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, costbenefit 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 systemthose that are of interest to the analyst/modelerin 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. 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 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 5

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 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 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

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.

T Fig: - frames 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 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 completion is described by the transition . Similarly, a process 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).

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CHAPTER -3

ELEMENTS OF PROBABILITY AND STATISTICS

3.1 INTRODUCTIONS
Many real-life systems exhibit behavior with random elements. Such systems encompass a vast array of application areas, such as the following: 1. Manufacturing Random demand for product held in an inventory system Random product processing time or transfer time Random machine failures and repairs

2. Transportation Random congestion on a highway Random weather patterns Random travel times between pairs of origination and destination points

3. Telecommunications Random traffic arriving at a telecommunications network Random transmission time (depending on available resources, such as buffer space and CPU) Indeed, simulation modeling with random elements is often referred to as Monte Carlo simulation, presumably after its namesake casino at Monte Carlo on the Mediterranean. This apt term commemorates the link between randomness and gambling, going back to the French scientist Blaise Pascal in the 17th century. Formally, modeling a random system as a discrete-event simulation simply means that randomness is introduced into events in two basic ways: Event occurrence times may be random.. Event state transitions may be random.

For instance, random interarrival times at a manufacturing station exemplify the first case, while random destinations of product units emerging from an inspection station (possibly needing re-work with some probability) exemplify the second. Either way, probability and statistics are fundamental to simulation models and to understanding 12

the underlying random phenomena in a real-life system under study. In particular, 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 {: X()

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 .

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For a discrete random variable X, the associated pmf is sometimes referred to as a pdf as well. This identification is justified by the fact that a mathematical abstraction allows us, in fact, to define differencing as the discrete analog of differentiation. Indeed, for a discrete real-valued random variable X, we can write

3.5 JOINT DISTRIBUTIONS

Let X1, X2, . . . , Xn be n real-valued random variables over a common probability space. The joint cdf of X1, X2, . . . , Xn is the function .

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

In this context, each cdf FXi (x) and pdf fXi (x) are commonly referred to as a marginal distribution and marginal density, respectively. The random variables X1, X2, . . . , Xn are mutually independent, if

provided that the densities exist. In other words, mutual independence is exhibited when joint distributions or densities factor out into their marginal components. A set of random variables, X1, X2, . . . , Xn, are said to be iid (independently, identically distributed), if they are mutually independent and each of them have the same marginal distribution.

3.6 EXPECTATIONS

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

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

3.7 MOMENTS

3.8 CORRELATIONS
Let X and Y be two real-valued random variables over a common probability space.It is sometimes necessary to obtain information on the nature of the association (probabilistic relation) between X and Y, beyond dependence or independence. A useful measure of statistical association between X and Y is their correlation coefficient (often abbreviated to just correlation), defined by

The correlation coefficient has the following properties:

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2. If X and Y are independent random variables, then X and Y are uncorrelated, that is r(X, Y) = 0 However, the converse is false, namely, X and Y may be

uncorrelated and dependent, simultaneously. 3. If Y is a (deterministic) linear function of X, that is, Y = aX b, then

3.9 COMMON DISCRETE DISTRIBUTIONS

3.10 GENERIC DISCRETE DISTRIBUTION

where [x] is the integral part of x. The generic discrete distribution may be used to model a variety of situations, characterized by a discrete outcome. In fact, all other discrete distributions are simply useful specializations of the generic case.

3.10.1 BERNOULLI DISTRIBUTION

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

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A Bernoulli random variable may be used to model whether a job departing from a machine is defective (failure) or not (success).

3.10.2 BINOMIAL DISTRIBUTION

The corresponding mean and variance are given by the formulas.

A binomial random variable may be used to model the total number of defective items in a given batch. Such a binomial trial can be a much faster procedure than conducting multiple Bernoulli trials.

3.10.3 GEOMETRIC DISTRIBUTION

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

3.10.4 POISSON DISTRIBUTION

and the corresponding mean and variance are given by

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3.11 COMMON CONTINUOUS DISTRIBUTIONS

This section reviews the most commonly used continuous distributions and the underlying random experiment, and discusses their use in simulation modeling.

3.11.1 UNIFORM DISTRIBUTION

and the cdf is

The corresponding mean and variance are given by the formulas.

A uniform random variable is commonly employed in the absence of information on the underlying distribution being modeled.

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3.11.2 STEP DISTRIBUTION

A step or histogram random variable, X, generalizes the uniform distribution in that it constitutes a probabilistic mixture of uniform random variables. The step distribution is denoted by Cont({(pj, lj, rj): j = 1, 2, . . . , J}), where the parameters have the following interpretation: , J. Thus, the state space of X is the union of intervals, with probability p j = 1, 2, . . .

Thus, the resulting pdf is a step function (mixture of uniform densities) as illustrated in by Figure and the corresponding cdf is given by

The corresponding mean and variance are given by the formulas

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

3.11.3 TRIANGULAR DISTRIBUTION

The corresponding mean and variance are given by the formulas

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

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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.

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3.11.5 LOGNORMAL DISTRIBUTION

3.11.6 GAMMA DISTRIBUTION

Mean and variance are

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Density functions of the Gamm(1,1), Gamm(2,1), and Gamm(3,1) distributions. 3.11.7 STUDENTS t DISTRIBUTION

Density function of the t(10) distribution. 3.11.8 F DISTRIBUTION

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Density function of the F(1, 1) distribution. 3.11.9 BETA DISTRIBUTION

Where

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

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3.11.10 WEIBULL DISTRIBUTION

Density functions of the Weib(1,1), Weib(2,1), and Weib(3,1) distributions. STOCHASTIC PROCESSES The auto correlation function of a stochastic process is the correlation coefficient of its lagged random variables,

3.12 VARIATE GENERATION USING THE INVERSE TRANSFORM METHOD

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The Inverse Transform method. 3.12.1 GENERATION OF UNIFORM VARIATES

3.12.2 GENERATION OF EXPONENTIAL VARIATES where u is given and x is unknown. Solving the above for x readily yields the formula

It can be simplified into the equivalent formula

3.12.3 GENERATION OF DISCRETE VARIATES

or equivalently,

The Inverse Transform method for generating a discrete variate.

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3.12.4 GENERATION OF STEP VARIATES FROM HISTOGRAMS

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CHAPTER-4 FREQUENTLY USED ARENA MODULES

Following is a subset of frequently used Arena modules, the associated template panel, and a brief explanation of module function and operation. The term parameter stands for the contents of the corresponding field in the module dialog box.

1 .ACCESS MODULE (ADVANCED TRANSFER)

Function: Used to allocate one or more cells of a conveyor to an entity for movement from one station to another. Operation: When an entity arrives at this module, it waits until the appropriate number of contiguous cells on the conveyor become empty and align with the entitys 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 entitys 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 entitys 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 entitys station location, unless otherwise specified in the Transporter module.

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Free

10 .HALT MODULE (ADVANCED TRANSFER)

Function: Used to change the status of a transporter unit to inactive. Operation: When an entity enters this module it tries to halt the requisite transporter unit. If that unit is idle at the time, then its status is set immediately to inactive. If, however, that unit is busy at the time, then its status changes immediately to busy and inactive. If later on the entity that controls the halted unit proceeds to free it, then its status changes to inactive only at that point in time. Once a transporter unit has been halted, no entities can gain control of that unit until it is activated
Halt

11. HOLD MODULE (ADVANCED PROCESS)

Function: Used to hold an entity in a queue to either wait for a signal, wait for a specified condition to become true, or to be held indefinitely. Operation: When an entity arrives at this module and the value of the Type attribute is Wait for Signal, then a Signal module must be used to send the requisite signal that allows the entity to move on to the next module. If the value of the Type attribute is Scan for Condition, then the entity will remain at the module until the condition(s) defined in the Condition parameter become(s) true. On the other hand, if the value is Infinite Hold, then the hold period is indefinite, unless a Remove module is used to allow the entity to continue processing. The waiting queue for the entities can be specified in the Queue Type attribute as the module s internal queue or another queue.
Hold

12 .MATCH MODULE (ADVANCED PROCESS)

Function: Used to bring together (synchronize) a specified number of entities waiting in different queues at this module. Operation: An entity arriving at this module is placed in one of up to five associated queues, based on its entry point, and remains in its queue until a match materializes (a match may be accomplished when there is at least one entity in each 32

queue). At that point in time, one matching entity from each queue is removed, and all these entities exit the module simultaneously via their respective exit point. All exit points must be connected to some modules.
Match

13. PICKSTATION MODULE (ADVANCED TRANSFER)

Function: Used to select a particular station. Operation: When an entity arrives at this module, a station is selected from a station group, based on the selection logic specified in the Selection Based On . . . section. The entity may then route, transport, convey, or connect to the selected station depending on the value of the Transfer Type parameter. The station selection process is based on the minimum or maximum value of a variety of system variables and expressions depending on the value of the Test Condition parameter.
PickStation

14. PICKUP MODULE (ADVANCED PROCESS)

Function: Used to remove a number of consecutive entities from a given queue. Operation: When an entity group arrives at this module, it removes a specified number of entities from a specified queue starting at a specified rank in the queue. The picked up entities are added to the end of the incoming entity group.
Pickup

15. PROCESS MODULE (BASIC PROCESS)

Function: Used as the main processing method for various functions such as delaying, seizing, and releasing resources and queuing Operation: Entities arriving at this module are processed differently, depending on the specified value for the Action parameter. Additionally, the user can choose the sub model option as the Type parameter, and specify a hierarchy of userdefined sub models and their logic. Process times and associated costs are allocated to incoming entities using the Allocation parameter, including Value Added, Non-Value

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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 entitys 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 entitys 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 entitys 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 entitys 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 entitys 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) Processing time of first process = 10 min = 9 min

Processing time of second process = 9 min Replication Length Number of replication Warm up period = 10000min =3 = 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 3 Drag and drop assign module. 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 5 Drag and drop process module 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 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 Unit: min

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 Process 1 (nos) Replication 1 Replication 2 Replication 3 5.12 5.2422 4.3774 Process 2 (nos) 4.5643 2.9566 6.2512 111.75 103.42 124.19 Total Time In System (min)

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 Process 1 (nos) Replication 1 Replication 2 Replication 3 2.6403 2.3885 2.9010 Process 2 (nos) 3.5889 4.5907 4.4385 79.98 87.863 91.204 Total Time In System (min)

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 Process 1 (nos) Replication 1 Replication 2 Replication 3 3.0241 3.8485 5.3293 Process 2 (nos) 0 0 0 47.885 55.785 69.265 System (min)

Average

4.0673

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 Process 1 (nos) Replication 1 0 Replication 2 0 Replication 3 0 0 0 18 18 0 18 Process 2 (nos) Total Time In System (min)

Average

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) process 1 Model 1.4 Model 1.3 Model 1.2 Model 1.4 0 4.067 2.645 4.913 process 2 0 0 4.206 4.597 Total time in system (min) 18 57.645 86.349 113.12

Table 1.5 average no in queue and total time in system

GRAPH
Graph is obtained from above information

6 5 4

avg no 3 in queue
2 1 0 model 1.4 model 1.3 model1.2 model 1.1

process 1 process 2

models

Graph 1.1:-average no in queue vs model During constant inter arrival time constant processing time , average no in queue is zero.

46

120 100 80

Total time in system

60 40 20 0 model 1.4 model 1.3 model 1.2 model 1.1

Total time in system

Model

Graph 1.2:-model vs total time During 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.

48

A1M
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 2 Drag and drop create module to model area 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 4 Drag and drop assign module 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 49

Delay type: CONST 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 50

Unit: minutes 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 51

17 Then change the rework probability of 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 1 2 3 Total Time (minutes) 73.01 71.89 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 1 2 3 Total Time (minutes) 78.11 78.89 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 1 2 3

Total Time (minutes) 87.01 88.01 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 1 2 3 Total Time (minutes) 102.01 102.89 102.23

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 1 2 3 Total Time (minutes) 119.11 118.89 117.56

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 1 2 3

Total Time (minutes) 168.01 168.89 169.11

Table 2.6 Probability of rework at 10% 58

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.
180 160 140 120 100 80 60 40 20 0 1 2 3 4 5 6 Rework % 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.

cycle time

Rework %

Graph 2.1:- rework vs. cycle time

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) Uptimes 1 2 3 4 8.5 8.3 8.6 8.6 475 570 665 475 Repair 20, 30 24, 36 28, 42 20, 30 (minutes) Uptimes 47.5 57.0 66.5 47.5 Repair 2, 3 2.4, 3.6 2.8, 4.2 2, 3 Jam Means

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 Uptimes 1 2 3 4 8.5 8.3 8.6 8.6 475 570 665 475 Repair 20, 30 24, 36 28, 42 20, 30 Uptimes 47.5 57.0 66.5 47.5 Repair 2, 3 2.4, 3.6 2.8, 4.2 2, 3 Jam Means

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 Value= tnow

61

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

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

Delay and drop dispose module from basic process

Change run setup to No of replication=3 Warm up period= 500min Replication length=1000min

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.

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 State % Idle % Busy % Major Failure % Jam Number in queue Work Station 1 0.066 89.88 5.43 4.62 90.009 Work Station 2 2.36 87.69 5.033 4.923 3.9713 Work Station 3 0.833 90.153 4.373 4.66 6.8476 Work Station 4 1.13 88.963 5.46 4.446 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.

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

1) WORK STATION VS FAILURE STATE

6 5

% Failure State

% idle %m failure % jam

4 3 2 1 0 1 2 3 4

Work Station
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.

2) QUEUE VS NUMBER IN QUEUE

100 90 80 70 60 50 40 30 20 10 0 1 2 3 4

Number in Queue

no in queue

Queue
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 Type: Standard Action: Seize, delay, release Resource type: resource Resource name: c1, c2, c3 67 Delay type: uniform unit: minutes minimum: 8 maximum: 10

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. Click run menu go Run set up menu No of replications: 3 Warm up period: 5000 Replication length: 1000 min Click ok.

8.

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

Drag and drop process modules corresponding to each arrival and assign. Name: For clerks Type: Standard Action: Seize, delay, release Resource type: resource Delay type: uniform unit: minutes minimum: 8 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 1 2 3 average 1870 1862.13 1809.29 1847.13 Total Time

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 1 2 3 average 48.121 34.447 33.551 38.706 Total Time

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

1940 1920 1900 1880 1860 1840 1820 1800 1780 1760 1740 1 2 3

Time

Replication

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 Replica tion Through put time Agnt 1 Agnt 2 Agnt 3 Agnt Agnt 5 4 Agnt 6 Agnt 7 Domestic Packing Inter national stn % Utilization Average no in queue

169.30

.50951

.2082 7

9242.9

.00478

169.20

.50753

.2080 0

9264

.0053

170.98

.50416

.2137 4

9366.7

.00470

Avg

169.8266 67

.50706 667

.2100 0333

9291.2

.00492667

77

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
171.5 171 170.5 170 169.5 169 168.5 168 1

Replication

Fig 5.1 Replication vs Throughput time

The throughput time of the system increases when the replication number increases from 1-3

78

packing station
9380 9360 9340 9320 9300 9280 9260 9240 9220 9200 9180 1 2 3

No in queue

Series1

Replication

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
0.0054 0.0053 0.0052 0.0051

International

No in queue

0.005 0.0049 0.0048 0.0047 0.0046 0.0045 0.0044 1 2 3 Series1

Replication

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

% of utalization

1.2 1 0.8 0.6 0.4 0.2 0 1 2

utalization of agent

utalizati

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. 3) Increase in the number of AGVs, increases the system performance initially and the decreases it. 81

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 coefficient 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 Distance between each segment Replication Length Number of replication Warm up time 20 meter/minute 10 meter 100000 1 500 minute

82

SYSTEM LAYOUT

Fig :- system layout

83

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 -Set Queue type as First in First Out

84

ADVANCED TRANSFER/DISTANCETransporter1.Distance Add 10 rows No. 1 2 3 4 5 6 7 8 9 10 Beginning station Arrive Dock Station1 Station2 Staion3 Arrive Dock Arrive Dock Arrive Dock Station1 Station1 Station2 Ending station Station1 Station2 Station3 Exit shop Station2 Station3 Exit shop Station3 Exit shop Exit shop Distance 20 20 30 20 20 30 30 30 30 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 Double click on it, make following entries Name: Time 85

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 Station Name: Station1 Units: Hours 86

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 87

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 88

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 89

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 90

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 Double click on it, make following entries Name: Free Truck at exit 91

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 utilizations, output in

(15,2),Normal(15,4),Normal(15,6),Normal(15,8)) . The

numbers and throughput time for the three machines and AGV are obtained as given in the table below. No IAT . Utilization Machine Machine Machine AGV 1 2 3 Output(n o.) Throughp ut Time(min ) 1 Normal(15,.0 01) 2 3 4 5 Normal(15,2) Normal(15,4) Normal(15,6) Normal(15,8) .99653 .99172 .99113 .98124 .99653 .99173 .99113 .98124 .99653 .99173 .99111 .98120 .48169 6610 .48247 6578 .49117 6574 .49780 6509 90.198 124.09 119.77 154.17 1 1 1 .3999 6634 51.136

Table 6.2 :- Performance variation with respect to inter arrival time variation From the above results it is significant variation for found that machine utilization same IATs. When IAT should not have

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

IAT Vs OUTPUT
6650 6600 6550 6500 6450 6400 IAT

OUTPUT

OUTPUT

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. .

IAT Vs MACHINE UTILAZTION

MACHINE UTILIZATION 1.01 1 0.99 0.98 0.97

Machine1 Machine2 Machine3 IAT

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

IAT Vs THROUGHPUT TIME

THROUGHPUT TIME 200 150 100 50 0

THROUGHPUT TIME IAT

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.

IAT Vs AGV Utilization

AGV Utilization 0.6 0.5 0.4 0.3 0.2 0.1 0 AGV Utilization IAT

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/DISTANCETransporter1.Distance Add 10 rows

No. 1 2 3 4 5 6 7 8 9 10

Beginning station Arrive Dock Station1 Station2 Staion3 Arrive Dock Arrive Dock Arrive Dock Station1 Station1 Station2

Ending station Station1 Station2 Station3 Exit shop Station2 Station3 Exit shop Station3 Exit shop Exit shop

Distance 20 20 30 20 20 30 30 30 30 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

Time in System Load/Unload time 1 2 3 4 5 With Failure 327.59 335.99 342.89 354.89 359.44 Without Failure 57.136 66.121 75.032 81.544 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.
500 450 400 350 300 250 200 150 100 50 0 1 2 3 4 5

system time

with out failure with failure

load / unload time

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 AGVs 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/DISTANCETransporter1.Distance Add 10 rows
No. 1 2 3 4 5 6 7 8 9 10 Beginning station Arrive Dock Station1 Station2 Staion3 Arrive Dock Arrive Dock Arrive Dock Station1 Station1 Station2 Ending station Station1 Station2 Station3 Exit shop Station2 Station3 Exit shop Station3 Exit shop Exit shop Distance 20 20 30 20 20 30 30 30 30 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 Units: per minute

109

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 Type: Standard 110

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 Double click on it, make following entries 111

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 Click ok 112

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 Double click on it, make following entries 113

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 27. Drag and drop Transport module from advanced transfer process to the model area 114

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. System Utilization No of AGVs 1 2 3 4 5 6 M1 .98862 .99548 .99940 .99940 .99413 .99940 M2 .98564 .98581 .98918 .98917 .99260 .98917 M3 .98468 .99359 .98757 .98984 .98768 .98984 AGV Utilization .55195 .25936 .16402 .12189 .09751 .08118 Throughput Time 731.00 815.06 1069.2 1348.5 811.25 1348.5

Output

6483.0 6512.0 6483.0 6470.0 6480.0 6470.0

Table 8.2 Performance variation with respect to no. of AGVs 116

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 AGVs. The utilization of machine M2 and M3 also increases initially and then decreases. With increase in number of AGVs, the utilization is decreasing. Maximum output is corresponding to two AGVs, only slight variation in output for other cases. Throughput time increase with increase in number of AGVs, 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 AGVs 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 AGVs. Machine M1, M2, M3 achieve the maximum utilization corresponding to 3, 5, 2 no. of AGVs.

No. of AGV v/s AGV Utilization

0.6

AGV Utilization

0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6

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 AGVs as per the graph above.

117

No. of AGV v/s Throghput time

1600 1400 1200 1000 800 600 400 200 0 1 2 3 4 5 6

Through Put Time

No.of AGV's

Figure8.2 No. of AGV v/s Throghput time Throughput time shows fluctuation with variation in nuber of AGVs, it inially increaes , reaches a maximum value and then decreses. It again shows postive trend with further increase in number of AGVs. AGV utilization is maximum at 4 and 6 no. of AGVs.

6520 6510 6500 6490 6480 6470

No. of AGV v/s Output

Output

6460 6450 6440 1 2 3 4 5 6

No.of AGV's

Figure8.3 No. of AGV vs. Output The output varies slightly with the increase in number of AGVs. The trend is to increase initially, then to decrease. The maximum output corresponds to 2 AGVs.

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 AGVs. The AGV utilization continually shows a down ward trend. Here the test considers the AGVs 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) Processing time (PT) Norm (15, 8) min 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 Part Type Number of replication 1 1 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/DISTANCETransporter1.Distance Add 10 rows No. 1 2 3 4 5 6 7 8 9 10 Beginning station Arrive Dock Station1 Station2 Staion3 Arrive Dock Arrive Dock Arrive Dock Station1 Station1 Station2 Ending station Station1 Station2 Station3 Exit shop Station2 Station3 Exit shop Station3 Exit shop Exit shop Distance 20 20 30 20 20 30 30 30 30 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 Add Attribute 121

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 Click ok 122

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 Transporter Name: Transporter1 123

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 Click ok 124

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 Station Name: Station 3 125

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 Type: Standard 126

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 Double click on it, make following entries 127

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 =/ 34 Vary the processing time of the three machines and find the machine utilization. = Standard deviation/mean

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 of Variation of PT of Variation of PT of Machine 1 Machine 2 Machine 3 M1 M2 M3 M1 M2 M3 M1 M2 M3 Norm(15,0) 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Norm(15,2) .99984 .99633 .99632 .99999 .99827 .99723 .99998 .99996 Norm(15,4) .99942 .99603 .99603 .99998 .99901 .99420 .99997 .99996 Norm(15,6) .99753 .99544 .99540 .99999 .99968 .98871 .99998 .99996 Norm(15,8) .99701 .98543 .98542 .99998 .99799 .99333 .99997 .99994 .99987 .99805 .99582 .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:

VARIATION IN PROCESSING TIME OF MACHINE3

1.002 1 0.998 0.996 0.994 0.992 0.99 0.988 0.986 0.984 0.982 Norm(15,0) Norm(15,2) Norm(15,4) Norm(15,6) MACNINE UTILISATION

PT Norm(15,8)

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