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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:
1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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:
9
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).
10
11
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,
12
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
13
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 .
14
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
15
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:
16
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:
17
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
18
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.
19
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
20
Density function of the Cont({(0.3, 0, 3), (0.2, 3, 4), (0.5, 4, 8)}) distribution
3.11.3 TRIANGULAR DISTRIBUTION
The corresponding mean and variance are given by the formulas
Density function of the Tria(5, 7, 10) distribution.
21
3.11.3 EXPONENTIAL DISTRIBUTION
and the cdf is
The corresponding mean and variance are given by the formulas
3.11.4 NORMAL DISTRIBUTION
The corresponding mean and variance are given by the formulas
Density function of the Norm(0,1) distribution.
22
3.11.5 LOGNORMAL DISTRIBUTION
3.11.6 GAMMA DISTRIBUTION
Mean and variance are
23
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
24
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.
25
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
26
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.
27
3.12.4 GENERATION OF STEP VARIATES FROM HISTOGRAMS
28
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
29
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
30
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.
31
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
Attribute name: arrival time
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)
EXPERIMENT MODEL -1.2
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
EXPERIMENT MODEL -1.3
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).
EXPERIMENT MODEL -1.4
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
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 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
Table 1.3 Avg no in queue and total time in system for model 1.3
44
From this simulation we get the average number in queue for first process as
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:
Average No In Queue Total Time In
System (min)Process 1
(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
Table 1.3 Avg no in queue and total time in system for model 1.3
From this simulation we get the average number in queue for first process as
4.0673 ,the average number in queue for 2nd process as 0.00 and also the total
time for the entire system is 57.645 minutes.
EXPERIMENT 1.4
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
0 0 18
Replication 2
0 0 18
Replication 3 0 0 18
Average 0 0 18
Table 1.4 Avg no in queue and total time in system for model 1.4
45
From this simulation we get the average number in queue for first process as
0.00 ,the average number in queue for 2nd process as 0.00 and also the total
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
Action: seize delay release
Add Resource: Resource1.2
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
Action: seize delay release
Add Resource: Resource1.3
Delay type: CONST
Unit: minutes
Value: 11
Click OK
9 Drag and drop decide module ,double click on it enter data
Name: Rework at workstation 3
Type: two way by chance
If true: workstation 4 and if false workstation 2
10 Drag and drop 4th process module ,double click on it enter data
Name: workstation4
Action: seize delay release
Add Resource: Resource1.4
Delay type: CONST
Unit: minutes
50
Value: 11
Click OK
11 Drag and drop decide module ,double click on it enter data
Name: Rework at workstation 4
Type: two way by chance
If true: workstation 5 and if false workstation 3
12 Drag and drop 5th process module ,double click on it enter data
Name: workstation 5
Action: seize delay release
Add Resource: Resource1.5
Delay type: CONST
Unit: minutes
Value: 12
Click OK
13 Drag and drop decide module ,double click on it enter data
Name: Rework at workstation 4
Type: two way by chance
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
Attribute name: arrival time
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
For Analysis of a production system with 5 serial automatic work stations and part
re processing with probability of re-visit at 6%, 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.
52
Fig.2.2 Model with probability of revisit at 6 %
Case 3
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.2.3 Model with probability of revisit at 7 %
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
Fig.2.4 Model with probability of revisit at 8 %
Case 5
For Analysis of a production system with 5 serial automatic work stations and part
re processing with probability of re-visit at 9%, 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.2.5 Model with probability of revisit at 9%
54
Case 6
For Analysis of a production system with 5 serial automatic work stations and part
re processing with probability of re-visit at 10%, 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.2.6 Model with probability of revisit at 10 %
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
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 78.11
2 78.89
3 78.11
Table 2.2 Probability of rework at 6%
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
When probability of rework is 7%, 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.
56
No Of
Replication
Total Time
(minutes)
1 87.01
2 88.01
3 86.77
Table2.3 Probability of rework at 7%
For first replication total time is 87.01 minutes, for second replication total time is
88.01 minutes and for third replication total time is 86.77 minutes and Average Total
cycle time = 87.76 minutes.
Case 4
When probability of rework is 8%, 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)
1 102.01
2 102.89
3 102.23
Table 2.4 Probability of rework at 8%
For first replication total time is 102.01 minutes, for second replication total time is
102.89 minutes and for third replication total time is 102.23 minutes and Average
Total cycle time=102.107 minutes.
57
Case 5
When probability of rework is 9%, 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)
1 119.11
2 118.89
3 117.56
Table 2.5 Probability of rework at 9%
For first replication total time is 119.11 minutes, for second replication total time is
118.89 minutes and for third replication total time is 117.56 minutes and Average
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
Table 2.6 Probability of rework at 10%
For first replication total time is 168.01 minutes, for second replication total time is
168.89 minutes and for third replication total time is 169.11 minutes and Average
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
Action: seize, delay, release
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
Action: seize, delay, release
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
Delay Type: Triangular
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
Delay Type: Triangular
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
Delay Type: Triangular
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
3 Station2 Station3 30
4 Staion3 Exit shop 20
5 Arrive Dock Station2 20
6 Arrive Dock Station3 30
7 Arrive Dock Exit shop 30
8 Station1 Station3 30
9 Station1 Exit shop 30
10 Station2 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
Double click on it, make following entries
Name: Assign job type
Add Attribute
Attribute Name-Entity. Type
New Value-ABS (1)
Click ok
3. Drag and drop Assign module to the model area
85
Double click on it, make following entries
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
Double click on it, make following entries
Name: Arrive station
Station Name: Arrive Dock
Click ok
5. Drag and drop Request module from advanced transfer process to the model area
Double click on it, make following entries
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
Double click on it, make following entries
Name: Transport to shop floor
Transporter Name: Transporter1
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
Double click on it, make following entries
Name: Entry to station1
Station type: station
86
Station Name: Station1
Units: Hours
Click ok
8. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at station1
Transporter Name: Transporter1
Click ok
9. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
10. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
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
11. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
12. Drag and drop Request module from advanced transfer process to the model
area
87
Double click on it, make following entries
Name: Request Truck at station1
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
13. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station1
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 2
Velocity: 20m
Units: per minute
Click ok
14. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry station2
Station type: station
Station Name: Station2
Units: Hours
Click ok
15. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion2
Transporter Name: Transporter1
Click ok
16. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone2
Type: Standard
88
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
17. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation2
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource2; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 0.001
Click ok
18. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
19. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station2
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
20. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station2
89
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 3
Velocity: 20m
Units: per minute
Click ok
21. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry to station3
Station type: station
Station Name: Station3
Units: Hours
Click ok
22. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion3
Transporter Name: Transporter1
Click ok
23. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
24. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation3
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource3; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 0.001
90
Click ok
25. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
26. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station3
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
27. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station3
Transporter Name: Transporter1
Entity destination type: station
Station Name: exit shop
Velocity: 20m
Units: per minute
Click ok
28. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Exit
Station Name: exit shop
Click ok
29. Drag and drop Free module from advanced transfer process to the model area
91
Double click on it, make following entries
Name: Free Truck at exit
Transporter Name: Transporter1
Click ok
30. Drag and drop Record module from basic process to the model area
Double click on it, make following entries
Name: total time
Type: Time Interval
Attribute Name: aTime
Click ok
31. Drag and drop Dispose module from basic process to the model area
Double click on it, make following entries
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)
ADVANCED TRANSFER MODULES:
Enter (3), station (2), Request (4), Free (4), Transport (4)
BASIC PROCESS/QUEUE
-Set Queue type as First in First Out
96
ADVANCED TRANSFER/DISTANCE-
Transporter1.Distance
Add 10 rows
No. Beginning station Ending station Distance
1 Arrive Dock Station1 20
2 Station1 Station2 20
3 Station2 Station3 30
4 Staion3 Exit shop 20
5 Arrive Dock Station2 20
6 Arrive Dock Station3 30
7 Arrive Dock Exit shop 30
8 Station1 Station3 30
9 Station1 Exit shop 30
10 Station2 Exit shop 30
Table 7.1 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, 8)
Click ok
2. Drag and drop Assign module to the model area
Double click on it, make following entries
Name: Assign job type
Add Attribute
Attribute Name-Entity. Type
New Value-ABS (1)
Click ok
3. Drag and drop Assign module to the model area
Double click on it, make following entries
Name: Time
97
Add Attribute
Attribute Name-aTime
New Value-tnow
Click ok
4. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Arrive station
Station Name: Arrive Dock
Click ok
5. Drag and drop Request module from advanced transfer process to the model area
Double click on it, make following entries
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
Transporter Name: Transporter1
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
Station Name: Station1
Units: Hours
Click ok
8. Drag and drop Free module from advanced transfer process to the model area
98
Name: Free Truck at station1
Transporter Name: Transporter1
Click ok
9. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
10. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
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: 8
Click ok
11. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
12. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station1
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
99
Velocity: 20m
Units: per minute
Click ok
13. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station1
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 2
Velocity: 20m
Units: per minute
Click ok
14. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry station2
Station type: station
Station Name: Station2
Units: Hours
Click ok
15. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion 2
Transporter Name: Transporter1
Click ok
16. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
17. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
100
Name: Operation2
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource2; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 8
Click ok
18. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
19. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station2
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
20. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station2
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 3
Velocity: 20m
Units: per minute
101
Click ok
21. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry to station3
Station type: station
Station Name: Station3
Units: Hours
Click ok
22. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion3
Transporter Name: Transporter1
Click ok
23. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
24. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation3
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource3; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 8
Click ok
25. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone3
Type: Standard
102
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
26. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station3
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
27. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station3
Transporter Name: Transporter1
Entity destination type: station
Station Name: exit shop
Velocity: 20m
Units: per minute
Click ok
28. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Exit
Station Name: exit shop
Click ok
29. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at exit
Transporter Name: Transporter1
Click ok
30. Drag and drop Record module from basic process to the model area
103
Double click on it, make following entries
Name: total time
Type: Time Interval
Attribute Name: aTime
Click ok
31. Drag and drop Dispose module from basic process to the model area
Double click on it, make following entries
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:
Create (1), Assign (2), Process (9), Record (1), and Dispose (1)
ADVANCED TRANSFER MODULES:
Enter (3), station (2), Request (4), Free (4), Transport (4)
BASIC PROCESS/QUEUE
-Set Queue type as First in First Out
SPREAD SHEET MODULE: ADVANCED TRANSFER/DISTANCE-
Transporter1.Distance
Add 10 rows
No. Beginning station Ending station Distance
1 Arrive Dock Station1 20
2 Station1 Station2 20
3 Station2 Station3 30
4 Staion3 Exit shop 20
5 Arrive Dock Station2 20
6 Arrive Dock Station3 30
7 Arrive Dock Exit shop 30
8 Station1 Station3 30
9 Station1 Exit shop 30
10 Station2 Exit shop 30
Table 8.1Distance between stations
108
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 (15,8)
Click ok
2. Drag and drop Assign module to the model area
Double click on it, make following entries
Name: Assign job type
Add Attribute
Attribute Name-Entity. Type
New Value-ABS (1)
Click ok
3. Drag and drop Assign module to the model area
Double click on it, make following entries
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
Double click on it, make following entries
Name: Arrive station
Station Name: Arrive Dock
Click ok
5. Drag and drop Request module from advanced transfer process to the model area
Double click on it, make following entries
Name: Request Truck
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
109
Units: per minute
Click ok
6. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport to shop floor
Transporter Name: Transporter1
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
Double click on it, make following entries
Name: Entry to station1
Station type: station
Station Name: Station1
Units: Hours
Click ok
8. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at station1
Transporter Name: Transporter1
Click ok
9. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
10. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation1
110
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: 8
Click ok
11. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
12. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station1
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
13. Drag and drop Transport module from advanced transfer process to the model
area
Name: Transport from station1
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 2
Velocity: 20m
Units: per minute
Click ok
14. Drag and drop Enter module from advanced transfer process to the model area
111
Double click on it, make following entries
Name: Entry station2
Station type: station
Station Name: Station2
Units: Hours
Click ok
15. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion2
Transporter Name: Transporter1
Click ok
16. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
17. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation2
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource2; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 8
Click ok
18. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
112
Click ok
19. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station2
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
20. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station2
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 3
Velocity: 20m
Units: per minute
Click ok
21. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry to station3
Station type: station
Station Name: Station3
Units: Hours
Click ok
22. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion3
Transporter Name: Transporter1
Click ok
23. Drag and drop Process module from basic process to the model area
113
Double click on it, make following entries
Name: Loading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
24. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation3
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource3; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 8
Click ok
25. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
26. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station3
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
114
27. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station3
Transporter Name: Transporter1
Entity destination type: station
Station Name: exit shop
Velocity: 20m
Units: per minute
Click ok
28. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Exit
Station Name: exit shop
Click ok
29. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at exit
Transporter Name: Transporter1
Click ok
30. Drag and drop Record module from basic process to the model area
Double click on it, make following entries
Name: total time
Type: Time Interval
Attribute Name: aTime
Click ok
31. Drag and drop Dispose module from basic process to the model area
Double click on it, make following entries
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
RESULT AND DISCUSSION
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:
Create (1), Assign (2), Process (9), Record (1), and Dispose (1)
ADVANCED TRANSFER MODULES:
Enter (3), station (2), Request (4), Free (4), Transport (4)
SPREAD SHEET MODULES:
Nil
BASIC PROCESS/QUEUE
-Set Queue type as First in First Out
120
ADVANCED TRANSFER/DISTANCE-
Transporter1.Distance
Add 10 rows
No. Beginning station Ending station Distance
1 Arrive Dock Station1 20
2 Station1 Station2 20
3 Station2 Station3 30
4 Staion3 Exit shop 20
5 Arrive Dock Station2 20
6 Arrive Dock Station3 30
7 Arrive Dock Exit shop 30
8 Station1 Station3 30
9 Station1 Exit shop 30
10 Station2 Exit shop 30
Table 9.1 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
Double click on it, make following entries
Name: Assign job type
Add Attribute
Attribute Name-Entity. Type
New Value-ABS (1)
Click ok
3. Drag and drop Assign module to the model area
Double click on it, make following entries
Name: Time
121
Add Attribute
Attribute Name-a Time
New Value-tnow
Click ok
4. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Arrive station
Station Name: Arrive Dock
Click ok
5. Drag and drop Request module from advanced transfer process to the model area
Double click on it, make following entries
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
Double click on it, make following entries
Name: Transport to shop floor
Transporter Name: Transporter1
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
Double click on it, make following entries
Name: Entry to station1
Station type: station
Station Name: Station1
Units: Hours
122
Click ok
8. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at station1
Transporter Name: Transporter1
Click ok
9. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
10. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
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
11. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone1
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
12. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station1
123
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
13. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station1
Transporter Name: Transporter1
Entity destination type: station
Station Name: Station 2
Velocity: 20m
Units: per minute
Click ok
14. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry station2
Station type: station
Station Name: Station2
Units: Hours
Click ok
15. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion2
Transporter Name: Transporter1
Click ok
16. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
124
Click ok
17. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation2
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource2; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 0.001
Click ok
18. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Unloading Zone2
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
19. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station2
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
20. Drag and drop Transport module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Transport from station2
Transporter Name: Transporter1
Entity destination type: station
125
Station Name: Station 3
Velocity: 20m
Units: per minute
Click ok
21. Drag and drop Enter module from advanced transfer process to the model area
Double click on it, make following entries
Name: Entry to station3
Station type: station
Station Name: Station3
Units: Hours
Click ok
22. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free truck at staion3
Transporter Name: Transporter1
Click ok
23. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Loading Zone3
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
24. Drag and drop Process module from basic process to the model area
Double click on it, make following entries
Name: Operation3
Type: Standard
Action: Seize Delay Release
Priority: Medium
Add Resources; Resource; Name: Resource3; Quantity: 1
Delay Type: Normal; Units: Minutes; Value: 0
Value: 15; Standard Deviation: 0.001
Click ok
25. Drag and drop Process module from basic process to the model area
126
Type: Standard
Action: Delay
Delay Type: Constant; Units: Minutes; Value: 0
Click ok
26. Drag and drop Request module from advanced transfer process to the model
area
Double click on it, make following entries
Name: Request Truck at station3
Transporter Name: Transporter1
Selection Rule: Smallest Distance
Priority: High
Velocity: 20m
Units: per minute
Click ok
27. Drag and drop Transport module from advanced transfer process to the model
area
Name: Transport from station3
Transporter Name: Transporter1
Entity destination type: station
Station Name: exit shop
Velocity: 20m
Units: per minute
Click ok
28. Drag and drop Station module from advanced transfer process to the model area
Double click on it, make following entries
Name: Exit
Station Name: exit shop
Click ok
29. Drag and drop Free module from advanced transfer process to the model area
Double click on it, make following entries
Name: Free Truck at exit
Transporter Name: Transporter1
Click ok
30. Drag and drop Record module from basic process to the model area
127
Double click on it, make following entries
Name: total time
Type: Time Interval
Attribute Name: aTime
Click ok
31. Drag and drop Dispose module from basic process to the model area
Double click on it, make following entries
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
RESULT AND DISCUSSION
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
Variation of PT ofMachine 2
Variation of PT ofMachine 3
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 :
Fig 1.2 Graph showing variation in processing time of machine2
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
Fig 1.3 Graph showing variation in processing time of machine3
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
132
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