ams - hollier mehods

Group Technology Group Technology and Cellular and Cellular

ManufacturingManufacturing

What is Group Technology What is Group Technology (GT)(GT)??

GT is a theory of management based on GT is a theory of management based on the principle that similar things should be the principle that similar things should be done similarlydone similarly

GT is the realization that many problems GT is the realization that many problems are similar, and that by grouping similar are similar, and that by grouping similar problems, a single solution can be found to problems, a single solution can be found to a set of problems thus saving time and a set of problems thus saving time and efforteffort

GT is a manufacturing philosophy in which GT is a manufacturing philosophy in which similar parts are identified and grouped similar parts are identified and grouped together to take advantage of their together to take advantage of their similarities in design and productionsimilarities in design and production

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Implementing GTImplementing GT

Where to implement GT?Where to implement GT? „„Plants using traditional batch Plants using traditional batch

production and „process type layoutproduction and „process type layout „ „ If the parts can be grouped into part If the parts can be grouped into part

familiesfamilies

„„How to implement GT?How to implement GT? „„Identify part familiesIdentify part families „„Rearrange production machines into Rearrange production machines into

machine cellsmachine cells

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Types of LayoutTypes of LayoutIn most of today’s factories it is possible to divide all the made components into families and all the machines into groups, in such a way that all the parts in each family can be completely processed in one group only.

The three main types of layout are:

• Line (product) Layout

• Functional Layout

• Group Layout44

LineLine (product) (product) Layout Layout•It involves the arrangements of machines in one line, depending on the sequence of operations. In product layout, if there is a more than one line of production, there are as many lines of machines.

•Line Layout is used at present in simple process industries, in continuous assembly, and for mass production of components required in very large quantities.

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Functional LayoutFunctional Layout•In Functional Layout, all machines of the same type are laid out together in the same section under the same foreman. Each foreman and his team of workers specialize in one process and work independently. This type of layout is based on process specialization.

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Group LayoutGroup Layout

•In Group Layout, each foreman and his team specialize in the production of one list of parts and co-operate in the completion of common task. This type of layouts based on component specialization.

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The Difference between group and functional The Difference between group and functional layoutlayout::

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Large manufacturing system can Large manufacturing system can be decomposed into smaller be decomposed into smaller subsystems of part families based subsystems of part families based on similarities inon similarities in

1. 1. design attributesdesign attributes and and 2. 2. manufacturing manufacturing

featuresfeatures99

Identifying Part Identifying Part FamiliesFamilies

Design Attributes:Design Attributes: part configuration part configuration (round or (round or

prismatic)prismatic) dimensional envelope dimensional envelope (length to (length to

diameter ratio)diameter ratio) surface integrity surface integrity (surface roughness, (surface roughness,

dimensional tolerances) dimensional tolerances) material typematerial type raw material state raw material state (casting, forging, (casting, forging,

bar stock, etc.)bar stock, etc.) 1010


Part Manufacturing Features:Part Manufacturing Features: operations and operation sequences operations and operation sequences

(turning, milling, etc.)(turning, milling, etc.) batch sizesbatch sizes machine toolsmachine tools cutting toolscutting tools work holding deviceswork holding devices processing timesprocessing times

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Group technologyGroup technology emphasis emphasis on part families based on on part families based on similarities in design similarities in design attributes and manufacturing, attributes and manufacturing, therefore therefore GTGT contributes to contributes to the integration of CAD and the integration of CAD and CAM. CAM.

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Part FamiliesPart FamiliesA part family is a collection having similar:

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Three methods for identifying parts families

• Visual inspection

• Classification and coding

• Production flow analysis

Forming Part Families –Forming Part Families –1. Visual Inspection Method1. Visual Inspection Method

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incorrect resultsincorrect resultshuman errorhuman errordifferent judgment by different different judgment by different

peoplepeopleinexpensive inexpensive least sophisticatedleast sophisticatedgood for small companies having good for small companies having

smaller number of partssmaller number of parts1515

Forming Part Families –Forming Part Families –1. Visual Inspection Method1. Visual Inspection Method

Forming Part Families –Forming Part Families –2. Classification and Coding2. Classification and Coding

Coding:Coding: The process of assigning symbols to The process of assigning symbols to

the parts. Where the symbols the parts. Where the symbols represent design attributes of parts, represent design attributes of parts, manufacturing features of parts, or manufacturing features of parts, or both both

Classification:Classification: „„The process of categorization of a set The process of categorization of a set

of parts into part familiesof parts into part families1616

A GT code is a string of characters A GT code is a string of characters capturing information about an item capturing information about an item

Three main types of coding systems Three main types of coding systems structure: structure:

„„Mono-code or hierarchical structure Mono-code or hierarchical structure „„Poly-code, or chain-type structurePoly-code, or chain-type structure „„Mixed-mode structureMixed-mode structure

Forming Part Families –Forming Part Families –Classification and CodingClassification and Coding

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Mono-codeMono-code

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A monocodeA monocode (hierarchical code) (hierarchical code) provides a large amount of provides a large amount of information in a relatively small information in a relatively small number of digitsnumber of digits

Useful for storage and retrieval of Useful for storage and retrieval of design-related information such as design-related information such as part geometry, material, sizepart geometry, material, size, , etc.etc.

it is difficult to capture information it is difficult to capture information on manufacturing sequences in on manufacturing sequences in hierarchical manner, so applicability hierarchical manner, so applicability of this code in manufacturing is of this code in manufacturing is rather limited rather limited

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Mono-codeMono-code

Poly-codePoly-code

The code symbols are independent of each The code symbols are independent of each otherother

Each digit in specific location of the code Each digit in specific location of the code describes a unique property of the work describes a unique property of the work piecepiece– it is easy to learn and useful in it is easy to learn and useful in

manufacturing situations where the manufacturing situations where the manufacturing process have to be manufacturing process have to be describeddescribed

– the length of a poly-code may become the length of a poly-code may become excessive because of its unlimited excessive because of its unlimited combinational featurescombinational features

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PolycodePolycode

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PolycodePolycode

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[[Mixed-modeMixed-mode ] ]The OPITZ The OPITZ classification systemclassification system::

it is a it is a mixedmixed (hybrid) coding system (hybrid) coding system developed by developed by OPTIZOPTIZ, Technical , Technical

University of Aachen, 1970University of Aachen, 1970 it is widely used in industryit is widely used in industry it provides a basic framework for it provides a basic framework for

understanding the classification and understanding the classification and coding processcoding process

it can be applied to machined parts, it can be applied to machined parts, non-machined parts (both formed and non-machined parts (both formed and cast) and purchased partscast) and purchased parts

it considers both it considers both designdesign and and manufacturingmanufacturing information information 2323

Mixed-modeMixed-mode

Form code:

„ Focus on part geometry dimensions and features relevant to part design

Supplementary code

„ Includes information relevant to manufacturing, such as raw material, tolerance, and surface roughness

Secondary code

„ Intended to identify the production operation type and sequence.

„ It can be designed by the user firm to serve its own needs 2424

Basic Structure of the OPTIZBasic Structure of the OPTIZ

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Basic Structure of the OPTIZ Basic Structure of the OPTIZ SystemSystem

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Form Code (digits 1 – 5)Form Code (digits 1 – 5)

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Example: Optiz part coding System• Given the rotational part design below, determine the form

code in the Optiz parts classification and coding system.

Solution• Length-to-diameter ratio: L/D = 1.5 Digit 1

= 1

• External shape: both ends stepped with screw thread on one endDigit 2 = 5

• Internal shape: part contains a through hole Digit 3 = 1

• Plane surface machining: none Digit 4 = 0

• Auxiliary holes, gear teeth, etc.: none Digit 5 = 0

The form code in the Optiz system is 15100

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ExampleExample

Part class:Part class:Rotational part, L/D = 9.9/4.8 ≈ 2.0 based on the pitch �Rotational part, L/D = 9.9/4.8 ≈ 2.0 based on the pitch �

circle diameter of the gear, so the first digit = 1circle diameter of the gear, so the first digit = 1 ��External shape:External shape:The part is stepped on one side with a functional groove, The part is stepped on one side with a functional groove,

so the second digit is 3so the second digit is 3 Internal shape:Internal shape: The third digit is 1 because of the through holeThe third digit is 1 because of the through hole ��Plain surface machining:Plain surface machining: The fourth digit is 0 because there is no plain surface �The fourth digit is 0 because there is no plain surface �

machiningmachining ��Auxiliary holes and gear teeth:Auxiliary holes and gear teeth: The fifth digit is 6 because there are spur gear teeth �The fifth digit is 6 because there are spur gear teeth �

on the parton the part 2929

Selection of Classification and Selection of Classification and Coding SystemsCoding Systems

Identified objectives, reasons and Identified objectives, reasons and usersusers

Robustness and ExpandabilityRobustness and Expandability Automation and EfficiencyAutomation and Efficiency Simplicity and User InterfaceSimplicity and User Interface CostCost

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Forming Part Families –Forming Part Families –Classification and Coding: Classification and Coding:

Production Flow Analysis (PFA)Production Flow Analysis (PFA) PFA is a method for identifying part families PFA is a method for identifying part families

and associated machine groupings based and associated machine groupings based on the required manufacturing processes on the required manufacturing processes need for each partneed for each part

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BENEFITS OF GROUP BENEFITS OF GROUP TECHNOLOGYTECHNOLOGY

It affects all areas of a company, including:It affects all areas of a company, including:

engineeringengineering equipment specification equipment specification facilities layout facilities layout process planningprocess planning production control production control quality control quality control tool design tool design purchasing purchasing serviceservice

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Cellular ManufacturingCellular Manufacturing

Cellular manufacturing �Cellular manufacturing �is an application of group technology in manufacturing in �is an application of group technology in manufacturing in �

which all or a portion of a firm’s manufacturing system has which all or a portion of a firm’s manufacturing system has been converted into cellsbeen converted into cells

A manufacturing cell �A manufacturing cell �is a cluster of machines or processes located in close proximity �is a cluster of machines or processes located in close proximity �

and dedicated to the manufacturing of a family of partsand dedicated to the manufacturing of a family of parts

��Why cellular manufacturing:Why cellular manufacturing: Reduce setup times: By using part family tooling and � �Reduce setup times: By using part family tooling and � �

sequencingsequencing Reduce flow times:By reducing setup and move times and �Reduce flow times:By reducing setup and move times and �

wait time for moves and using smaller batch sizeswait time for moves and using smaller batch sizes Reduce inventories�Reduce inventories� Reduce lead time�Reduce lead time�

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Cell DesignCell Design

Design of cellular manufacturing system Design of cellular manufacturing system is a complex exercise with broad is a complex exercise with broad implications for an organization. implications for an organization.

The The cell design processcell design process involves involves issues related to both issues related to both system system structurestructure (Structural Issues) (Structural Issues) and and system operationsystem operation (Procedures Issues) (Procedures Issues)

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StructuralStructural issues includeissues include:: Selection of part families and Selection of part families and

grouping of parts into familiesgrouping of parts into families Selection of machine and process Selection of machine and process

populations and grouping of these into populations and grouping of these into cellscells

Selection of tools, fixtures, and palletsSelection of tools, fixtures, and pallets Selection of material-handling Selection of material-handling

equipmentequipment Choice of equipment layoutChoice of equipment layout

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Procedures Issues include:Procedures Issues include: Detailed design of jobsDetailed design of jobs

Organization of supervisory and support personnelOrganization of supervisory and support personnel

Formulation of maintenance and inspection policiesFormulation of maintenance and inspection policies

Design of procedures Design of procedures for production planningfor production planning, , scheduling, controlscheduling, control, and , and acquisition of related acquisition of related software and hardwaresoftware and hardware

Modification of cost control and reward systemsModification of cost control and reward systems

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Evaluation of Cell Design Evaluation of Cell Design DecisionsDecisions

The evaluation of design decisions can The evaluation of design decisions can be categorized as related to either be categorized as related to either

the system structurethe system structure

or or the system operationthe system operation. .

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Typical considerations related to Typical considerations related to the the system structuresystem structure include: include:

Equipment and tooling investment Equipment and tooling investment (low)(low)

Equipment relocation cost (low)Equipment relocation cost (low) Material-handling costs (low)Material-handling costs (low) Floor space requirements (low)Floor space requirements (low) Extent to which parts are completed in Extent to which parts are completed in

a cell (high)a cell (high) Flexibility (high)Flexibility (high) 4646


Evaluations of cell system design are Evaluations of cell system design are incomplete unless they relate to the incomplete unless they relate to the

operation of the systemoperation of the system.. A few typical performance variables A few typical performance variables related to related to system operationsystem operation are: are:

Equipment utilization (high)Equipment utilization (high) Work-in-process inventory (low)Work-in-process inventory (low) Queue lengths at each workstation Queue lengths at each workstation

(short)(short) Job throughput time (short)Job throughput time (short) Job lateness (low)Job lateness (low) 4747

Evaluation of Cell DesignEvaluation of Cell Design

A major problem throughout the cell A major problem throughout the cell design process is the necessity of design process is the necessity of trading off against each other trading off against each other objectives related to objectives related to structural structural parametersparameters andand performance performance variablesvariables. .

For exampleFor example, higher machine utilization , higher machine utilization can be achieved if several cells route can be achieved if several cells route their parts through the same machine. their parts through the same machine. The drawbacks are The drawbacks are increased increased queuingqueuing and and control problemscontrol problems..

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Cell Formation ApproachesCell Formation Approaches

1. Machine - Component Group 1. Machine - Component Group AnalysisAnalysis::

Machine - Component Group AnalysisMachine - Component Group Analysis is based on is based on production flow production flow analysisanalysis

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Production flow analysisProduction flow analysis involves four involves four stages:stages:

Stage 1:Stage 1: Machine classificationMachine classification. .

Machines are classified on the basis Machines are classified on the basis of operations that can be performed of operations that can be performed on them. A machine type number is on them. A machine type number is assigned to machines capable of assigned to machines capable of performing similar operations.performing similar operations.

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Machine - Component Machine - Component Group AnalysisGroup Analysis

Stage 2:Stage 2: Checking parts list and Checking parts list and production route informationproduction route information..

For each part, information on the For each part, information on the operations to be undertaken and the operations to be undertaken and the machines required to perform each of machines required to perform each of these operations is checked thoroughly.these operations is checked thoroughly.

Production flow analysisProduction flow analysis involves four involves four stagesstages::

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Stage 3:Stage 3: Factory flow analysisFactory flow analysis..

This involves a micro-level This involves a micro-level examination of flow of components examination of flow of components through machines. This, in turn, through machines. This, in turn, allows the problem to be allows the problem to be decomposed into a number of decomposed into a number of machine-component groups.machine-component groups.


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Stage 4:Stage 4: Machine-component Machine-component group group analysisanalysis..

An intuitive manual method is An intuitive manual method is suggested to manipulate the matrix to suggested to manipulate the matrix to form cells. However, as the problem form cells. However, as the problem size becomes large, the manual size becomes large, the manual approach does not work. Therefore, approach does not work. Therefore, there is a need to develop analytical there is a need to develop analytical approaches to handle large problems approaches to handle large problems systematically.systematically.


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Example: Consider a problem of 4 machines Example: Consider a problem of 4 machines and 6 parts. Try to group them.and 6 parts. Try to group them.

Machines 1 2 3 4 5 6

M1 1 1 1

M2 1 1 1

M3 1 1 1

M4 1 1 1

Components

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Machines 2 4 6 1 3 5

M1 1 1 1

M2 1 1 1

M3 1 1 1

M4 1 1 1

Components

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SolutioSolutionn

Rank Order Clustering Rank Order Clustering AlgorithmAlgorithm

Rank Order Clustering AlgorithmRank Order Clustering Algorithm is a simple algorithm used to form is a simple algorithm used to form machine-part groups.machine-part groups.

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Step 1: Assign binary weight and Step 1: Assign binary weight and calculate a decimal weight for each calculate a decimal weight for each row and column using the following row and column using the following formulas:formulas:

Decimal we

Decimal we bpjn p

ight for row i = b

ight for column j =

ipm-p

p=1

m

p=1

n

2

2

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Step 2: Rank the rows in order of Step 2: Rank the rows in order of decreasing decimal weight values.decreasing decimal weight values.

Step 3: Repeat steps 1 and 2 for Step 3: Repeat steps 1 and 2 for each column.each column.

Step 4: Continue preceding steps Step 4: Continue preceding steps until there is no change in the until there is no change in the position of each element in the row position of each element in the row and the column.and the column. 5959


Example:Example:Consider a problem of 5 machines and 10 parts. Try Consider a problem of 5 machines and 10 parts. Try to group them by usingto group them by using Rank Order Clustering Rank Order Clustering Algorithm.Algorithm.

Machines 1 2 3 4 5 6 7 8 9 10

M1 1 1 1 1 1 1 1 1 1

M2 1 1 1 1 1

M3 1 1 1 1

M4 1 1 1 1 1 1

M5 1 1 1 1 1 1 1 1

Components

Table 1

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Machines 1 2 3 4 5 6 7 8 9 10 Decimalequivalent

M1 1 1 1 1 1 1 1 1 1 1007

M2 1 1 1 1 1 451

M3 1 1 1 1 568

M4 1 1 1 1 1 1 455

M5 1 1 1 1 1 1 1 1 1020

29 28 27 26 25 24 23 22 21 20Binary weight

Components

Table 2

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Binaryweight

Machines 1 2 3 4 5 6 7 8 9 10

24 M5 1 1 1 1 1 1 1 1

23 M1 1 1 1 1 1 1 1 1 1

22 M3 1 1 1 1

21 M4 1 1 1 1 1 1

20 M2 1 1 1 1 1Decimalequivalent 28 27 27 27 28 20 28 26 11 11

29 28 27 26 25 24 23 22 21 20Binary weight

Components

Table 3

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Binaryweight

Machines 1 5 7 2 3 4 8 6 9 10 Decimalequivalent

24 M5 1 1 1 1 1 1 1 1 1020

23 M1 1 1 1 1 1 1 1 1 1 1019

22 M3 1 1 1 1 900

21 M4 1 1 1 1 1 1 123

20 M2 1 1 1 1 1 115Decimalequivalent 28 28 28 27 27 27 26 20 11 11

29 28 27 26 25 24 23 22 21 20

Binary weight

Components

Table 4

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The ROC provides a simple analytical The ROC provides a simple analytical technique that can be easily technique that can be easily computerizedcomputerized

The ROC has fast convergence and The ROC has fast convergence and relatively low computation time relatively low computation time depending on the matrix sizedepending on the matrix size

The fact that ROC uses binary values The fact that ROC uses binary values will impose restrictions on the size of will impose restrictions on the size of the matrix that can be solvedthe matrix that can be solved

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Most computers have a maximum of Most computers have a maximum of 224848-1 for integer representation, which -1 for integer representation, which means that the maximum number of means that the maximum number of rows and columns is limited to 47 and rows and columns is limited to 47 and columns is limited to 47columns is limited to 47

The algorithm results depend on the The algorithm results depend on the initial matrix arrangementinitial matrix arrangement

The algorithm collects positive entries The algorithm collects positive entries (1s) in the top left-hand corner, leaving (1s) in the top left-hand corner, leaving the rest of the matrix disorganizedthe rest of the matrix disorganized

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Cluster Identification Cluster Identification Algorithm (CIA)Algorithm (CIA)

Designed to identify disconnected blocks if Designed to identify disconnected blocks if they existthey exist

If there are no disconnected blocks (the matrix If there are no disconnected blocks (the matrix is not mutually separable), the entire matrix is not mutually separable), the entire matrix will form one blockwill form one block

The algorithm begins by masking all columns The algorithm begins by masking all columns that have an entry of 1 in any row (selected that have an entry of 1 in any row (selected randomly), then all rows that have an entry of randomly), then all rows that have an entry of 1 in these columns are masked. This process is 1 in these columns are masked. This process is repeated until all intersecting columns and repeated until all intersecting columns and rows are masked.rows are masked.

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These masked columns and rows are These masked columns and rows are placed in a block and removed from the placed in a block and removed from the matrix removed from the matrix. matrix removed from the matrix.

Then the process of masking starts again Then the process of masking starts again and another block is identified. and another block is identified.

This will continue until all the entries in This will continue until all the entries in the matrix are assigned in blocks and all the matrix are assigned in blocks and all separable blocks are identified separable blocks are identified

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Cluster Identification Cluster Identification Algorithm (CIA)Algorithm (CIA)Example:

Step 1. Select any row i of the incidence matrix and draw a horizontal line hi through it.

Row 3 of the matrix is selected randomly and a horizontal line h3 is drawn.

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Step 2. For each entry of 1 crossed by the horizontal line h3

draw a vertical line vj.

Three vertical lines v2, v6, and v7 are drawn

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Step 3. For each entry of 1 crossed once by a vertical line vj

draw a horizontal line. A horizontal line h6 is drawn through all the crossed-once entries of the matrix:

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Cluster Identification Algorithm Cluster Identification Algorithm (CIA)(CIA)

Step 4. The preceding steps are repeated until no more crossed once entries are left.

• All the crossed-twice entries are grouped in a block and removed from the matrix.

•Parts 2, 6, 7 and machines 3, 6 are grouped in one block.

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Cluster Identification Algorithm Cluster Identification Algorithm (CIA)(CIA)

The grouped parts and machines are removed from the matrix

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Step 5: The above procedure is repeated for the

remaining matrix entries until all entries are grouped

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The resulting matrix is as follows:

Arranging Machines in a GT Cell

• After part-machine grouping have been identified by rank order clustering, the next problem is to organize the machines into the most logical arrangement.

• Hollier Method (I). This method uses the sums of flow “From” and “To” each machine in the cell. The method can be outlined as follows

1. Develop the From-To chart from part routing data. The data contained in the chart indicates numbers of part moves between the machines in the cell.

2. Determine the “From” and “To” sums for each machine. This is accomplished by summing all of the “From” trips and “To” trips for each machine. The “From” sum for a machine is determined by adding the entries

in the corresponding row.

The “To” sum is found by adding the entries in the corresponding column.

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3. Assign machines to the cell based on minimum “From” or “To” sums. The machine having the smallest sum is selected. If the minimum value is a “To” sum, then the machine is placed at

the beginning of the sequence.

If the minimum value is a “From” sum, then the machine is placed at the end of the sequence.

Tie breaker

If a tie occurs between minimum “To” sums or minimum “From” sums, then the machine with the minimum “From/To” ratio is selected.

If both “To” and “From” sums are equal for a selected machine, it is passed over and the machine with the next lowest sum is selected.

If a minimum “To” sum is equal to a minimum “From” sum, then both machines are selected and placed at the beginning and end of the sequence, respectively

4. Reformat the From-To chart. After each machine has been selected, restructure the From-To chart by eliminating the row and column corresponding to the selected machine and recalculate the “From” and “To” sums.

5. Repeat steps 3 and 4 until all machines have been assigned

Arranging Machines in a GT Cell

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Example of Arranging Machines in a GT Cell

• Suppose that four machines, 1, 2, 3, and 4 have been identified as belonging in a GT machine cell. An analysis of 50 parts processed on these machines has been summarized in the From-To chart presented below. Additional information is that 50 parts enter the machine grouping at machine 3, 20 parts leave after processing at machine 1, and 30 parts leave after machine 4. Determine a logical machine arrangement using Hollier method.

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• First iteration

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• Second iteration with machine 3 removed.

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• Third iteration with machine 2 removed.

• The resulting machine sequence 3 2 1 4

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• The flow diagram for machine cell in the Example is shown below. Flow of parts into and out of the cells has also been included

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Arranging Machines in a GT Arranging Machines in a GT CellCell

Hollier Method (II):Hollier Method (II):

In this method, the from-to ratio is In this method, the from-to ratio is calculated and the machines are calculated and the machines are ordered in one step: ordered in one step: machines with machines with minimum ratios are placed at the minimum ratios are placed at the endend. .

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Example Example Hollier Method (II)Hollier Method (II)::

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Evaluation of Machines Evaluation of Machines sequencesequence

Two measures are consideredTwo measures are considered

– Percentage of in-sequence between Percentage of in-sequence between adjacent moves to the total moves adjacent moves to the total moves between machines (between machines (should be highshould be high))

– Percentage of Backward moves between Percentage of Backward moves between machines to the total moves between machines to the total moves between machines (machines (should be lowshould be low) )

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Sometimes the output from Hollier Sometimes the output from Hollier Method I and (II) may be different and Method I and (II) may be different and the previous measures can be used to the previous measures can be used to select the better arrangement. select the better arrangement.

For example consider the two following For example consider the two following two arrangements which were resulted two arrangements which were resulted from method I and II respectivelyfrom method I and II respectively

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The in-sequence ratio = (75+85+70+80)/(75+85+70+80+20+10+20) =86.1% *

The Backward movement ratio = (10)/(75+85+70+80+20+10+20) =2.8% *

The in-sequence ratio = (10+85+20)/(10+85+20+80+70+75+20) =32%

The Backward movement ratio = (70)/(75+85+70+80+20+10+20) =19.4%

Machines layoutMachines layout

Arrangement 1 is preferredArrangement 1 is preferredThe layout of machines can be The layout of machines can be

organized as followsorganized as follows

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ams - hollier mehods

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