Layout 1

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  • 12

    Layout - Definition

    Layout: the physical arrangement of machines, equipment, workstations, people, and material handling equipment.

    The final layout plan is the end result of Facilities Design.

  • 2

    What is Facility Layout?

    Location or arrangement of everything within & around buildings

    Objectives are to maximize Customer satisfaction Utilization of space, equipment, & people Efficient flow of information, material, & people Employee morale & safety

    Objectives of Facility Layout

    Minimize investment in equipment.

    Minimize production time.

    Minimize material handling cost.

    Maximize utilization of space, equipment, & people

    Maintain flexibility of arrangement and operation.

    Provide safety and comfort to employees.

    Customer satisfaction

    Efficient flow of information, material, & people

  • 3

    Five Types of Facility Design Projects

    1. New Facility fewer restrictions and constraints on the layout since it is new

    2. New Product integration of a new product into the existing process and layout

    3. Design Changes incorporate the impact of design changes into the manufacturing process

    4. Cost Reduction redesign the existing layout to facilitate cost reduction programs and ideas

    5. Retrofit similar to a new facility layout except with the constraints present ( )

    Facility Layout

    A Layout problem may be to determine the location for a new machine, develop a new layout for an existing production plant, develop a layout for a new production plant, etc.

    A Layout problem may arises due to changes in the design of a product, addition or deletion of a product, change in the demand of a product, changes in the design of the process, addition or deletion of a process, replacement of equipment, etc.

  • 4

    Layout

    Developing the layout is an important step it serves to establish the physical relationships between activities.

    So, which comes first, the material handling system or the facility layout? Our answer is, "Both!" The layout and the handling system should be designed simultaneously,

    Layout

    The complexity of the design problem generally requires that a sequential process be used. For this reason, we recommend that a number of alternative handling systems be developed and the appropriate layout be designed for each.

  • 5

    Impact of Poor Plant Layout

    High material handling costs Cycle and lead time delays High WIP inventories Lower quality Product damage Safety and morale problems Poor equipment utilization Congested aisles Wasted floor space

    Basic Layout Types

    1. Fixed material location departments - Fixed product layouts

    2. Production line departments - Product layouts3. Product family departments - Product family layouts4. Process departments - Process layout5. Hybrid - Mass Customization Layout

  • 6

    Layout Procedures

    Two different categories:

    1. Construction - involves developing a new layout "from scratch

    2. Improvement - generate layout alternatives based on an existing layout

    Layout Procedures

    Appless Plant Layout Procedure(20 steps procedure)

    Reeds Plant Layout Procedure(10 steps procedure)

    Layout Planning Chart

  • 7Apples Plant Layout Procedure

    Apple recommended that the following detailed sequence of steps be used in designing a plant layout.

    1. Procure the basic data. 11. Determine storage requirements

    2. Analyze the basic data. 12. Plan service and auxiliary activities.

    3. Design the productive process. 13. Determine space requirements.

    4. Plan the material flow pattern. 14. Allocate activities to total space.

    5. Consider the general material handling plan. 15. Consider building type

    6. Calculate equipment requirements. 16. Consider master layouts.

    7. Plan individual work stations. 17. Evaluate, adjust and check the layout.

    8. Select specific material handling equipment. 18. Obtain approval.

    9. Coordinate groups of related operations. 19. Install the layout.

    10. Design activity relationships. 20. Follow up on implementation of the layout.

    Reeds Plant Layout Procedure

    In planning for and preparing the layout, Reed recommended that the following steps be taken in his systematic plan of attach:

    1. Analyze the product to be produced.

    2. Determine the process required to manufacture the product.

    3. Prepare layout planning charts.

    4. Determine work stations.

    5. Analyze storage area requirements.

    6. Establish minimum aisle widths.

    7. Establish office requirements.

    8. Consider personnel facilities and services.

    9. Survey plant services.

    10. Provide for future expansion.

  • 8

    Algorithmic Approaches

    1. Relationship Diagramming - for new layouts

    2. Pair-wise Exchange Method- for layout improvements

    3. Graph-Based Construction Method - for new layouts

    Muthers Systematic Layout Planning Procedure (SLP)

    1. It uses as its foundation the activity relationship chart,

    2. A material flow analysis (From-to-chart) and an activity relationship analysis (REL chart) are performed

    3. Relationship diagram is developed4. Determine the amount of space to be

    assigned each activity (use departmental service and area requirement sheets)

    5. Space templates are developed for each planning department this leads to the space relationship diagram

    6. Layout alternatives are developed

  • 9Product LayoutProduct Layout

    Input Data and Activities

    1, Flow of Materials 2, Activity Relationships

    3, Relationship Diagram

    4, Space Requirements 5, Space Available

    6, Space Relationship Diagram

    7, Modifying Considerations 8, Practical Limitations

    9, Develop Layout Alternatives

    10, Evaluation

    Anal

    ysis

    Sear

    chSe

    lect

    ion

    Input Data/ActivitiesInput Data/Activities

    The first step of SLP is to gather information about the building including how it will be used and what flows will be occurring.

    Product: What is being used/moved/created?Quantity: What volume of materials/people/

    machines?Routing: Where are things being moved?Support: What equipment and systems are needed

    to support main operations?Timing: When will activities occur?

  • 10

    Sources for Data:Sources for Data:

    Most of the information concerning the types of parts and assemblies that will produced will come from documents that you learned about in PP&S design. These documents include: Parts Lists Bill of Material Process Flow Chart Process Map Routing Sheets Assembly Chart Operations Process Chart Assembly Precedence Diagram Production Schedule

    Traditional Layout Configuration

    An Activity Relationship Diagram is developed from information in the activity relation chart, Essentially the relationship diagram is a block diagram of the various areas to be placed into the layout,

    The departments are shown linked together by a number of lines, The total number of lines joining departments reflects the strength of the relationship between the departments, e,g,, four joining lines indicate a need to have two departments located close together, whereas one line indicates a low priority on placing the departments adjacent to each other,

    The next step is to combine the relationship diagram with departmental space requirements to form a Space Relationship Diagram, Here, the blocks are scaled to reflect space needs while still maintaining the same relative placement in the layout,

    A Block Plan represents the final layout based on activity relationship information, If the layout is for an existing facility, the block plan may have to be modified to fit the building, In the case of a new facility, the shape of the building will confirm to layout requirements,

    A Rating

    E Rating

    I Rating

    O Rating

    U Rating

    X Rating

    Legend

  • 11

    Example 1

    Code Reason

    1 Flow of material2 Ease of supervision3 Common personnel4 Contact Necessary5 Conveniences

    Rating Definition

    A Absolutely NecessaryE Especially ImportantI ImportantO Ordinary Closeness OKU UnimportantX Undesirable

    1, Offices (1000)

    2, Foreman (125)

    3, Conference Room (125)

    4, Parcel Post (350)

    5, Parts Shipment (500)

    6, Repair and Service Parts(75)

    7, Service Areas (575)

    8, Receiving (200)

    9, Testing (900)

    10, General Storage (1750)

    O4I5U

    U

    U

    E3U

    U

    E3

    E5O4U

    O4U

    U

    E3A1

    O3I2U

    U

    U

    I4

    U

    U

    I2U

    U

    U

    U

    U

    I2U

    U

    A1

    U

    O2U

    I1

    U

    I2U

    U

    I2

    U

    REL chart:

    Example 1 (Cont,)

    10

    5 8 7

    9 6

    4 2 3

    1Activity Relationship

    Diagram

  • 12

    Example (Cont,)

    2(125)

    Space RelationshipDiagram

    3(125)

    1(1000)

    4(350)

    6(75)

    9(500)

    10(1750)

    5(500)

    8(200)

    7(575)

    Example (Cont,)

    Alternative 1

    2(125)

    3(125)

    1(1000)

    4(350)

    6(75)

    9(500)

    10(1750)

    5(500)

    8(200)

    7(575)

    Alternative 2

    2 (125) 3 (125)

    1(1000)4

    (350)

    6(75)

    9(500)

    10(1750)

    5(500)

    8(200)

    7(575)

  • 13

    10

    Systematic Layout PlanningExample 2: Reasons for Closeness

    Code

    1

    2

    3

    4

    5

    6

    Reason

    Type of customer

    Ease of supervision

    Common personnel

    Contact necessary

    Share same price

    Psychology

    11

    Systematic Layout Planning--Example (Importance of Closeness)

    Value

    A

    E

    I

    O

    U

    X

    Closeness LinecodeNumerical

    weightsAbsolutely necessary

    Especially important

    Important

    Ordinary closeness OK

    Unimportant

    Undesirable

    16

    8

    4

    2

    0

    -16

  • 14

    12

    Systematic Layout Planning--ExampleRelating Reasons and Importance

    From

    1, Credit department

    2, Toy department

    3, Adult books department

    4, Camera department

    5, Candy department

    6I

    --U

    4A

    --U

    --U

    1I

    1,6A

    --U

    1X

    1X

    To2 3 4 5

    Area(sq, ft,)

    100

    400

    300

    100

    100

    Letter

    Number

    Closeness rating

    Reason for rating

    13

    Systematic Layout Planning--Example

    Initial Relationship Diagram

    1

    2

    4

    3

    5

    U U

    E

    A

    I

  • 15

    14

    Systematic Layout Planning--Example

    Initial and Final Layouts

    1

    2 4

    3

    5

    Initial Layout

    Ignoring space andbuilding constraints

    2

    5 1 43

    50 ft

    20 ft

    Final Layout

    Adjusted by squarefootage and buildingsize

    Relationship Diagramming

    - Group Relationships1st level: A-E-I-O-U-X2nd level: AA, AE, A*,

    EE, EI, E*, II, I*,3rd Level, AAA, AAE,

    AA*, AEE, AE*,4th level,,,- The question to be

    answer is which department to be entered next,

    1, Offices (1000)

    2, Foreman (125)

    3, Conference Room (125)

    4, Parcel Post (350)

    5, Parts Shipment (500)

    6, Repair and Service Parts(75)

    7, Service Areas (575)

    8, Receiving (200)

    9, Testing (900)

    10, General Storage (1750)

    O4I5U

    U

    U

    E3U

    U

    E3

    E5O4U

    O4U

    U

    E3A1

    O3I2U

    U

    U

    I4

    U

    U

    I2U

    U

    U

    U

    U

    I2U

    U

    A1

    U

    O2U

    I1

    U

    I2U

    U

    I2

    U

    REL chart:

  • 16

    Relationship Diagramming

    - The 1st department to enter is 10- The 2nd one is the one that has the

    highest rate with 10 (5 and 8) are candidates, 5 enters since there is an I relationship with 2

    - The 3rd one

    is 8 with the highest rate of AU- The 4th one is 9

    1 2 3 4

    10 U I U I

    5 U I U U

    10

    5

    9

    8 6 7 9

    A U U E

    U U U U

    10 5

    10 8

    1 2 3 4

    10 U I U I

    8 U O U U

    5 U I U U

    6 7 9

    U U E

    U U U

    U U U

    5 10 8

    Relationship Diagramming

    - The 5th one to enter is 7

    - The 6th on to enter is 6

    - The 7th one to enter is 2

    - The 8th one to enter is 3

    - The 9th one to enter is 1

    - The 10th one to enter is 4

    7

    3

    9

    5 10 8

    7

    62

    9

    5 10 8

    7

    62

    9

    5 10 8

    4

    1

    3

    7

    62

    9

    5 10 8

  • 17

    - If the space impact is included the following could be an alternative layout

    Relationship Diagramming

    2 (125)

    1(1000)

    4(350)

    3 (125)

    6(75)

    9(500)

    10(1750)

    5(500)

    8(200)

    7(575)

    4

    1

    3

    7

    62

    9

    5 10 8

    9(500)

    Relationship Diagramming

    Final alternative

    1(1000)

    4(350)

    6(75)

    5(500)

    8(200)

    7(575)

    10(1750)

    2 (125)

    3 (125)

  • 18

    Graph-based Approach

    Keys: A node (O) represents a department An arc ( ___ ) represent a relationship

    A weight is assigned to each relationship (Closeness Rating Rel-Chart): Rules:

    No arc intersection is allowed Dimensional specifications are not considered The scores are very sensitive to the numerical weights assigned The scores do not represents distances

    Graph-Based Construction Method

    Directors Conference Room

    President

    Sales

    Personnel

    Plant manager

    23

    4

    5

    2

    1

    3

    4

    5

    9

    12

    1

    20

    2

    8

    10

    0137

    0

    Given the relationship chart

  • 19

    Graph-Based Construction Method

    Strategy: iteration is based on inserting a new node Step -1: Largest weight-pair departments

    Step -2: Largest weight-pair departments with respect to 3-4

    3 420

    2

    3 4

    13

    20

    12

    3 4 Total

    1 8 10 18

    2 12 13 25(Best)

    5 0 2 2

    Graph-Based Construction Method

    2

    3 4

    13

    20

    12

    2 3 4 Total

    1 9 8 10 27(Best)

    5 7 0 9 161

    108

    9

    Step-3

  • 20

    Graph-Based Step 42

    3 4

    13

    20

    12

    1 2 3 45 0 7 0 2

    1108

    9Faces Total

    1-2-3 71-2-4 9

    (best)1-3-4 22-3-4 9

    (best)

    50

    7

    2

    Adjacency Graphs Version A

    2

    3

    4

    5

    10

    2

    7

    9

    13

    20

    12

    Arc Weight1-2 91-5 02-3 122-4 132-5 73-4 204-5 2

    Total 63

  • 21

    Adjacency Graphs Version B

    1

    2

    3

    5

    4

    0

    10

    7

    9

    13

    20

    12

    Arc Weight1-5 02-5 71-2 91-4 102-4 132-3 123-4 20

    Total 71

    Block Layout From The Final Adjacency Graphs

    2

    34

    518

    0

    79

    13

    20

    12Arc Weight

    1-2 91-3 81-4 10

    1-5 02-3 122-4 13

    2-5 73-4 20

    4-5 2

    Total 81

    102

  • 22

    Pair-wise exchange method

    Improvement: redesign of an existing facility ( new machine, expansion of storage,

    Objective: Minimize the total cost of MH

    Min MH cost

    X=Number of moves C: cost of a move

    Procedure: Example: ( 4 departments with equal

    size) Existing layout and

    n

    i

    n

    jijijCXz

    1 1min

    1 3 42

    1 2 3 4

    1 - 10 15 20

    2 - 10 5

    3 - 5

    4 -

    Xij

    Pair-wise exchange method Develop the cost matrix

    Calculate the total cost

    TC= (10) ($1)+ (15)(2) +(20)(3)+ (10)(1)+(5)(2)+(5)(1)= $125

    Feasible alternatives (1-2), (1-3), (1-4), (2-3), 2-4), (3-4) because all the

    departments are equal in areas Check each alternatives

    Alternative 1 exchange 1 by 2 The layout will be

    The Cost matrix will be -------------

    1 3 42 1 2 3 41 - 1 2 3

    2 - 1 2

    3 - 1

    4 -

    Cij

    4

    1

    4

    1i jijijCXTotalCost

    2 3 41

    1 2 3 4

    1 - 1 1 2

    2 - 2 3

    3 - 1

    4 -

    Cij

  • 23

    Pair-wise exchange method TC1234 = 125 (existing layout cost) TC2134 = (10)(1)+(15)(1)+(20)(2)+(10)(2)+(5)(3)+(5)(1) =105 TC3214 = 95 Feasible exchange pair is 1-3 TC4231 = 120 TC1432 = 105 TC1324 = 120 TC1243 = 125Iteration 1 leads to the following layout Iteration 2 TC3214 = 95 (1st iteration layout cost) TC1234 = 125 TC3241 = 110 TC2314 = 90 Feasible exchange pair is 2-3 TCIteration 2 leads to the following layout

    3 1 42

    2 1 43

    SLP Example

    XYZ inc, has a facility with 6 depts, (A,B, C, D, E, and F), A summary of the processing sequence for 10 products and the weekly production forecasts for the products, and areas are given in the tables below:

    products Processing Seq,

    Weekly Production

    1 ABCDEF 960

    2 ABCBEDCF 1,200

    3 ABCDEF 720

    4 ABCEBCF 2,400

    5 ACEF 1,800

    6 ABCDEF 480

    7 ABDECBF 2,400

    8 ABDECBF 3,000

    9 ABCDF 960

    10 ABDEF 1,200

    Dimension(ft*ft)

    A 40 x 40

    B 45 x 45

    C 30 x 30

    D 50 x 50

    E 60 x 60

    F 50 x 50

    1. F To Chart2. Block laying diagramming using SLP3. Developing a block laying using

    Relationship diagramming

  • 24

    a)Construct the F T ChartA B C D E F

    A X 13,320 1,800 0 0 0

    B 0 X 11,400 6,600 4,920 5,400

    C 0 6,600 X 2,400 4,200 3,600

    D 0 3,000 1,200 X 5,040 960

    E 0 5,400 7,800 1,200 X 5,160

    F 0 0 0 0 0 X

    A-B = 960 + 1,200 + 720 + 2,400 + 480 + 2,400 + 3,000 + 960 + 1,200

    = 13,320B-A = 0B-C = 960 + 1,200 + 720 + 2,400 + 480 + 960 = 11,400C-B = 1,200 + 2,400 + 3,000 = 6,600

    Since we dont have the Rel chart we base our closeness rating on material flow information,

    A B C D E F

    A X 13,320 1,800 0 0 0

    B X 18,000 9,600 10,320 5,400

    C X 3,600 12,000 3,600

    D X 6,240 960

    E X 5,160

    F X

    AB = A-B + B-ABC= B-C+C-B....

    18,000, 13,320 12,000, 10,320, 9,600 6,240, 5,400, 5,160

    3,600 1,800, 960, 0, 0, 0

    A E I

    O

    U

    Rel. Chart: A E I O U

    AA BB CC DD EE FF

    AA - A U U U U

    BB - A E E I

    CC - O E O

    DD - I U

    EE - I

    FF -

    Rank and Code

    U

    A

    A

    O

    I

    I

    O

    I

    U

    U

    E

    E

    U

    E

    U

    A

    B

    F

    E

    D

    C

  • 25

    B C

    A B C

    A B C

    E

    B

    A B C

    ED

    A B C

    ED

    F

    U

    A

    A

    O

    I

    I

    O

    I

    U

    U

    E

    E

    U

    E

    U

    A

    B

    F

    E

    D

    C

    1st to enter is B (two As)

    2nd to enter is C (E & O)

    3rd to enter is A (A effect)

    DE F

    A U U U

    B E E I

    C O E O

    4th to enter is E

    D F

    A U U

    B E I

    C O O

    E I I

    5th to enter is D

    6th to enter is F

    B

    A

    F

    ED

    CB

    A

    E U

    I

    O

    Relationship Diagram

    F

    CBE

    D

    A AO

    I

    A

    I

    E EU E

    Block Diagram

    FC

    ED

    A

  • 26

    Given:4-equal size departments are Served by an AGV on a Linear bidirectional trackAs shown. Each machine blockIs 30X30 ft. The product routine Information and required productionAre given. Determine arrangement based on the pairwise exchange method. Assume P/D point as shown in the figure.

    1 BDCAC 300

    2 BDAC 700

    3 DBDCAC 900

    4 ABCA 200

    Pairwise Exchange Example

    B C DA

    Pair-wise Exchange Example

    A B C D

    A - 30 45 75

    B - 15 45

    C - 30

    D -

    A B C D

    A - 200 3300 700

    B - 200 2800

    C - 1200

    D -

    Arrangement/CostsABCD = 200 30 + 3,300 45 + 700 75 + 200 15 + 2,800 45 + 1,200 30 = 372,000BACD = 342,000

    A C DB

    CBAD = 507,000DBCA = 435,000ABCD = 372,000

    CABD = 351,000

    DACB = 468,000Find Arrangement BACD

  • 27

    Graph-based Approach Example

    The ABC cooling and heating company manufactures several different types of air conditioners. 5 departments are involved in the processing required for the products. A summary of the processing sequence required for the 5 major products and weekly production volumes for the products are shown in the table below along with the department area. Based on the graph-based approach construction method, develop a block layout

    Product Process sequence

    WeeklyProduction

    Department Area

    1 ABC 150 A 1500

    2 ABED 200 B 1500

    3 ACE 50 C 1000

    4 ACBE 200 D 2000

    5 ADE 250 E 2000

    Graph-based Approach Example

    Solution:a) Construct flow between departments A-B = 150 + 200 =350B-A= 0AB= A-B +B-A =350A-C= 50 +200 =250C-A = 0=================================b) Weights = flow

    1) the largest weight is for the 2 depts. D and E.2) the 3rd department to enter is B3) the 4th department to enter is A

    4) the 5th department to enter is C but where?.

    Dept A B

    A - 350

    B - -

    C

    D

    E

    C D E

    250 250 0

    350 0 400

    - 0 50

    - 450

    -

    D E Total

    A 250 0 250

    B 0 400 400

    C 0 50 50

    D E B Total

    A 250 0 350 600

    C 0 50 350 400

    A D E Total

    C 250 0 50 300

    A D B Total

    C 250 0 350 600

    A E B Total

    C 250 50 350 650

  • 28

    Graph-based Approach Example

    Adjacency Graph

    Block Layout

    D

    C

    A

    E B

    D

    C A

    B

    E

    Changes in the products Changes in design of product

    Eliminating products from the product line

    Introduction of new products

    Changes in the processes Change in sequence for existing products

    Replacement of equipment

    Changes in production quantities and

    schedule

    Changes in organizational structure (selected Mfg system)

    Need For Change

  • 29

    Impact of Changes

    Expansion Mirror image expansion: simple, free

    of bottlenecks and limited to one time expansion

    Straight line flow expansion: Unlimited, simple, low add on cost building but hard to selectively expand some departments

    T-shape expansion U-Shape expansion

    Computer Aided Layout

    Enhance productivity & Quality of Solution Can not Replace human Judgment Types of Algorithms

    Type of Input Data Qualitative Data- REL Chart Quantitative Data F-T chart

    Objectives: Minimizing the sum of flow times distance (Distance-Based Approach) Maximizing an adjacency score (Adjacency-Based Approach)

  • 30

    Computer Aided Layout

    a) Distance-Based Approachf: flow number between i and j

    d: distance from i and jc: cost of moving one unit from i to ji and j: departments n: number of departments

    b) Adjacency-Based Approach1) Z= adjacent score

    f: flow number between i and j

    x: adjacency score= 1 if i and j are adjacent= 0 otherwise

    n

    jijijij

    n

    icdfMinZ

    11

    n

    i

    n

    jijij xfMaxZ

    1 1

    Computer Aided Layout

    b) Distance-Based Approach2) Z* = Relative efficiency or Efficiency

    rating0 < Z* < 1

    as Z* 1 all the departments are adjacentCij = 1 for the same MH equipment

    3) Z^ = Relative efficiency or Efficiency rating for ve values of relationships Cij = 1 for the same MH equipment+F: positive Rel. group of Depts.- F: negative Rel. group of Depts.

    n

    i

    n

    jij

    n

    i

    n

    jijij fxfMax

    1 11 1/*

    n

    i

    n

    jFij

    n

    i

    n

    jFij

    n

    i

    n

    jFijij

    n

    i

    n

    jFijij ffxfxfMax

    1 11 11 11 1)/())1((^

  • 31

    Computer Aided Layout

    1 2 3 4 5

    1 - 1 1 0 0

    2 - 1 0 0

    3 - 1 1

    4 - 1

    5 -

    Example: Given the flow no. between departments and the first iteration layout, find the relative adjacency score.

    Solutiona) identify the adjacency matrix

    12

    45

    3

    1 2 3 4 5

    1 - 5 0 4 -3

    2 - 6 -1 2

    3 - -6 0

    4 - 3

    5 -

    Computer Aided Layout

    1 2 3 4 5

    1 - 1 1 0 0

    2 - 1 0 0

    3 - 1 1

    4 - 1

    5 -

    1 2 3 4 5

    1 - 5 0 4 -3

    2 - 6 -1 2

    3 - -6 0

    4 - 3

    5 -

    b) Calculate Z*= 5 +0+4-3+6-1+2-6+0+3 = 10

    = f12*X12 + f13*X13 + f14*X14 +f15*X15 + f23*X23 + f24*X24 + f25*X25 + f34*X34 + f35*X35 + f45*X45

    = 1*5 +1*0 +4*0+ -3*0 +6*1+ -1*0 + 2*0 + -6*1 + 0*1 +3*1 = 8

    Z* = 8/10 = 0.8 close to 1 good adjacency relationships

    12

    45

    3

    n

    jijf

    1

    n

    i

    n

    jijij xf

    1 1

  • 32

    Computer Aided Layout

    1 2 3 4 5

    1 - 1 1 0 0

    2 - 1 0 0

    3 - 1 1

    4 - 1

    5 -

    1 2 3 4 5

    1 - 5 0 4 -3

    2 - 6 -1 2

    3 - -6 0

    4 - 3

    5 -

    n

    jijf

    1

    c) Calculate Z^(+ve) = 5 +0+4+6+2+0+3 = 20(-ve) = -3-1-6 = -10

    (+ve) = f12*X12 + f13*X13 +f14*X14 + f23*X23 + f25*X25 + f35*X35 + f45*X45

    = 1*5 +1*0 +4*0+ 6*1+ 2*0 + 0*1 + 3*1= 14

    (-ve) = f15*X15 + f24*X24 + f34*X34= -3*1 +-1*1 + -6*0= -4

    Z^ = (14- (-4))/(20 (-10)) = 0.6 Not close to 1 good adjacency relationships

    12

    45

    3 n

    i

    n

    jijij xf

    1 1

    F (-ve): (1,5), (2,4), (3,4)

    F (+ve): the restn

    jijf

    1

    n

    i

    n

    jijij xf

    1 1

    Computer Aided Layout

    Layout Representation Format

    Discrete: - Area of each department is rounded to the

    nearest integer - Grid size affects the resolution and the

    computation time

    Continuous- No grid - More difficult - Restricted to rectangular shape