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    9-1

    Operations

    Management

    Layout StrategyChapter 9

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    Outline

    Strategic Importance of Layout Decisions.

    Fixed-Position Layout.

    Office Layout. Process-Oriented Layout (Flow graphs).

    Retail Layout.

    Warehouse Layout.

    Product-Oriented Layout (Assembly line balancing).

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    What is Facility Layout

    Location or arrangement of everythingwithin & around buildings.

    Objectives are to maximize:

    Utilization of space, equipment, & people.

    Efficient flow of information, material, & people.

    Employee morale & safety.

    Trend is towards flexible and dynamic layouts.

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    Facility Layout

    Helps achieve competitive advantage:

    Better, faster, cheaper.

    Determines productivity, cost, quality,flexibility, image, etc.

    May involve a blend of strategies.

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    Six Layout Strategies

    1. Fixed-position layout.

    For large unique projects such as ships and buildings.

    2. Office layout. Positions workers, equipment, and spaces/offices to

    provide for movement of information and material.

    3. Process-oriented layout. For low-volume, high-variety production.

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    Six Layout Strategies - continued

    4. Retail/service layout.

    Arranges facility and allocates shelf space in light ofcustomer behavior.

    5. Warehouse layout.

    Addresses trade-offs between space utilization andmaterial handling.

    6. Product-oriented layout.

    For repetitive or continuous production.

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    Layout Strategies

    Project

    (fixed-position)

    Job Shop

    (Process-oriented) Office

    Examples

    Problem

    Ingal ShipBuilding

    Pittsburgh Airport

    ShouldiceHospital

    Olive Garden

    AllstateInsurance

    Microsoft

    Move materialto limited

    storage areasat the site.

    Manage variedmaterial flow for

    each product.

    Locate workersrequiring contact

    close to eachother.

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    Layout Strategies

    RetailWarehouse

    (storage)

    Repetitive/Continuous

    (Product-oriented)

    Examples

    Problem

    Krogers

    Supermarket

    Famous-Barr

    Federal-MogulsWarehouse

    The Gaps

    distribution center

    Sonys TVAssembly Line

    DodgeCaravans

    Exposecustomer tohigh-margin

    items.

    Balance cost forstorage and

    materialhandling.

    Equalize thetask time at

    eachworkstation.

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    Requirements for a Good Layout

    Understand capacity and space requirements.

    Understand information flows.

    Understand cost of people and product flows.

    Select appropriate material handling equipment.

    Consider environment and aesthetics.Consider safety and regulations.

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    Constraints on Layout Objectives

    Product/service design.

    Volume of business.

    Process equipment & capacity.

    Quality of work life.

    Building and site.

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    1. Fixed-Position Layout

    Project is stationary.

    Special purpose: Construction, shipbuilding, etc.

    Workers and equipment come to site.Complicating factors.

    Limited space at site.

    Changing material needs.

    Unique projects.

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    2. Office Layout

    Positions people, equipment, & offices. Usually for maximum information flow.

    Also can consider material flow.

    Arranged by process or product.

    Example: Payroll dept. is by process.

    Different cultures have differentexpectations for space.

    Relationship (or proximity) chart used.

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    Relationship (Proximity) Chart

    Uses 6 levels to express desired proximity.

    A = Absolutely necessaryE = Especially important

    I = Important

    O= Ordinary importanceU = Unimportant

    X = Not desirable

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    Relationship (Proximity) Chart

    1 PresidentO

    2 Costing U

    E A3 Engineering I

    U4 Presidents Secretary

    5 Photocopiers

    UE

    A

    X

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    Relationship (Proximity) Chart

    1 PresidentO

    2 Costing UE A

    3 Engineering IU

    4 Presidents Secretary

    5 Photocopiers

    UE

    A

    X

    1

    4

    3

    2

    5A

    A

    E

    E

    I

    X

    Can determine layoutusing proximity diagram

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    Office Layout

    1 President O2 Costing U

    E A3 Engineering I

    U4 Presidents Secretary

    5 Photocopiers

    UE

    A

    X

    1

    4

    3

    2

    5A

    A

    E

    E

    I

    X

    Locate 5 offices in a rectangular

    space.Offices 2-5 are to be same size.

    Office 1 (Presidents) is twice as

    large.

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    Office Layout

    Costing

    (3)

    Photocopiers(5)

    PresidentsSecretary

    (4)

    (2)

    President(1)

    Engineering

    Corridor

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    3. Process-Oriented Layout

    Place departments with large flows ofmaterial or people close together.

    Similar processes and equipment arelocated in close proximity.

    For example, all x-ray machines in same area.

    Used with process-focused processes.

    Low volume, high variety.

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    Emergency Room Layout

    E.R. beds Pharmacy Billing/exit

    E.R.Triage

    room

    Patient B - erratic

    pacemaker

    Patient A -broken leg

    Hallway

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    Process-Oriented Layout Advantages

    Flexibility.

    Allows wide variety of products.

    Low fixed costs for generalpurpose equipment.

    Breakdown of one machine or

    worker does not stopprocessing.

    Process Oriented Layout

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    Process-Oriented LayoutDisadvantages

    Scheduling is difficult.

    High variable cost.

    High work-in-processinventory and waiting.

    High labor skills required.

    Developing a Process Oriented

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    Developing a Process-OrientedLayout by Hand

    Goal: Minimize cost of moving between departments.

    1 Construct a from-to matrix.

    2 Determine space requirements for each department.

    3 Develop an initial layout and try to place departmentswith large flows close together.

    4 Determine the cost of this initial layout.

    5 Improve the initial layout (by hand or moresophisticated means).

    6 Consider factors in addition to transportation cost.

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    Cost of Process-Oriented Layout

    jiij

    C

    jiij

    X

    i,j

    n

    ijC

    ijX

    n

    i

    n

    j

    departmentanddepartmentbetweenloadamovetocost

    departmenttodepartmentfrommovedloadsofnumber

    sdepartmentindividual

    sdepartmentorcentersworkofnumbertotalwhere

    costM inimize

    1 1

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    1 2 3 4 5 6

    1

    2

    3

    45

    6

    40 100 0 0 0

    10 40 10 0

    0 0 80

    50 00

    10

    0

    00

    20

    20

    10

    0

    0

    200

    20

    0

    0 0

    Flows of Parts (loads/week)

    to

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    Interdepartmental Flow of Parts

    1 2 3 4 5 6

    1

    2

    3

    4

    5

    6

    50 100 0 0 20

    30 50 10 0

    20 0 100

    50 00

    Number of loads/week between departments

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    Initial Layout

    AssemblyDepartment

    (1)

    PrintingDepartment

    (2)

    Machine shopDepartment

    (3)

    ReceivingDepartment

    (4)

    ShippingDepartment

    (5)

    TestingDepartment

    (6)

    Room 1 Room 2 Room 3

    Room 4 Room 5 Room 6

    Initial Layout Flow Graph Showing

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    Initial Layout Flow Graph ShowingLoads/Week

    100

    50 30

    10

    50

    100

    1 2

    4 5 6

    3

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    Cost of Initial Layout

    100

    50 30

    10

    50

    100

    1 2

    4 5 6

    3

    1-2 50 = 50*1

    1-3 200 = 100*2

    1-6 40 = 20*2

    2-3 30 = 30*12-4 50 = 50*1

    2-5 10 = 10*1

    3-4 40 = 20*2

    3-6 100 = 100*1

    4-5 50 = 50*1

    Total = $570

    Cost per load for adjacent locations = $1

    Cost per load for non-adjacent locations = $2

    L Fl i I iti l L t

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    Large Flows in Initial Layout100

    50 30

    10

    50

    100

    1 2

    4 56

    3

    Largest Flows: 100 for 1-3 & 3-6, so put 3 close to 1 and 6.

    50 for 1-2, 2-4 & 4-5 ,

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    Improved Layout Flow Graph

    100

    10050

    30

    50

    2

    4

    31

    5 6

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    Improved Layout

    PrintingDepartment

    (2)

    AssemblyDepartment

    (1)

    Machine shopDepartment

    (3)

    ReceivingDepartment

    (4)

    ShippingDepartment

    (5)

    TestingDepartment

    (6)

    Room 1 Room 2 Room 3

    Room 4 Room 5 Room 6

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    Cost of Improved Layout

    1-2 50 = 50*1

    1-3 100 = 100*1

    1-6 20 = 20*1

    2-3 60 = 30*22-4 50 = 50*1

    2-5 10 = 10*1

    3-4 40 = 20*2

    3-6 100 = 100*1

    4-5 50 = 50*1

    Total = $480

    Cost per load for adjacent locations = $1

    Cost per load for non-adjacent locations = $2

    10050

    30

    50

    2

    4

    31

    5 6

    100

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    Alternative Improved Layout

    50

    100100

    20

    50

    1

    2

    63

    4 5

    10

    Cost of Alternative Improved Layout

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    Cost of Alternative Improved Layout

    1-2 50 = 50*1

    1-3 100 = 100*1

    1-6 40 = 20*2

    2-3 30 = 30*12-4 50 = 50*1

    2-5 20 = 10*2

    3-4 20 = 20*1

    3-6 100 = 100*1

    4-5 50 = 50*1

    Total = $460

    Cost per load for adjacent locations = $1

    Cost per load for non-adjacent locations = $2

    50

    100100

    20

    50

    1

    2

    63

    4 5

    10

    Is this best?

    Alt ti I d L t

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    Alternative Improved Layout

    PrintingDepartment

    (2)

    AssemblyDepartment

    (1)

    Machine shopDepartment

    (3)

    ReceivingDepartment

    (4)

    ShippingDepartment

    (5)

    TestingDepartment

    (6)

    Room 1 Room 2 Room 3

    Room 4 Room 5 Room 6

    L t E l 2

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    Layout Example 2Given the following tables of interdepartmental flows and distances

    between locations A-E, locate the five departments to minimize the totaldistancexflow.

    Interdepartmental flows

    1 2 3 4 51 - 13 18 3 0

    2 - 15 0 6

    3 - 0 4

    4 - 4

    A B C D EA - 9 8 12 14

    B 9 - 9 6 7

    C 8 9 - 4 9

    D 12 6 4 - 14

    Distances between locations

    E 14 7 9 14 -

    L t E l 2

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    Layout Example 2Largest flow 1-3 (flow=18) should be in closest locations: C&D

    Could have: Solution 1: C=1 and D=3 orSolution 2: C=3 and D=1

    Interdepartmental flows

    1 2 3 4 51 - 13 18 3 0

    2 - 15 0 6

    3 - 0 4

    4 - 4

    A B C D EA - 9 8 12 14

    B 9 - 9 6 7

    C 8 9 - 4 9

    D 12 6 4 - 14

    Distances between locations

    E 14 7 9 14 -

    L t E l 2

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    Layout Example 2Next largest flow is 2-3, so 2 should be placed in location closest to 3.

    Solution 1: D=3 and closest open location to D is B, so B=2, C=1, D=3.Solution 2: C=3 and closest open location to C is A, so A=2, C=3, D=1.

    Interdepartmental flows

    1 2 3 4 51 - 13 18 3 0

    2 - 15 0 6

    3 - 0 4

    4 - 4

    A B C D EA - 9 8 12 14

    B 9 - 9 6 7

    C 8 9 - 4 9

    D 12 6 4 - 14

    Distances between locations

    E 14 7 9 14 -

    L t E l 2

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    Layout Example 2Next largest flow is 1-2, but 1 and 2 are already located.

    So consider next largest flow 2-5.Solution 1: B=2 and closest open location to B is E, so A=4,B=2,C=1, D=3,E=5.Solution 2: A=2 and closest open location to A is B, so A=2,B=5,C=3, D=1,E=4.

    Interdepartmental flows

    1 2 3 4 5

    1 - 13 18 3 0

    2 - 15 0 6

    3 - 0 4

    4 - 4

    A B C D E

    A - 9 8 12 14

    B 9 - 9 6 7

    C 8 9 - 4 9

    D 12 6 4 - 14

    Distances between locations

    E 14 7 9 14 -

    Layout Example 2

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    Layout Example 2Solution 1: A=4,B=2,C=1, D=3,E=5.

    Distance = 13x9 + 18x4 + 3x8 + 15x6 + 6x7 + 4x14 + 4x14 = 457

    Solution 2: A=2,B=5,C=3, D=1,E=4.Distance = 13x12 + 18x4 + 3x14 + 15x8 + 6x9 + 4x9 + 4x7 = 508

    Interdepartmental flows

    1 2 3 4 5

    1 - 13 18 3 0

    2 - 15 0 6

    3 - 0 4

    4 - 4

    A B C D E

    A - 9 8 12 14

    B 9 - 9 6 7

    C 8 9 - 4 9

    D 12 6 4 - 14

    Distances between locations

    E 14 7 9 14 -

    Solution 1

    is best!

    Computer Programs for Layout

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    Computer Programs for Layout

    Many different programs: CRAFT

    SPACECRAFT

    CRAFT 3-D CORELAP

    ALDEP

    All are heuristic - not necessarily optimal!!

    Work Cells in Process Layouts

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    Work Cells in Process Layouts

    Special case of product-oriented layout - in aprocess-oriented facility.

    Differentmachines brought together to make a product.

    Use when high volume warrants special arrangement.

    For 1 product or a small group of products.

    Temporary arrangement.

    Example: Assembly line set up to produce 3000identical parts in a job shop.

    Work Cell Floor Plan

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    Work Cell Floor Plan

    Office

    Tool Room Work Cell

    Saws Drills

    Work Cell Advantages

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    Work Cell Advantages

    Lower:

    Inventory.Floor space.

    Direct labor costs.

    Higher:

    Equipment utilization.Employeeparticipation.

    Quality.

    Work Cells, Focused WorkC d h F d F

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    Centers and the Focused Factory

    Work Cell A temporaryassembly-line-orientedarrangementof machines and personnel inwhat is ordinarily a process-oriented facility.

    Focused WorkCenter

    Apermanentassembly-line-orientedarrangementof machines and personnel inwhat is ordinarily a process-oriented facility.

    Focused Factory Apermanent facilityto produce a product orcomponent in a product-oriented facility.

    4 Retail/Service Layout

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    4. Retail/Service Layout

    Maximize product exposure to customers. Maximize profitability per square foot of floor space or

    per linear foot of shelf space.

    Decision variables:

    Arrangement of store.

    Store flow pattern.

    Allocation of (shelf) space to products.

    Video

    Retail Layouts - Rules of Thumb

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    Retail Layouts Rules of Thumb

    Locate high-draw items around the periphery.

    Use prominent locations (end aisle locations; first orlast aisle) for high-impulse and high margin items.

    Remove crossover aisles to prevent customers from

    moving between aisles.

    Distribute power items (that dominate a shopping

    trip) around store to increase the viewing of other

    items. Locate far apart.

    Locate on both sides of an aisle.

    Grocery Store Layout

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    y y

    Retail Store Shelf Space

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    Retail Store Shelf Space

    Consider prominence ofshelf location and numberof facings.

    Can use computerized toolsto manage shelf-space.

    Track sales and product

    location (scanner data).

    5facings

    PERT

    PERT

    PERT

    PERT

    PERT

    Servicescape Considerations

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    Servicescape Considerations

    Ambient conditions.

    Background characteristics such as lighting, sound,smell, and temperature.

    Spatial layout and functionality.

    Customer circulation, aisle width, shelf spacing, etc.

    Signs, Symbols, and Artifacts. Various other characteristics of design (carpeting,

    greeters, etc.).

    5 Warehouse Layout

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    5. Warehouse Layout

    Balance space utilization & handling cost. Similar to process layout.

    Items moved between loading docks

    & various storage areas.

    Optimum layout depends on:

    Variety of items stored.

    Number of items picked.

    Space Utilization vs. Handling

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    Costs

    High space utilization (for storage).

    Small, narrow aisles.

    Product stacked high and deep (not easily accessible).

    Ease of material handling.

    Wide, short aisles.

    Product easily accessible.

    Design facility to optimize space utilization andhandling costs tradeoff.

    Assigned vs. Random StockL ti

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    Locations

    Assigned locations for products: May be inefficient use of space.

    Easier order picking and re-stocking.

    Random locations: More efficient use of space.

    Added costs to track location of inventory and open space.

    More difficult order picking and re-stocking.

    Stock products to optimize cost and efficienciestradeoffs.

    Cross Docking (Wal-Mart)

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    Cross Docking (Wal Mart) Transferring goods:

    From incomingtrucks at receivingdocks.

    To outgoingtrucks at shipping docks.

    Avoids placing goods intostorage.

    Requires suppliers provide

    effective addressing (bar codes)and packaging for rapidtransshipment.

    In-

    comingOutgoing

    Order Picking

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    Collecting items on a customer order from various

    locations in the warehouse.

    Sequence items to minimize travel time in

    warehouse to pick order.

    Also, should locate items to be efficient to pick.

    Combine several orders to reduce picking time.

    Zoning: Assign separate pickers to differentzones in the warehouse.

    Split order among several pickers.

    6. Product-Oriented Layout

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    6. Product Oriented Layout

    Used with product-focussed processes. Facility organized around product.

    High volume, low variety.

    Types:

    Fabrication line - Builds components.

    Assembly line - Assembles components intoproducts.

    Product-Oriented Layout

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    y

    Divide work into small tasks. To be done byworkers or machines.

    Assign tasks to workstations.

    Balance output of each workstation.

    To smooth operations of the line.

    To make workload equal.

    To minimize idle time.

    To achieve desired output.

    Product-Oriented Requirements

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    q

    Standardized product.

    High production volume.

    Stable production quantities.Uniform quality of raw materials &

    components.

    Product-Oriented Layout Advantages

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    Product Oriented Layout Advantages

    Lower variable cost per unit.

    Lower material handling costs.

    Lower work-in-processinventories.

    Rapid throughput.

    Easier training & supervision.

    Product-Oriented LayoutDisadvantages

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    Disadvantages

    Higher capital investment forspecial equipment.

    Any work stoppage stopswhole process.

    Lack of flexibility in volume

    and product.

    Repetitive Layout

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    Note: 5 tasks or operations (T1-T5);

    3 work stations (orange rectangles)

    T1 T3

    T2

    T4

    T5

    Work Station 1

    Office

    Belt Conveyor

    WorkStation 3

    Work Station 2

    Assembly Line Balancing Steps

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    y g p

    1. Determine tasks (operations) & task times.2. Determine sequence of tasks.

    3. Draw precedence diagram.

    4. Calculate cycle time .

    5. Calculate minimum number of work stations, N.

    6. Assign tasks.7. Calculate efficiency.

    Assembly Line Balancing Data

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    Usually we are given:

    Production rate.

    Units of product to be produced per unit time.

    Production time available per day.

    Tasks (operations) & task times.

    Sequence of tasks.

    Assembly Line BalancingGeneral Procedure

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    General Procedure

    1. Determine cycle time - The time betweenproduction of successive units. (May bemeasured in seconds, minutes, etc.)

    2. Calculate the theoretical minimum number ofworkstations, denoted N. (May not be achievable.)

    3. Assign tasksto workstations to balance the line.Compute the efficiency.

    Assembly Line Balancing Equations

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    y g q

    Cycle time =Production time available

    Production rate

    Minimum

    number ofwork stations

    Task timesCycle time

    Efficiency =

    =

    Task times

    * (Cycle time)(Actual numberof work stations)

    = N Rounded up

    Assembly Line Balancing Example

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    Task Time PredecessorA 0.1 min. -B 0.7 min. AC 1.0 min. B

    D 0.5 min. CE 0.2 min. D

    2.5 min.

    Immediate

    A B C D E

    0.1 0.20.7 1.0

    0.5

    Suppose we want to

    produce 300 units/day

    and 8 hours are

    available each day.

    Assembly Line Balancing Example

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    Task Time PredecessorA 0.1 min. -B 0.7 min. AC 1.0 min. BD 0.5 min. CE 0.2 min. D

    2.5 min.

    Immediate

    Suppose we want toproduce 300 units/day

    and 8 hours are

    available each day.

    nsworkstatioortesminu

    tesminu

    N

    unittesminudayunits

    daytesminutimecycle

    25625.16.1

    5.2

    /6.1/300

    /480

    So assign tasks A-E to 2 workstations, where neither workstation

    should exceed 1.6 minutes.

    Assembly Line Balancing Example

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    A B C D E

    0.1 0.20.7 1.

    0

    0.5

    Suppose we want toproduce 300 units/day

    and 8 hours are

    available each day.

    Can not use only 2 workstations! Must use 3.

    Efficiency=2.5/(3*1.6) = 52.1%

    Task Time PredecessorA 0.1 min. -B 0.7 min. AC 1.0 min. BD 0.5 min. CE 0.2 min. D

    2.5 min.

    Immediate

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    A B C D E0.1 0.20.7 1.

    00.5

    Both of these can

    produce 300/day in8 hours.

    Efficiency=2.5/(3*1.6) = 52.1%

    A B C D E

    0.1 0.20.7 1.

    0

    0.5

    Efficiency=2.5/(3*1.6) = 52.1%

    Better balance!

    Note: this line could produce 300 units in 5 hours (1 per minute)

    Efficiency=2.5/(3*1.0) = 83.3%

    Assembly Line Balancing Example

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    A B C D E

    0.1 0.20.7 1.0

    0.5

    If 2 workstations were required, then it will take more than 8 hours

    to produce 300 units.

    Cycle time = 1.7 minutes

    Efficiency=2.5/(2*1.7) = 73.5%

    Time to produce 300 units

    1.7 min/unit*300 units = 510 minutes = 8.5 hours

    Assembly Line Balancing Heuristics

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    Longest (or shortest) task time.

    Choose task with longest (or shortest) operation time.

    Most following tasks.

    Choose task with largest number of following tasks.

    Ranked positional weight.

    Choose task where the sum of the times for each

    following task is longest.

    Least number of following tasks.

    Choose task with fewest subsequent tasks.

    Ranked Positional Weight Heuristic

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    Positional weight = Sum of times for a task and all

    tasks that must follow it.

    1. Calculate positional weight for each task.

    2. Assign task with largest positional weight to theearliest workstation where it fits.- Obey precedence relations.- Do not exceed cycle time.

    3. Repeat step 2 until all tasks are assigned.

    Line Balancing Example 2

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    Task Time PredecessorA 0.2 min. -B 0.6 min. A,CC 0.5 min. -

    D 0.3 min. -E 1.0 min. B,DF 0.2 min. DG 0.9 min. E,F

    3.7 min.

    Immediate

    Suppose we want toproduce 450 units/dayand 8 hours are

    available each day.

    Line Balancing Example 2

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    Task Time PredecessorA 0.2 min. -B 0.6 min. A,CC 0.5 min. -D 0.3 min. -E 1.0 min. B,D

    F 0.2 min. DG 0.9 min. E,F3.7 min.

    Immediate

    Suppose we want toproduce 450 units/dayand 8 hours are

    available each day.

    nsworkstatioortesminu

    tesminuN

    unittesminu

    dayunits

    daytesminutimecycle

    4...47.30667.1

    7.3

    /0667.1

    /450

    /480

    Precedence Diagram - Example 2

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    A

    BEC

    D F

    G

    0.2

    0.5

    0.3

    0.6

    0.2

    1.0

    0.9

    Example 2 - Positional Weight

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    Task Time Predecessor weightA 0.2 min. - 2.7B 0.6 min. A,C 2.5C 0.5 min. - 3.0

    D 0.3 min. - 2.4E 1.0 min. B,D 1.9F 0.2 min. D 1.1G 0.9 min. E,F 0.9

    3.7 min.

    Immediate Positional

    Example 2 - Assign Tasks

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    Task Time Predecessor weightA 0.2 min. - 2.7B 0.6 min. A,C 2.5C 0.5 min. - 3.0D 0.3 min. - 2.4

    E 1.0 min. B,D 1.9F 0.2 min. D 1.1G 0.9 min. E,F 0.9

    3.7 min.

    Immediate Positional

    Cycle time = 1.07 min.

    N= 4 workstations

    WS1 WS2 WS3 WS4C(0.5)

    A(0.2)

    Example 2 - Assign Tasks (cont.)

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    Task Time Predecessor weightA 0.2 min. - 2.7B 0.6 min. A,C 2.5C 0.5 min. - 3.0D 0.3 min. - 2.4

    E 1.0 min. B,D 1.9F 0.2 min. D 1.1G 0.9 min. E,F 0.9

    3.7 min.

    Immediate Positional

    Cycle time = 1.07 min.

    N= 4 workstations

    WS1 WS2 WS3 WS4C(0.5) B(0.6)

    A(0.2)D(0.3)

    Example 2 - Assign Tasks (cont.)

    I di t P iti l

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    Task Time Predecessor weightA 0.2 min. - 2.7B 0.6 min. A,C 2.5C 0.5 min. - 3.0D 0.3 min. - 2.4

    E 1.0 min. B,D 1.9F 0.2 min. D 1.1G 0.9 min. E,F 0.9

    3.7 min.

    Immediate Positional

    Cycle time = 1.07 min.

    N= 4 workstations

    WS1 WS2 WS3 WS4C(0.5) B(0.6) E(1.0) G(0.9)

    A(0.2) F(0.2)D(0.3)

    Efficiency =

    3.7/(4*1.07) = 86.4%

    Precedence Diagram - Example 2

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    A

    B

    EC

    D F

    G

    0.2

    0.5

    0.3

    0.6

    0.2

    1.0

    0.9

    WS1 WS2

    WS3

    WS4

    Example 2 - Final Comment

    Immediate

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    Task Time PredecessorA 0.2 min. -B 0.6 min. A,CC 0.5 min. -D 0.3 min. -

    E 1.0 min. B,DF 0.2 min. DG 0.9 min. E,F

    3.7 min.

    Immediate

    Could use a cycle time of

    1 minute & produce 450

    units in 7.5 hours

    WS1 WS2 WS3 WS4C(0.5) B(0.6) E(1.0) G(0.9)

    A(0.2) F(0.2)D(0.3)

    Efficiency =

    3.7/(4*1.0) = 92.5%