packin

g stn

Inter national

1 169.30 1 1 1 1 1 .50951 .2082

7

0 9242.9 .00478

2 169.20 1 1 1 1 1 .50753 .2080

0

0 9264 .0053

3 170.98 1 1 1 1 1 .50416 .2137

4

0 9366.7 .00470

Avg 169.8266

67

1 1 1 1 1 .50706

667

.2100

0333

0 9291.2 .00492667

Table 5.1

The experiment is conducted with three replication. The throughput time

increased with the increase of replication number. The percentage utilization of the

first five agents remains same for all replications. After that for the sixth and seventh

agents the percentage utilization started varying. The average number in queue for

domestic agent is zero for all replication. The average number in queue for the

packing station increased with increase in replication number. The average number in

queue for the international agent changed with the replication number.

GRAPH

The graph is drawn from the above information

1 2 3168

168.5

169

169.5

170

170.5

171

171.5

Chart Title

Series1

Replication

Thr

ough

put t

ime

Fig 5.1 Replication vs Throughput time

The throughput time of the system increases when the replication number increases

from 1-3

78

1 2 391809200922092409260928093009320934093609380

Series1

Replication

packing station

No

in q

ueu

e

Fig 5.2. Replication vs no in queue (packing station)

In the packing station the number in queue increases as the replication number

increases from 1 to 3

1 2 30.0044

0.0045

0.0046

0.0047

0.0048

0.0049

0.005

0.0051

0.0052

0.0053

0.0054

Series1

Replication

International

No

in q

ueu

e

Fig 5.3.Replication vs no in queue (international)

The number in queue increases first when the replication number is increase from 1-2

and the decreases gradually when replication number is increased from 2-3

79

1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2utalization of agent

utalizat...% o

f u

tali

zati

on

Agents

Fig 5.4. Agents vs % utilization

The percentage utilization of agents remains same for the first three agents and after

that the percentage utilization decreases gradually

INFERENCE

From the above graphs we can infer that the throughput time of the

system increases with the increase of the replication number. The number in

queue of the packing station increases with the increase in the replication

number. The number in queue of the international agent increases for the first

two replication and then decreases for the third replication. The percentage

utilization remains same for the first three agents and it decreases gradually for

the remaining agents

80

Cycle 2 STUDY

Model the given Flexible manufacturing system and test the following hypothesis

`

To study the impact of uncertainties and the benefits of flexibilities a

Flexible Manufacturing System is studied by “Tabucanon” et al (1994), which

consists of 3 workstations, AGV (Automated guided vehicles) and various

loading and unloading stations. The following assumptions are made in this

experimental set up.

1) Each Workstation is continuously available for processing, ie, machine

breakdowns are not considered. Machines are never unable to perform a

required operation for lack of operator, tool or raw material. Each machine can

process one part at a time.

2) Pre-emption is not allowed

3) AVGs are continuously in operation without any breakdown. They carry

single load and follow shortest distance.

4) Setup times are small or negligible, due dates are not specified, batch type

arrival is not considered.

5) The performance measures studied in this set up are resource utilization

(machine utilization) as well as AGV utilization), time-in system (throughput)

time and output.

In this study the demand variability and the machine time uncertainty are modeled and

to respond to these uncertainties volume flexibility and machine flexibility are

considered. Experimental factors taken are Inter-arrival time, processing time, number

of AGVs, load/unload time, failure rate (down time of 4 minutes for a count rate of 50

units and part type).

The following are the hypothesis tested.

1) As demand uncertainty increases, machine utilization decreases.

2) Increase in load/unload time along with failure rate deteriorates time in

system performance.

81

3) Increase in the number of AGVs, increases the system performance

initially and the decreases it.

4) Under the variation in processing times, workstation is more sensitive than

the rest

( sensitivity analysis)

DATA GIVEN

Incremental Time: Norm (15, 0.001) min

To study the effect of demand uncertainty, IAT is varied with a co-

efficient of variance of 0.13, 0.26, 0.4, and 0.53 respectively.

Processing Time: Norm (15, 0.001) min

To check which machine has minimum impact, the processing time of

machine are made to vary with a co-efficient of variance of 0.13, 0.26, 0.4, and 0.53

respectively.

Load/Unload time:

To check the variation of performance with respect to load/unload

times, the load/unload times are increased from 1, 2,3,4,5 minutes.

No of AGVs:

To analyze the system performance with respect to number of AGVs,

the number is increased from 1,2,3,4 and 5 respectively.

Other parameters given are:

AGV velocity 20 meter/minute

Distance between each segment 10 meter

Replication Length 100000

Number of replication 1

Warm up time 500 minute

82

SYSTEM LAYOUT

Fig :- system layout

83

ws1

ws2

ws3

InOut

10m 10m

10m 10m

10m

EXPERIMENT 6

Effect of demand uncertainty Vs FMS performance

AIM:

Hypothesis tested: As demand uncertainty increases FMS system

performance decreases .

DATA GIVEN:

IAT-Normal (15, 0.001) with covariance 0.13, 0.26, 0.4, 0.53

PT-Normal (15, 0.001)

No loading/Unloading, No failure rate

Number of AGV-1

Part type-1

AGV Velocity-20m/min

Distance between each segment-10m

Replication length-1,00,000min,

Number of replication -1

Warm up period-500 min

BASIC MODULES:

Create(1),Assign(2),Process(9), Record(1),Dispose(1)

ADVANCED TRANSFER MODULES:

Enter(3),station(2),Request(4),Free(4),Transport(4)

SPREAD SHEET MODULES:

Nil

BASIC PROCESS/QUEUE

84

-Set Queue type as First in First Out

ADVANCED TRANSFER/DISTANCE-

Transporter1.Distance

Add 10 rows

No. Beginning station Ending station Distance

1 Arrive Dock Station1 20

2 Station1 Station2 20


4 Staion3 Exit shop 20



7 Arrive Dock Exit shop 30


9 Station1 Exit shop 30


Table:6.1 Distance between stations.

PROCEDURE:

1. Drag and drop Create module from basic process to the model area

Double click on it, make following entries

Name: Create part

Type: Expression/Norm (15,001)

Click ok

2. Drag and drop Assign module to the model area


Name: Assign job type

Add Attribute

Attribute Name-Entity. Type

New Value-ABS (1)

Click ok


85


Name: Time

Add Attribute

Attribute Name-aTime

New Value-tnow

Click ok

4. Drag and drop Station module from advanced transfer process to the model area


Name: Arrive station

Station Name: Arrive Dock

Click ok

5. Drag and drop Request module from advanced transfer process to the model area


Name: Request Truck

Transporter Name: Transporter1

Selection Rule: Smallest Distance

Priority: High

Velocity: 20m

Units: per minute

Click ok

6. Drag and drop Transport module from advanced transfer process to the model

area


Name: Transport to shop floor


Entity destination type: station

Station Name: Station1

Velocity: 20m

Units: per minute

Click ok

7. Drag and drop Enter module from advanced transfer process to the model area


Name: Entry to station1

Station type: station

86


Units: Hours

Click ok

8. Drag and drop Free module from advanced transfer process to the model area


Name: Free Truck at station1


Click ok

9. Drag and drop Process module from basic process to the model area


Name: Loading Zone1

Type: Standard

Action: Delay

Delay Type: Constant; Units: Minutes; Value: 0

Click ok



Name: Operation1

Type: Standard

Action: Seize Delay Release

Priority: Medium

Add Resources; Resource; Name: Resource1; Quantity: 1

Delay Type: Normal; Units: Minutes; Value:0

Value:15 ;Standard Deviation: 0.001

Click ok



Name: Unloading Zone1

Type: Standard

Action: Delay


Click ok

12. Drag and drop Request module from advanced transfer process to the model

area

87


Name: Request Truck at station1



Priority: High

Velocity: 20m

Units: per minute

Click ok


area


Name: Transport from station1



Station Name: Station 2

Velocity: 20m

Units: per minute

Click ok



Name: Entry station2



Units: Hours

Click ok



Name: Free truck at staion2


Click ok



Name: Loading Zone2

Type: Standard

88

Action: Delay


Click ok



Name: Operation2

Type: Standard


Priority: Medium


Delay Type: Normal; Units: Minutes; Value: 0

Value: 15; Standard Deviation: 0.001

Click ok




Type: Standard

Action: Delay


Click ok


area





Priority: High

Velocity: 20m

Units: per minute

Click ok


area



89




Velocity: 20m

Units: per minute

Click ok






Units: Hours

Click ok





Click ok



Name: Loading Zone3

Type: Standard

Action: Delay


Click ok



Name: Operation3

Type: Standard


Priority: Medium




90

Click ok




Type: Standard

Action: Delay


Click ok


area





Priority: High

Velocity: 20m

Units: per minute

Click ok


area





Station Name: exit shop

Velocity: 20m

Units: per minute

Click ok



Name: Exit


Click ok


91


Name: Free Truck at exit


Click ok

30. Drag and drop Record module from basic process to the model area


Name: total time

Type: Time Interval

Attribute Name: aTime

Click ok

31. Drag and drop Dispose module from basic process to the model area


Name: Dispose

Click ok

32. To study the effect of demand uncertainty, IAT is varied with a co-efficient of

variance of 0.13, 0.26, 0.4, and 0.53 respectively.

Make the following changes in the create module in step 1 for different co variances.

The standard deviations change to 0.2, 0.4, 0.6, and 0.8 respectively.

MODEL DESCRIPTION

There are 3 machines and one AGV.IAT Normal (15,0.001)with covariance

0.13,0.26,0.4,0.53 and processing time is kept as Normal(15,0.001) and

corresponding machine utilization, output and throughput time for the three

machines and AGV, are to be found out.

Fig:6.1 Simulation model of demand uncertainty Vs FMS.

92

RESULT AND DISCUSSION:

According to the given data the replication length is set as 1,00,000 minute and for a

warm up period of 500 minute for 5 different IAT( Normal(15,001),Normal

(15,2),Normal(15,4),Normal(15,6),Normal(15,8)) . The utilizations, output in

numbers and throughput time for the three machines and AGV are obtained as given

in the table below.

No

.

IAT Utilization Output(n

o.)

Throughp

ut

Time(min

)

Machine

1

Machine

2

Machin

e3

AGV

1 Normal(15,.0

01)

1 1 1 .3999 6634 51.136

2 Normal(15,2) .99653 .99653 .99653 .48169 6610 90.198

3 Normal(15,4) .99172 .99173 .99173 .48247 6578 124.09

4 Normal(15,6) .99113 .99113 .99111 .49117 6574 119.77

5 Normal(15,8) .98124 .98124 .98120 .49780 6509 154.17

Table 6.2 :- Performance variation with respect to inter arrival time variation

From the above results it is found that machine utilization should not have

significant variation for same IATs. When IAT are changing from

Normal(15,.001) to Normal (15,8) the machine utilization decreases,output decreases

and throughput time increases.

From the above results the graphs are drawn for

1. IAT Vs Output

2. IAT Vs Machine utilization

3. IAT Vs Throughput time

4. IAT Vs AGV utilization.

93

Norm(15,.0

01)

Norm(15,2)

Norm(15,4)

Norm(15,6)

Norm(15,8)

6400

6500

6600

IAT Vs OUTPUT

OUTPUT

IAT

OUT

PUT

Fig 6.1:- Inter arrival time vs output.

From the above graph it is understood that according to the changes in Inter arrival

time the output decreases.

.

Norm(15,.0

01)

Norm(15,2)

Norm(15,4)

Norm(15,6)

Norm(15,8)

0.97

0.985

1

IAT Vs MACHINE UTILAZTION

Machine1Machine2Machine3

IAT

MAC

HIN

E UT

ILIZA

TIO

N

Fig 6.2 :- Inter arrival time vs machine utilization

From the above graph it is understood that according to the changes in Inter arrival

time the machine utilization decreases

Norm(15,.00

1)

Norm(15,2)

Norm(15,4)

Norm(15,6)

Norm(15,8)

050

100150200

IAT Vs THROUGHPUT TIME

THROUGHPUT TIME

IAT

THRO

UGHP

UT T

IME

Fig 6.3 :- Inter arrival time vs throughput time

94

From the above graph it is observed that the throughput time increases with increase

of IAT.

Norm(15,.00

1)

Norm(15,2)

Norm(15,4)

Norm(15,6)

Norm(15,8)

00.10.20.30.40.50.6

IAT Vs AGV Utilization

AGV Utilization

IAT

AGV

Utiliz

ation

Fig 6.4:- inter arrival time vs AGV utilization

From the above graph change in AGV utilization is significantly small with

increase of IAT.

INFERENCES:

From the above results it is found that machine utilization should not

have significant variation for same IATs. When IAT are changing from

Normal(15,.001) to Normal (15,8) the machine utilization decreases, output

decreases and throughput time increases. So we can say the Hypothesis is

accepted.

95

EXPERIMENT NO: 7

A set of load/unload time with and without failure rate Vs FMS

performance

AIM

Hypothesis Tested: Increase load \unload time along with failure rate

deteriorates time in system performance.

DATA GIVEN:

Inter arrival time: Norm (15, 8) min

Processing Time: Norm (15, 8) min

Part type: 1

No of AGVs: 1

Loading \unloading time: 1, 2,3,4,5 min

Failure rate: 4 min for 50 units

BASIC MODULES:

Create (1), Assign (2), Process (9), Record (1), and Dispose (1)


Enter (3), station (2), Request (4), Free (4), Transport (4)

BASIC PROCESS/QUEUE


96



Add 10 rows












Table 7.1 Distance between stations

PROCEDURE:



Name: Create part

Type: Expression/Norm (15, 8)

Click ok




Add Attribute


New Value-ABS (1)

Click ok



Name: Time

97

Add Attribute


New Value-tnow

Click ok





Click ok



Name: Request Truck



Priority: High

Velocity: 20m

Units: per minute

Click ok


area





Velocity: 20m

Units: per minute

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Name: Loading Zone1

Type: Standard

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Name: Operation1

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Value:15 ;Standard Deviation: 8

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Name: Free truck at staion 2


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Name: Loading Zone2

Type: Standard

Action: Delay


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Name: Operation2

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Priority: Medium



Value: 15; Standard Deviation: 8

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Click ok






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Action: Delay


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Name: Exit


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103


Name: total time

Type: Time Interval


Click ok



Name: Dispose

32 . Click on ‘Loading zone 1’ and change value to 1, 2, 3, 4, and 5 respectively for

each run. Click on ‘Loading zone 2’ and change value to 1, 2, 3, 4, and 5 respectively

for each run. Click on ‘Loading zone 3’ and change value to 1, 2, 3, 4, and 5

respectively for each run. Click on ‘Unloading zone 1’ and change value to 1, 2, 3, 4,

and 5 respectively for each run. Click on ‘Unloading zone 2’ and change value to 1,

2, 3, 4, and 5 respectively for each run.

Note the system time for each run.

33 Select Spread sheet module from advanced process.

Double click on it and Set failure type as time. Set time as 4 min for 50 units

34 Click on ‘Loading zone 1’ and change value to 1, 2, 3, 4, and 5 respectively for

each run. Click on ‘Loading zone 2’ and change value to 1, 2, 3, 4, and 5 respectively

for each run. Click on ‘Loading zone 3’ and change value to 1, 2, 3, 4, and 5

respectively for each run. Click on ‘Unloading zone 1’ and change value to 1, 2, 3, 4,

and 5 respectively for each run. Click on ‘Unloading zone 2’ and change value to 1,

2, 3, 4, and 5 respectively for each run.

Note the system time for each run.

104

MODEL DESCRIPTION

Model created in AREA based on the above procedure. In this model, loading &

unloading time is initially set as one and it is increased to two, three, four and five

respectively for each run of the model. There are 4 loading and unloading modules in

this model and time is varied in each of them separately for each run.

Figure 7.1 Simulation model for checking the effect of changing the load/unload time

with and without failure rate on FMS performance

RESULT AND DISCUSSION

In the experiment, the loading and unloading time is 1, 2, 3, 4 and 5 minutes for 3

loading module and 3 unloading modules. The time in system are noted from the

output sheets after running the simulation model by including failure rate and without

failure rate.

105

Load/Unload time

Time in System

With Failure Without Failure

1 327.59 57.136

2 335.99 66.121

3 342.89 75.032

4 354.89 81.544

5 359.44 95.999

Table 7.2 Performance variation with respect to load/unload time variation

From the above observed data, it can be seen that, as the loading and unloading time

are increased from one to five, system time is increasing steadily. That means system

performance is deteriorating as the loading and unloading time is increasing. Without

failure, the system time are much less compared to that of the system time with

failure. Even in the case of system time without failure, it is observed that system time

is increasing steadily as the loading and unloading time is increased, which shows that

with or without failure, system performance deteriorates with increase in load and

unloading time.

GRAPH

Graph is drawn on system time against load/unloading time. System time with

failure and without failure against each of the load / unload time is plotted.

1 2 3 4 50

50100150200250300350400450500

with out failure

with failure

load / unload time

syst

em

tim

e

Figure 7.1System time v/s Load/unload time

106

The graph of system time with and without failure shows that, the system time with

failure is much higher compared to that of without failure

INFERENCE

From the experiment it can be seen that as the loading and unloading

time is steadily increased, the total time taken in the system also increases

proportionately. This experiment shows that as the loading and unloading time

is increased, system performance is degrading gradually. The graph of system

time with and without failure shows that, the system time with failure is much

higher compared to that of without failure. So it is clear that, failures are

causing high deterioration of performance of the system. With failure and

without failure, as the load and unload time is varied, system time is increasing

accordingly which menas system performance is deteriorating accordingly.

107

EXPERIMENT NO: 8

Effect of number of AGV’s on FMS performance

AIM

Hypothesis Tested: Increase in the number of AGVs increases the

system performance initially and then decreases it.

DATA GIVEN:

Inter arrival time: Norm (15, 8) minute

Processing Time: Norm (15, 8) minute

No loading \unloading time

Part type: 1

No of AGVs: 1, 2, 3,4,5,6

BASIC MODULES:




BASIC PROCESS/QUEUE


SPREAD SHEET MODULE: ADVANCED TRANSFER/DISTANCE-


Add 10 rows












Table 8.1Distance between stations

108

PROCEDURE:



Name: Create part


Click ok




Add Attribute


New Value-ABS (1)

Click ok



Name: Time

Add Attribute


New Value-tnow

Click ok





Click ok



Name: Request Truck



Priority: High

Velocity: 20m

109

Units: per minute

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area






Velocity: 20m

Units: per minute

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Units: Hours

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Name: Loading Zone1

Type: Standard

Action: Delay


Click ok



Name: Operation1

110

Type: Standard


Priority: Medium



Value:15 ;Standard Deviation: 8

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Type: Standard

Action: Delay


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area





Priority: High

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Units: per minute

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Units: Hours

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Name: Loading Zone2

Type: Standard

Action: Delay


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Name: Operation2

Type: Standard


Priority: Medium




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Type: Standard

Action: Delay


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113


Name: Loading Zone3

Type: Standard

Action: Delay


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Name: Operation3

Type: Standard


Priority: Medium




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Type: Standard

Action: Delay


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area





Priority: High

Velocity: 20m

Units: per minute

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114


area






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Units: per minute

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Name: Exit


Click ok





Click ok



Name: total time

Type: Time Interval


Click ok



Name: Dispose

32 Select “Transporter” module from “Advanced Transfer” and change “number

of units” to 1, 2, and 3,4,5,6 respectively

115

MODEL DESCRIPTION

Model created in AREA based on the above procedure. Here in this model the number

of transporter is initially set as one. The number of AGV varied to2, 3, 4, 5 and 6. To

get variation in model performance the processing time is set as Norm (15, 8).

Figure 6.1 Simulation model for checking the effect of number of AGV on system

performance


In the experiment the number of AGV is varied as 1, 2, 3, 4, 5 and 6. The utilization

of the three machines M1, M2, M3, AGV utilization, output, throughput time are

noted from the output sheets after running the simulation model.

No of

AGVs

System Utilization AGV

UtilizationOutput

Throughput

TimeM1 M2 M3

1 .98862 .98564 .98468 .55195 6483.0 731.00

2 .99548 .98581 .99359 .25936 6512.0 815.06

3 .99940 .98918 .98757 .16402 6483.0 1069.2

4 .99940 .98917 .98984 .12189 6470.0 1348.5

5 .99413 .99260 .98768 .09751 6480.0 811.25

116

6 .99940 .98917 .98984 .08118 6470.0 1348.5

From the above observation it can be seen that, the number of AGV are increased

from one to six. Utilization of M1 machine is increasing with number of AGV s and

then become steady at 3 AGV’s. The utilization of machine M2 and M3 also increases

initially and then decreases. With increase in number of AGV’s, the utilization is

decreasing. Maximum output is corresponding to two AGV’s, only slight variation in

output for other cases. Throughput time increase with increase in number of AGV’s,

but record a sudden decrease when number of AGV is five.

It can be concluded that the test hypothesis can be accepted, i.e. Increase in number of

AGV’s initially increase system performance and then decreases it.

GRAPH:

The following graphs are drawn based on the data obtained from experiment.

1. Number of AGV v/s Machine utilization

2. Number of AGV v/s AGV utilization

3. Number of AGV v/s Output

4. Number of AGV v/s Throughput time.

From above graph, it can be seen that machine utilization initially increases and

shows decreasing trend with increase in number of AGV’s. Machine M1, M2, M3

achieve the maximum utilization corresponding to 3, 5, 2 no. of AGV’s.

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6No. of AGV v/s AGV Utilization

AGV

Util

izati

on

No.of AGV's

Figure 8.1 No. of AGV v/s AGV Utilization

AGV utilization shows a downward trend with increase in number of AGV’s as per

the graph above.

117

Table 8.2 Performance variation with respect to no. of AGV’s

1 2 3 4 5 60

200

400

600

800

1000

1200

1400

1600

No. of AGV v/s Throghput time

Thro

ugh

Put T

ime

No.of AGV's

Figure8.2 No. of AGV v/s Throghput time

Throughput time shows fluctuation with variation in nuber of AGV’s, it inially

increaes , reaches a maximum value and then decreses. It again shows postive trend

with further increase in number of AGV’s. AGV utilization is maximum at 4 and 6

no. of AGV’s.

1 2 3 4 5 66440

6450

6460

6470

6480

6490

6500

6510

6520 No. of AGV v/s Output

No.of AGV's

Out

put

Figure8.3 No. of AGV vs. Output

The output varies slightly with the increase in number of AGV’s. The trend is to

increase initially, then to decrease. The maximum output corresponds to 2 AGV’s.

118

INFERENCE

From the simulation it can be seen that the increase in performance of

the system is small compared to the decrease in AGV utilization with respect

to the variation in no. of AGV’s. The AGV utilization continually shows a

down ward trend. Here the test considers the AGV’s without specifying the

route or variation in speed. Also the loading/unloading time assumed to be

zero. But practical situations may be different from the assumed. As the

uncertainties in processing time and inter arrival time increases, the effect of

no. of AGV on utilization of resources also increase. To account that effect

here both the time are considered as Norm (15, 8) instead of Norm (15, .001)

in other experiments.

119

EXPERIMENT NO: 9

Sensitivity analysis

AIM:

Hypothesis test –under the variations in process time workstation 1 is

more sensitive than the rest. (Sensitivity Analysis)

DATA GIVEN:

Interarrival time (IAT) Norm (15, 8) min

Processing time (PT) Norm (15, 8) and to check which machine has

maximum impact on processing time when the coefficient of variations are 0.13, 0.26,

0.40 and 0.50.

No loading or unloading time or failure time.

Number of variability 1

Part Type 1

Number of replication 1

BASIC MODULES:




SPREAD SHEET MODULES:

Nil

BASIC PROCESS/QUEUE


120



Add 10 rows












Table 9.1 Distance between stations

PROCEDURE:



Name: Create part


Click ok




Add Attribute


New Value-ABS (1)

Click ok



Name: Time

121

Add Attribute

Attribute Name-a Time

New Value-tnow

Click ok





Click ok



Name: Request Truck



Priority: High

Velocity: 20m

Units: per minute

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area






Velocity: 20m

Units: per minute

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Units: Hours

122

Click ok





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Name: Loading Zone1

Type: Standard

Action: Delay


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Name: Operation1

Type: Standard


Priority: Medium




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Type: Standard

Action: Delay


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123



Priority: High

Velocity: 20m

Units: per minute

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Velocity: 20m

Units: per minute

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Units: Hours

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Name: Loading Zone2

Type: Standard

Action: Delay


124

Click ok



Name: Operation2

Type: Standard


Priority: Medium




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Type: Standard

Action: Delay


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area





Priority: High

Velocity: 20m

Units: per minute

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125


Velocity: 20m

Units: per minute

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Units: Hours

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Name: Loading Zone3

Type: Standard

Action: Delay


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Name: Operation3

Type: Standard


Priority: Medium




Click ok


126

Type: Standard

Action: Delay


Click ok


area





Priority: High

Velocity: 20m

Units: per minute

Click ok


area





Velocity: 20m

Units: per minute

Click ok



Name: Exit


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127


Name: total time

Type: Time Interval


Click ok



Name: Dispose

32 Processing time of machines are varied according to the co variances 0.13, 0.26,

0.40 and 0.50

33 Calculate the standard deviation corresponding to the covariance using the

equation co variance = Standard deviation/mean

=σ/µ

34 Vary the processing time of the three machines and find the machine utilization.

MODEL DESCRIPTION

There are 3 machines and coefficients of variances are given 0.13,

0.26, 0.40 and 0.50. Processing time is varied from norm(15,0) norm(15,2)

norm(15,4) norm(15,6) norm(15,8). For each machine m1, m2, m3 the

processing time is kept constant and corresponding machine utilization is

found out.

Fig 1.1:- Model of sensitivity analysis

128


When the processing time was varied for each machine the machine utilizations of

three machines are as shown:

Processing Time(PT)

Variation of PT ofMachine 1



M1 M2 M3 M1 M2 M3 M1 M2 M3Norm(15,0) 1.000

0 1.0000 1.0000 1.000

01.0000 1.0000 1.0000 1.0000 1.0000

Norm(15,2) .99984

.99633 .99632 .99999

.99827 .99723 .99998 .99996 .99987

Norm(15,4) .99942

.99603 .99603 .99998

.99901 .99420 .99997 .99996 .99805

Norm(15,6) .99753

.99544 .99540 .99999

.99968 .98871 .99998 .99996 .99582

Norm(15,8) .99701

.98543 .98542 .99998

.99799 .99333 .99997 .99994 .99801

In the first case the processing time of machine 1 is varied keeping processing time of

in machines 2 and 3 constant norm (15, 0). It is observed that as the uncertaninty in

process time increases the utilization of machines decreases. Also it is observed that

there is a variation in the degree of utilization when we increase the probability in

processing time of each machine corresponding to the variation in the utilization when

we increase the probability in processing time of each machine corresponding to the

variation in utilization when we increase the probability in processing time of the next

subsequent machines and so on.

GRAPH

Graph is the machine utilization with respect to the variation in process time and

machine 1 is as shown below:

129

Fig 1.1 Graph showing variation in processing time of machine1

In first graph, there is slight variation machine utilization for machine 1and it

maintains the same value at norm (15, 8), in machine 2 the utilization decreases as it

reaches norm (15, 8 ) And in machine 3 it maintains the same value throughout.

Graph is the machine utilization with respect to variation in processing time and

machine 2 is as shown in figure :


130

In the second graph, machine 1 maintains the same value throughout, in machine 2

there is slight variation at norm (15, 8) and in machine 3 there is variation from norm

(15, 2) to norm (15,8).

Graph shown is the machine utilization with respect to variation in processing time and machine 3 is as shown in figure:

Norm(15,0) Norm(15,2) Norm(15,4) Norm(15,6) Norm(15,8)0.9820.9840.9860.988

0.990.9920.9940.9960.998

11.002

VARIATION IN PROCESSING TIME OF MACHINE3

PT

MAC

NIN

E UT

ILISA

TIO

N


In the third graph,, machine 1 maintains the same value throughout, in machine 2

variation takes place at norm(15,8) and in machine 3 variation is at norm(15,6).

INFERENCE :

From the simulation it is seen that while we vary the processing time of machine 1

from N(15,0)to N(15,8) the machine utilization of 2 and 3 varies drastically compared

to variation of machines 1 and 3. Similarly when we vary the processing time of

machines 2 and 3 there is not much drastic change. So it is evident that machine 1 is

more sensitive than 2 and 3.

131

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