Simulation

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DAYANANDA SAGAR COLLEGE OF ENGINEERING

DEPARTMENT OF INDUSTRIAL ENGINEERING AND MANAGEMENT

DAYANANDA SAGAR COLLEGE OF ENGINEERING

Shavige Malleswara Hills, Kumaraswamy Layout, Bangalore - 560 078 Ph No : 080 – 2666226, 080 – 42161741, Fax No : 080- 2666789

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VISION

“To strive at creating the Institution as a center of excellence, so as

to create an overall intellectual atmosphere with each deriving

strength from the other top transforms individuals into great

engineers, scientists and professionals.”

MISSION

“To serve its region, state, the nation and globally by preparing

students to make meaningful contributions in an increasingly

complex global society, by encouraging reflection on and valuation

of emerging needs and priorities, and by supporting research and

service that enhance technological, health, economic, human and

cultural development”

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VISION

“To emerge as an excellent center for imparting quality education

and generating highly proficient technical manpower with

managerial competence to adapt to the constantly changing global

scenario with professional and ethical values”

MISSION

Creating a sound academic environment for students & teachers to

update their knowledge with excellent ambience of teaching learning

process.

Industry institute interaction in the form of faculty exchange,

projects, workshops and seminars.

Developing human relations and social engineering for students in

the form of extracurricular & co-curricular activities

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A few years after graduation, graduates of Industrial Engineering & Management

(IE & M) will:

1.

Be able to apply the principles of IE & M, mathematics, and scientific

investigation to solve real world problems appropriate to the discipline.

(PE01)

2.

Be able to apply current industry accepted industrial engineering skills and

practices, new emerging technologies to understand, analyze , design,

Implement and verify high quality solutions to real world problems. (PE02)

3.

Exhibit teamwork and effective communication skills (PEO3)

4.

Be able to ethically and appropriately apply knowledge of societal impacts of

computing technologies in the course of carrier related activities. (PEO4)

5.

Be successfully employed or accepted into a graduate program, research,

pursue higher education and demonstrate a pursuit of lifelong learning.

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Each student learning outcome maps to one of the program educational objectives (PEOs) as indicated in parenthesis following the outcome. Graduates of the program will :

a. Demonstrate an ability to apply mathematical and quantitative methods to the IE & M discipline and shall demonstrate an understanding of industrial and system engineering, design, development and understanding the architecture. (PEO1)

b. Demonstrate a problem solving ability in recognition of a problem, statement , collect, collate, classify and analyze the data interpretation to the suggest recommended. (PEO1)

c. Demonstrate an ability to design a system, method or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety,

manufacturability, and sustainability. (PEO2)

d. Be able to work effectively and efficiently on a multi-disciplinary teams.(PEO3)

e. Demonstrate an understanding of the principles and practices for IE & M skills and development to real world problems. (PEO2)

f. Demonstrate an understanding of the professional and ethical consideration of industrial and system engineering. (PEO4)

g. Be able to effectively communicate orally and in written form. (PEO3)

h. Demonstrate knowledge of the impact of engineering solutions in a economic, societal, global and environmental context. (PEO4)

i. Demonstrate the knowledge and capabilities necessary for pursuing a professional career or take up entrepreneurship ventures at graduate studies and recognize the need for and show ability for continuing professional development. (PEO5)

j. Enhance the knowledge of contemporary issues. (PEO5)

k. Demonstrate an understanding of emerging technologies and a working knowledge of currently available sectors of economy and industries. (PEO2)

The industrial Engineering and Management program outcomes leading to the achievement of the objectives are summarized in the following table

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Bangalore

Department of Industrial Engineering & Management

SIMULATION LAB

Name of the Laboratory

:

CAD / CAM LAB (10 IML 68)

Semester

:

VI-2014

No. of Students/Batch

:

20

No. of Computers

:

23

Major Equipments

:

Workstation, Printer, Scanner

Operating System &

Application software

:

Windows XP/7 , Rockwell Arena

Lab Incharge

:

Prof.Rajesh S.M

Prof. Radha Halagalli

Instructor

:

Mr. K Ramesh Shetty

Mr. Ravi Raj Yadav

Dr.H Ramakrishna

Head of the Department

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SIMULATION

LAB

(10 IML 68)

1. CO1: Able to understand the basics of simulation and their applications.

2. CO2: Able to understand the application of simulation with analytical problems.

3. CO3: Able to build models and analysis of models

4. CO4: Able to test the models and to draw useful inferences.

PART - A

Introduction to Simulation Packages Understanding the Simulation Package

Identifying probability distributions for given data

Building simulation models for manufacturing operations (Electronic assy – With Basic templates) Building simulation models for manufacturing operations (Electronic assy – With Common templates)

Building simulation models for manufacturing operations with transport System Building simulation models for manufacturing operations with layout

PART – B

Building simulation models for manufacturing operations with layout and transport System Building simulation Models for Banking service ( Bank teller problem)

Building simulation Models for Mortgage application problem Building simulation Models for food processing problem Building simulation Models for Post office animation Statistical Analysis of Simulation models ( input analysis) Statistical Analysis of Simulation models (output analysis)

Suggested Software Packages: Promodel/Arena/Quest/Witness/Extend.

Note: A minimum of 12 exercises are to be conduct

Subject Code : 10 IML 68 IA Marks : 25 No. of Lab Hrs./ Week : 03 Exam Hours : 03 Total No. of Lab Hrs. : 42 Exam Marks : 50

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Exercise No. Title Page No. PART -A

1 Introduction to Simulation Packages 1 2 Understanding the Simulation Package 4 3 Identifying probability distributions for given data 8 4 Building simulation models for manufacturing operations

(Electronic assembly – With Basic templates)

9

5 Building simulation models for manufacturing operations (Electronic assembly – With Common templates)

10

6 Building simulation models for manufacturing operations with transport System

11

7 Simulation of grocery store problem (Single channel queue) 13 8 Building simulation Models for Banking service ( Bank

teller problem-Single channel)

14

9 Simulation of airline checking system 15

PART -B

10 Building simulation Models for Banking service ( Bank teller problem-Multi channel)

17

11 Building simulation Models for Mortgage application

problem 19

12 Building simulation Models for food processing problem 20 13 Building simulation Models for Post office animation. 24 14 Building simulation models for manufacturing operations

(Multi arrivals)

25

15 Statistical Analysis of Simulation models ( input analysis) 27

Problems for Practice 31

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1. Introduction to Simulation Packages SIMULATION

Creating a model of a real or proposed system for the purpose of evaluating the systems behavior for various conditions.

• Allows the analyst to draw inferences about new systems without building them or ake changes to existing systems without disturbing them.

• The only tool that will allow system interactions (System integration) to be analyzed. • Permits managers to visualize the operation of a new or existing system under a variety of conditions.

• Understand how various components interact with each other and how they effect overall system performance.

WHY SIMULATE?

• Provide genera’ insight into the nature of a process.

• Identify specific problems or problem areas within a system. • Develop specific policies or plans for a process.

• Test new concepts and/or systems prior to implementation. • Improve the effectiveness of a system

• Provide an insurance policy” for system performance.

SIMULATION

• cannot optimize — It can only describe the results of “what if” questions • Cannot give accurate results if the data are inaccurate.

• Cannot describe system characteristics that have not been explicitly modeled. • cannot solve problems. it can only provide information.

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PROJECT MANAGEMENT-THE PLAYERS

• Simulation project team • System design team • Data/information sources • Implementation team • Contractors • Decision makers/management. ESTABLISH RESPONSIBILITY • Project manager

• One individual representing each major group • Hopefully a small no. of groups.

STARTING THE STUDY

• Have clearly stated and accepted objectives • Get input from everyone.

• Make certain all agendas are understood.

THE SIMULATION PROCESS

• Define-functional specification • Formulate- the simulation mode’ • Verify/validate-input from all players • Analyze- statistical evaluation

• Recommend- alternatives to the decision makers

WHY HAVE A FUNCTIONAL SPECIFICATION? • Defines the problem completely

• Requires system understanding fro the start • Provides vision of the task

• Defines how simulation will be used.

• Defines all assumptions of the simulation model • Identifies data requirements.

• Identifies required output statistics and analysis

A FUNCTIONAL SPECIFICATION

• Objectives • Assumptions • Inputs

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Dept. of IE&M, DSCE, Bangalore Page 3 • Outputs • Control logic • Level of detail • Flexibility • Analysis MODEL FORMULATION

• One or more analysts. • Data structure requirements. • Model control logic

• Level of detail • Flexibility

• Statistical requirements.

VERIFICATION AND VALIDATION

• Verification — Ensuring that the model behaves in The way it was intended. • Validation; Ensuring the model behaves the same as the real system Requires • Involvement of all players

• Use of animation and data • Reasonable and robust model

THE ANALYSIS

• Addresses the project objectives • An iterative process

• Helps the analyst understand the results • Establishes result accuracy and sensitivity

THE FINAL PRESENTATION

• Keep it short and simple • Answer the right questions • Address the audience

• Provide reasons for the results.

COMPONENTS OF A SIMULATION MODEL

• Entities • Resources • Control logic • Statistics

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TYPICAL ENTITIES

• Physical objects Parts or products, paper work customers, patients etc. • Logical entities; Failure control, requests, system control, staff breaks, etc.

TYPICAL RESOURCES

• Constrained resources: machines, space, tables, hospital beds, etc • Material handling Fork trucks, AGVs, conveyor wheel) chairs, etc • Staffing operators, material handlers, doctors, waiters etc.

TYPICAL CONTROL LOGIC

• Order release • Dispatching • Sequencing • Assernb4y • Material handling • Queue priority • Resource priority TYPICAL STATISTICS

• Resource utilization : busy, idle, failed etc.

• Waiting time: Queue, material handling, assembly etc • Cycle time : throughput, area, resource etc

• Production rates: product, area, shift et

• Performance due dates, inventory, overtime etc.

2. Understanding the Simulation Package

Concepts and Terminologies

ENTITIES

Entities represent any person, object or thing, whether real or imaginary, whose movement through the system causes a change in the status of the system. Examples: Customers moving through a -Restaurant, or parts moving through a factory.

ATTRIBUTES

• With in a system, there may be many types of entities, each having a unique characteristics called attributes.

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• Attributes represent user defined values associated with individual entities, such as customer type. product size, time job entered the system etc.

• All entities have the same set of attributes (priority, arrival time etc.) with different values. • An assignment made to an entity’s attribute affects only that entity.

VARIABLES

• A set of changeable values characterizing The components of the system as a whole, not the characteristics of individual entities

• Two types: user variables and system variables

• User variables are defined (named) by the modeler and can be changed during the simulation run (within the model or interactively).

• Examples: Arrival rate, current inventory, number of patients registered, etc.

• System variables are predefined characteristics of model components that provide the system state.

• Examples: No of entities waiting in a queue (NQ) or current value of a counter (NC)

STATIONS

• Arena approaches the modeling of systems by dividing them into sub system locations or stations.

• Stations are used to represent processing areas of the systems being modeled. Stations:

• Make the modeling effort more manageable • Provide a framework for the control of entity flaw.

• Provide a means to model entity movement .Example: a machining area, service counter, a warehouse etc.

RESOURCES

• A resource is one or more identical

• The number of identical resource units corresponding to a specific resource is called the resource capacity.

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• Resources may be used to represent people. machines floor space etc • Resources may be defined as stationary or positional

• Entities seize resources to get control of one or more units of the resource • Entities release resources when they are no longer required

QUEUES

• Waiting areas for entities whose movement through the system has been suspended due to the system status.

Example: a caller waits in a queue to be processed by a customer service operator.

ROUTES

• The movement of entities from one station to another.

• Routing assumes that time may be required to move the entity between stations, but it assumes that no additional delay will be incurred because of unavailable constraints, such as material handling devices

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3. Identifying probability distributions for given data

Goodness of fit for probability distributions

Generate 50 random digits using RAND function in MS Excel and test the goodness of fit for I) exponential distribution ii) Poisson distribution iii) Normal distribution using INPUT ANALYZER.

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4. Building simulation models for manufacturing operations (Electronic assembly – With Basic templates)

This system represents the final operations of the production of two different sealed electronic units. The arriving parts are cast metal cases for the units that have already been machined to accept the electronic parts.

The first Unit, named Part A are produced in an adjacent department, outside the bounds of this model, with inter arrival times to our model being exponentially distributed with a mean of 5 minutes. Upon arrival they are transferred to the Part A Prep area with a transit time of 2 minutes. At the Part A Prep area, the mating faces of the cases are machined to assure a good seal.

And the part is then deburred and cleaned; the process time for the combined operation follows a triangular (1,4,8 ) distribution, The part is then transferred to the sealer, with a transit time of 2 minutes.

The Second units named part B, are Produced in a different building outside this Model’s bounds where they are held until a batch of 4 units is available; the batch is then sent to the final production area we are modeling. The time between the arrivals of successive batches of part B to our model is exponential with a mean of 30 minutes. Upon arrival at the part B Prep area, the batch is separated into the four units, which are produced individually. The processing at the Part B Prep area has the same three steps as at the Part A prep area except that the process time for the combined operation followed a triangular (3,5,10). Distribution. The part is then sent to the sealer, with a transit time of 2 minutes.

At the sealer operation, the electronic components are inserted, the case is assembled and sealed, and the sealed unit is tested. The total process time for this operation depends on the Part type; Triangular (1,3,4) for Part A and weibull (2.5,5.3) for Part B (2.5, is the mean and 5.3 is the standard deviation) Ninety one Percent of the parts pass the inspection and are transferred directly to the shipping department. The remaining parts are transferred to the rework area where the parts are disassembled, repaired, cleaned, assembled and re-tested. Eighty percent of the parts here are salvaged and transferred to the shipping department as rework parts, The remaining part are transferred to the Scrap area. The time to rework a part follows an exponential distribution with a mean of 45 minutes and is independent of part type or part status, salvaged or scarped. Assume all transfer times are 2 minutes.

(It is required to collect the statistics in each area on resource utilization, number in queue, time in queue, the cycle time (or Flow time0 by shipped parts, salvaged parts, or scraped parts. Initially run the simulation for 2000 minutes.)

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5. Building simulation models for manufacturing operations (Electronic assembly – With Common templates)

The System to be modeled consists of Part arrivals, 4 manufacturing cells and part departures. Cell 1,2 & 4 ach have a single machine and Cell 3 has got 2 machines. The 2 machines at cell 3 are not identical; one of them is newer model that can process parts in 805 of the required by the older machine. The system produces 3 part types, each visiting a different sequence of stations. The part steps and process times are given below;

Part Type Cell / Time Cell / Time Cell / Time Cell / Time Cell / Time

1 1 6,8,10 2 5,8,10 3 15,20,25 4 8,12,16 2 1 11,13,15 2 4,6,8 4 15,18,21 2 6,9,12 3 27,33,39 3 2 7,9,11 1 7,10,13 3 18,23,28

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All process times are triangularly distributed; The process time given at Cell 3 are of the older machine.

The inter arrival times between successive part arrivals (all types combined) are exponentially distributed with a mean of 13 minutes. The distribution by type is 26% Part 1; 48% Part 2 and 26% Part 3. Parts enter from left and exit at right, and move only in a clockwise direction through the system. Time to move between any 2 cells is 2 minutes. Model the System using Arena and collect the statistics on resource utilization, time and number in queue, as well as cycle time ( time in system from entry to exit) by part type. Run the simulation for 2000 minutes.

6. Building simulation models for manufacturing operations with transport System

Simulate a simple processing system which consists of a drilling machine and the processing tie varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The Part enters the system with a random exponential value of 5 minutes, and then leaves the system. All time units are in minutes. Animate the resource and queue. Simulate the process for 20 minutes. Plot the number waiting at the drill center queue and number busy at the drill press. Report the simulation run statistics.

Add a second machine to which all the parts go immediately after exiting the first machine for a separate kind of processing (Rewash). Processing ties at the second machine are the same as for the first machine. Gather all the statistics as before, plus the time in queue, queue length and utilization at the second machine.

Immediately after the second machine, there is a pass/fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; Queuing is possible at inspection, and the queue is first in and first out. All parts exit the system regardless of whether they pass the test. Count the number that fail and the number that pass, and gather statistics on the time in queue, queue length and utilization at the inspection center. Run the simulation for 480 minutes.

In the above exercise, suppose that parts that fail inspection after being washed are sent back ad rewashed, instead of leaving, such rewashed parts must then undergo the same

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inspection and the same probability of failing. There is no limit on how many times a given part might have to loop back through the waster. Run this model under the same conditions and compare the results for the time in queue length and utilization at the inspection center.

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7. Simulation of grocery store problem (Single channel queue)

A small grocery store has only one check out counter. Customers arrive at this check out counter at random from 1 to 8 minutes apart. Each possible value of inter arrival times has the same probability of occurance. The service times vary from 1 to 6 minutes with the probabilities as shown in the table. The problem is to analyze the system by simulating the arrival and service of 20 customers. Service time in mins. Probability 1 0.10 2 0.20 3 0.30 4 0.25 5 0.1 6 0.05

a) Model the system.

b) Simulate the system for 20 customers.

c) Introduce appropriate animation and dynamic graphs. d) Generate report of simulation run statistics

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8. Building simulation Models for Banking service ( Bank teller problem-Single channel)

A bank has a drive- in teller. The times between customer arrival are :

Time between arrivals

(Minutes) 0 1 2 3 4 5 Probability 0.09 0.17 0.27 0.20 0.15 0.12

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The service distribution of teller is :

Service time (Minutes) 1 2 3 4

Probability 0.20 0.40 0.28 0.12 i) Model the above bank teller system.

ii) Simulate for 8 hr business transaction. iii) Introduce appropriate animation.

iv) Generate the reports of simulation run statistics.

9. Simulation of airline checking system

Travellers arrive at the main entrance door of an airline terminal according to an exponential inter-arrival time distribution with mean 1.6 minutes. The travel time from the entrance to the check-in is distributed uniformly between 2 and 3 minutes. At the check-in counter, travelers wait in a single line until one of five agents is available to serve them. The check-in time follows a weibull distribution with parameters β = 7.76 and α = 3.91. Upon completion of their check-in, they are free to travel to their gates. Create a simulation model, with animation, of this system. Run the simulation for 16 hours to determine the average time in system, number of passengers completing check-in, and the average length of the check-in queue.

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PART-B

10. Building simulation Models for Banking service ( Bank teller problem-Multi channel)

Customers arrive at the Bank and enter a queue to wait for the single teller. When the customer reaches the teller, he performs his transaction. When the initial transaction is completed, the teller determines if the customer must see the supervisor. If this is the case the customer moves to the single supervisor. When finished, the customer returns to the teller queue to redo his transaction. If the customer is not required to see the supervisor, he leaves the bank.

The time between customer arrivals is exponentially distributed with a mean of 5 minutes. The travel times from the entrance to the teller queue and from the teller to the exit are both 1 minute. All teller transaction times are normally distributed with a mean of 3 minutes and standard deviation of 1. 10% of the customers are required to see the supervisor. It is possible for a customer to see the supervisor several times. Travel times to and from the supervisor takes 1.5 minutes and the supervisor time follows a triangular distribution (12,15,20).

Collect statistics on the teller and the supervisor utilization, customer flow time and number in the teller queue. Run the simulation for an 8.5 hours a day.

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11. Building simulation Models for Mortgage application problem

The typical example shows the different stages in a mortgage as shown in the following diagram:

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Build a Simulation Model and collect the statistics for run time of 480 mins.

12. Building simulation Models for food processing problem

People arrive at a self-service cafeteria at the rate of one every 30 ± 20 sec.Forty % go to the sandwich counter, where one worker makes a sandwich in 60 ± 30 sec. The rest go to the main counter, where one server spoons the prepared meal on to a plate in 45 ± 30 sec.All customers must pay a single cashier, which takes 25 ± 10 sec. For all customers eating takes 20 ± 10 min. After eating, 10% of the people go back for dessert, spending an additional 10 ± 2 min. altogether in the cafeteria. Simulate until 100 people have left the cafeteria. How many people are left in the cafeteria, and what are they doing, at the time simulation stops?

SOLUTION:

Arrival Record ver-1 Record ver-2 Manager

TRIA (7, 10, 13) ie, 10 3 min TRIA (6, 10, 14) Ie, 10 4 min NORM (3.1) 10%

Counter 1-Record ver-1 Counter 2- Record ver-2 Counter 3-Manager

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13. Building simulation models for Post office animation.

Customers arrive at the post office according to an exponential inter-arrival time distribution with mean 3 mins.There are two counters 1 is letter weighing with triangular distribution (7,10,13) and stamping counter with triangular distribution (6,10,14).The customers who comes to post his letters has to check his letters at the inspection counters. The inspection time follows triangular distribution (12,15,20) and 10% of the letters gets rejected and sent back to counter 1 and others go to deposit and are free to travel to their exit. The deposit counter has triangular distribution (6,10,14). Run the simulation for 20 customers to determine the avg. time in system.

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14. Building simulation models for manufacturing operations (Multi arrivals)

Simulate a simple processing system which consists of a drilling machine and the processing tie varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The Part enters the system with a random exponential value of 5 minutes, and then leaves the system. All time units are in minutes. Animate the resource and queue. Simulate the process for 20 minutes. Plot the number waiting at the drill center queue and number busy at the drill press. Report the simulation run statistics.

Add a second machine to which all the parts go immediately after exiting the first machine for a separate kind of processing (Rewash). Processing ties at the second machine are the same as for the first machine. Gather all the statistics as before, plus the time in queue, queue length and utilization at the second machine.

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Dept. of IE&M, DSCE, Bangalore Page 26

Immediately after the second machine, there is a pass/fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; Queuing is possible at inspection, and the queue is first in and first out. All parts exit the system regardless of whether they pass the test. Count the number that fail and the number that pass, and gather statistics on the time in queue, queue length and utilization at the inspection center. Run the simulation for 480 minutes.

In the above exercise, suppose that parts that fail inspection after being washed are sent back ad rewashed, instead of leaving, such rewashed parts must then undergo the same inspection and the same probability of failing. There is no limit on how many times a given part might have to loop back through the waster. Run this model under the same conditions and compare the results for the time in queue length and utilization at the inspection center.

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15. Statistical Analysis of Simulation models ( input analysis)

Generate 50 random numbers using RAND function in MS Excel and using them , further generate exponential variates using inverse transform technique. Test the goodness of fit.

SOLUTION: Random No. Random Variates (mean=0.5) Random Variates (mean=1) Random Variates (mean=2) 0.34942426 2.102936922 1.051468461 0.525734231

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Dept. of IE&M, DSCE, Bangalore Page 28 0.75398787 0.564757999 0.282379 0.1411895 0.83119928 0.369771406 0.184885703 0.092442851 0.19707692 3.248322341 1.624161171 0.812080585 0.95939372 0.082907478 0.041453739 0.02072687 0.19679708 3.251164262 1.625582131 0.812791066 0.67341197 0.790795988 0.395397994 0.197698997 0.01182342 8.875346555 4.437673277 2.218836639 0.69035954 0.741085475 0.370542738 0.185271369 0.5680591 1.13105964 0.56552982 0.28276491 0.20272889 3.191771405 1.595885703 0.797942851 0.12322261 4.187525414 2.093762707 1.046881354 0.9604718 0.080661324 0.040330662 0.020165331 0.61783486 0.963068149 0.481534075 0.240767037 0.54440614 1.216119442 0.608059721 0.304029861 0.42772325 1.69855779 0.849278895 0.424639448 0.93817615 0.127635103 0.063817552 0.031908776 0.07021059 5.312512364 2.656256182 1.328128091 0.20173488 3.2016018 1.6008009 0.80040045 0.51447138 1.329230705 0.664615352 0.332307676 0.73889691 0.605193721 0.30259686 0.15129843 0.1535534 3.747413771 1.873706886 0.936853443 0.11885466 4.259707671 2.129853835 1.064926918 0.92109534 0.164383471 0.082191735 0.041095868 0.74612934 0.585712627 0.292856314 0.146428157 0.11096276 4.397121272 2.198560636 1.099280318 0.14292567 3.890861152 1.945430576 0.972715288

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Dept. of IE&M, DSCE, Bangalore Page 29 0.86837213 0.282269881 0.141134941 0.07056747 0.95016848 0.102231933 0.051115966 0.025557983 0.08687523 4.886564662 2.443282331 1.221641166 0.31878421 2.286481707 1.143240853 0.571620427 0.21023089 3.119097724 1.559548862 0.779774431 0.85270564 0.318681759 0.159340879 0.07967044 0.47450091 1.490983497 0.745491749 0.372745874 0.64069869 0.890392003 0.445196002 0.222598001 0.34739541 2.114583301 1.057291651 0.528645825 0.58908043 1.058385094 0.529192547 0.264596273 0.43517295 1.664023461 0.83201173 0.416005865 0.13344206 4.028175789 2.014087894 1.007043947 0.02800066 7.151054503 3.575527251 1.787763626 0.5971271 1.031250586 0.515625293 0.257812647 0.72270844 0.649498795 0.324749398 0.162374699 0.56911198 1.12735612 0.56367806 0.28183903 0.30782299 2.35646074 1.17823037 0.589115185 0.40621095 1.801765359 0.900882679 0.45044134 0.83066526 0.371056753 0.185528377 0.092764188 0.95793161 0.085957773 0.042978887 0.021489443 0.21657064 3.059677024 1.529838512 0.764919256 0.50232396 1.37702007 0.688510035 0.344255018 0.72944748 0.630935811 0.315467906 0.157733953

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Dept. of IE&M, DSCE, Bangalore Page 31

Problems for Practice:

1. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes. And then leaves the system. All time units are in minutes. Animate the resource and queue. Simulate the process for 20 minutes. Plot number waiting at drilling center queue and number busy at drill press. And report the following data

 The average total time in the system (part) and

 Utilization of drill press

 The last part number which entered the system

 Number of parts which leaves the system

 Average and maximum number of parts in process (wip)

 Make 5 replications of the above simulation. And observe the changes in output. Tabulate the readings.

2. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. After processing at 2 machine the part leaves the system. All time units are in minutes. Gather all statistics:

 The average total time in the system (part)

 Utilization of drill press and utilization at the second machine

 The last part number which entered the system

 Number of parts which leaves the system

 Average and maximum number of parts in process (wip)

 Time in queue, queue length.

 Animate the resource and queue.

 Plot number waiting at drilling center queue and number busy at drill press & rewash.

(40)

Dept. of IE&M, DSCE, Bangalore Page 32

3.Simulate a simple processing system in which The part enters the system with a random exponential value of 5 minutes. The part moves to a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; queuing is possible at inspection, and the queue is first in and first out. All parts exit the system regardless of whether they pass the test. All time units are in minutes.

Gather all statistics:

 The average total time in the system (part)

 Utilization of drill press, at second machine, at inspection center

 The last part number which entered the system

 Count number that fail and number that pass

 Average and maximum number of parts in process (wip)

 Time in queue, queue length.

 Animate the resource and queue.

 Add plots to track the queue length and number busy at all three stations.

 Run the simulation for 480 minutes

4. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; queuing is possible at inspection, and the queue is first in and first out. The parts that fail inspection after being washed are sent back and rewashed, instead of leaving; such re-washed parts must then undergo the same inspection, and have the same probability of failing. There’s no limit on how many times a given part might have to loop back through the washer. All parts exit the system regardless of whether they pass the test. All time units are in minutes.

(41)

Dept. of IE&M, DSCE, Bangalore Page 33  The average total time in the system (part)

 Utilization of drill press, at second machine, at inspection center

 The last part number which entered the system

 Count number that fail and number that pass

 Average and maximum number of parts in process (wip)

 Time in queue, queue length.

 Animate the resource and queue.

 Add plots to track the queue length and number busy at all three stations.

 Run the simulation for 480 minutes

5. Simulate a simple processing system in which the part enters the system with a random exponential value of 5 minutes. The part moves to the drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and queuing is possible at inspection, and the queue is first in and first out. The inspection can result in one of the three outcomes; pass (probability 0.8) fail (probability 0.09) and rewash (probability 0.11). Failures leave immediately, and rewashes loop back to the washer. The above probabilities hold for each part undergoing inspection, regardless of its past history. All time units are in minutes.

Gather all statistics:

 The average total time in the system (part)

 Utilization of drill press, at second machine, at inspection center

 The last part number which entered the system

 Count number that fail and number that pass

 Average and maximum number of parts in process (wip)

 Time in queue, queue length.

 Animate the resource and queue.

 Add plots to track the queue length and number busy at all three stations. Run the simulation for 480 minutes

(42)

Dept. of IE&M, DSCE, Bangalore Page 34

1. Define simulation. When is simulation the appropriate tool? 2. What are the advantages and disadvantages of simulation? 3. List the areas of applications of simulation.

4. What is a system?, and what is a model of a system? 5. Discuss the various types of models with examples. 6. What are the steps in a simulation study?

7. Name several entities, attributes, activities, events and state variables for the following systems: Cafeteria, Automobile assembly line, Grocery store, Hospital emergency room. 8. Differentiate between continuous and discrete systems.

9. What is pmf, pdf and cdf in probability distributions? 10. What are the characteristics of queuing systems?

11. List some simulation packages & briefly explain their applications. 12. What are the various methods of generation of random numbers? 13. What is Monte Carlo Simulation?

14. What are the various tests for random numbers? 15. What are the properties of randomness?

16. What are the four steps in the development of a useful model for input data?

17. What are the ways to obtain information about a process even if data are not available? 18. What are verification and validation of simulation models?

19. What are the various models of manufacturing and material handling systems? 20. How does this Simulation lab help you in your professional career?

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