Session 9 CannonWorld, Event-driven Programming, and Border Layout.
Session 07 Capacity and Layout
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Transcript of Session 07 Capacity and Layout
Capacity and FacilitiesCapacity and Facilities
Lecture OutlineLecture Outline
Capacity Planning Basic Layouts Designing Process Layouts Designing Service Layouts Designing Product Layouts Hybrid Layouts
CapacityCapacity
Maximum capability to produceMaximum capability to produce Affects product lead timeAffects product lead time Affects Customer responsivenessAffects Customer responsiveness Affects Operating costsAffects Operating costs Affects firm’s ability to competeAffects firm’s ability to compete
Capacity planning
Capacity planningCapacity planning establishes overall level of productive establishes overall level of productive
resources for a firmresources for a firm
3 basic strategies for timing of capacity 3 basic strategies for timing of capacity expansion in relation to steady growth in expansion in relation to steady growth in demand (lead, lag, and average)demand (lead, lag, and average)
Capacity Expansion Strategies
Capacity (cont.)
Capacity increase depends on volume and certainty of anticipated demand strategic objectives costs of expansion and operation
Best operating level % of capacity utilization that minimizes unit costs
Capacity cushion % of capacity held in reserve for unexpected
occurrences
Economies of ScaleEconomies of Scale
it costs less per unit to produce high levels of output fixed costs can be spread over a larger number of
units production or operating costs do not increase
linearly with output levels quantity discounts are available for material
purchases operating efficiency increases as workers gain
experience
Best Operating Level
Economies of ScaleBest OperatingLevel
Averageunit costof output
Volume
Diseconomies of Scale
Machine Objectives of Machine Objectives of Facility LayoutFacility Layout
Minimize material-handling costs
Utilize space efficiently Utilize labor efficiently Eliminate bottlenecks Facilitate communication and
interaction Reduce manufacturing cycle
time Reduce customer service time Eliminate wasted or
redundant movement Increase capacity
Facilitate entry, exit, and placement of material, products, and people
Incorporate safety and security measures
Promote product and service quality
Encourage proper maintenance activities
Provide a visual control of activities
Provide flexibility to adapt to changing conditions
Arrangement of areas within a facility to:
BASIC LAYOUTS
Process layouts group similar activities together
according to process or function they perform
Product layouts arrange activities in line according to
sequence of operations for a particular product or service
Fixed-position layouts are used for projects in which product
cannot be moved
Process Layout: Process Layout: Interdepartmental FlowInterdepartmental Flow
GivenGiven The flow (number of moves) to and from all The flow (number of moves) to and from all
departmentsdepartments The cost of moving from one department The cost of moving from one department
to anotherto another The existing or planned physical layout of The existing or planned physical layout of
the plantthe plant DetermineDetermine
The “best” locations for each department, The “best” locations for each department, where best means maximizing flow, which where best means maximizing flow, which minimizing costs minimizing costs
Process Layout: Process Layout: CRAFT ApproachCRAFT Approach
It is a heuristic program; it uses a simple rule It is a heuristic program; it uses a simple rule of thumb in making evaluations: of thumb in making evaluations: "Compare two departments at a time and "Compare two departments at a time and
exchange them if it reduces the total cost of the exchange them if it reduces the total cost of the layout."layout."
It does not guarantee an optimal solutionIt does not guarantee an optimal solution
CRAFT assumes the existence of variable path CRAFT assumes the existence of variable path material handling equipment such as forklift material handling equipment such as forklift truckstrucks
CRAFTCRAFT
Load inputLoad input Initial layoutInitial layout Transportation costTransportation cost Calculate dept centresCalculate dept centres Calculate cost of mat handCalculate cost of mat hand Make paired exchangeMake paired exchange If total cost decrease then repeat the If total cost decrease then repeat the
process else stopprocess else stop
Process Layout: Process Layout: Systematic Layout PlanningSystematic Layout Planning
Numerical flow of items between departments Numerical flow of items between departments Can be impractical to obtainCan be impractical to obtain Does not account for the qualitative factors that Does not account for the qualitative factors that
may be crucial to the placement decisionmay be crucial to the placement decision Systematic Layout PlanningSystematic Layout Planning
Accounts for the importance of having each Accounts for the importance of having each department located next to every other department located next to every other departmentdepartment
Is also guided by trial and errorIs also guided by trial and error Switching departments then checking the results of Switching departments then checking the results of
the “closeness” score the “closeness” score
Process Layout in ServicesProcess Layout in Services
Women’s lingerie
Women’s dresses
Women’s sportswear
Shoes
Cosmetics and jewelry
Entry and display area
Housewares
Children’s department
Men’s department
Manufacturing Process LayoutManufacturing Process Layout
A Product LayoutA Product Layout
InIn
OutOut
Description
Type of process
Product
Demand Volume Equipment
Description
Type of process
Product
Demand Volume Equipment
Sequential arrangement of activities
Continuous, mass production, mainly assembly
Standardized, made to stock
Stable High Special purpose
Process
Comparison of ProductComparison of Productand Process Layoutsand Process Layouts
Functional grouping of activities
Intermittent, job shop, batch production, mainly fabrication
Varied, made to order
Fluctuating Low General purpose
Product
Workers Inventory
Storage space Material handling Aisles Scheduling Layout decision Goal
Advantage
Workers Inventory
Storage space Material handling Aisles Scheduling Layout decision Goal
Advantage
Limited skills Low in-process, high
finished goods Small Fixed path (conveyor) Narrow Part of balancing Line balancing Equalize work at each
station Efficiency
Process
Comparison of ProductComparison of Productand Process Layoutsand Process Layouts
Varied skills High in-process, low
finished goods Large Variable path (forklift) Wide Dynamic Machine location Minimize material
handling cost Flexibility
Product
Fixed-Position LayoutsFixed-Position Layouts
Typical of projects in Typical of projects in which product produced which product produced is too fragile, bulky, or is too fragile, bulky, or heavy to moveheavy to move
Equipment, workers, Equipment, workers, materials, other materials, other resources brought to the resources brought to the sitesite
Low equipment utilizationLow equipment utilization Highly skilled laborHighly skilled labor Typically low fixed costTypically low fixed cost Often high variable costsOften high variable costs
Designing Process LayoutsDesigning Process Layouts
Goal: minimize material handling costsGoal: minimize material handling costs Block DiagrammingBlock Diagramming
minimize nonadjacent loads minimize nonadjacent loads use when quantitative data is availableuse when quantitative data is available
Relationship DiagrammingRelationship Diagramming based on location preference between areasbased on location preference between areas use when quantitative data is not availableuse when quantitative data is not available
Block DiagrammingBlock Diagramming
Unit loadUnit load quantity in which quantity in which
material is normally material is normally movedmoved
Nonadjacent loadNonadjacent load distance farther distance farther
than the next blockthan the next block
STEPSSTEPS create load summary chartcreate load summary chart calculate composite (two calculate composite (two
way) movementsway) movements develop trial layouts develop trial layouts
minimizing number of minimizing number of nonadjacent loadsnonadjacent loads
Block Diagramming: ExampleBlock Diagramming: Example
DepartmentDepartment 11 22 33 44 55
Load Summary ChartLoad Summary Chart
FROM/TOFROM/TO DEPARTMENTDEPARTMENT
11 —— 100100 505022 — — 200200 505033 6060 — — 4040 505044 100100 — — 606055 5050 — —
1 2 3
4 5
Block Diagramming: Block Diagramming: Example (cont.)Example (cont.)
2 3 200 loads2 4 150 loads1 3 110 loads1 2 100 loads4 5 60 loads3 5 50 loads2 5 50 loads3 4 40 loads1 4 0 loads1 5 0 loads
1 2 3
4 5
100 200
150 50 50
60
40
110
Grid 1
Nonadjacent Loads:110+40=150
1 2
3
4
5
100
200
150
50
50 6040110
Grid 2
Nonadjacent Loads:0
Block Diagramming: Block Diagramming: Example (cont.)Example (cont.)
12
3
4
53
2
5
1 4
(a) Initial block diagram(a) Initial block diagram (b) Final block diagram(b) Final block diagram
Block Diagram type of schematic layout diagram; includes space requirements
Relationship DiagrammingRelationship Diagramming
Schematic diagram that Schematic diagram that uses weighted lines to uses weighted lines to denote location preferencedenote location preference
Muther’s gridMuther’s grid format for displaying manager preferences for department locations
Relationship Diagramming: ExcelRelationship Diagramming: Excel
Relationship Relationship Diagramming: ExampleDiagramming: Example
ProductionProduction
OfficesOffices
StockroomStockroom
Shipping and Shipping and receivingreceiving
Locker roomLocker room
ToolroomToolroom
AA AA
AA OO
OO
OOOO
OO
UU
UU UU
UU
EEXX
II
A Absolutely necessaryE Especially importantI ImportantO OkayU UnimportantX Undesirable
A Absolutely necessaryE Especially importantI ImportantO OkayU UnimportantX Undesirable
Relationship Diagrams: Example (cont.)Relationship Diagrams: Example (cont.)
(a) Relationship diagram of original layout(a) Relationship diagram of original layout
Key:Key: AAEEIIOOUUXX
OfficesOffices
StockroomStockroom
Locker Locker roomroom
ToolroomToolroom
Shipping Shipping and and
receivingreceiving
ProductionProduction
(b) Relationship diagram of revised layout(b) Relationship diagram of revised layout
OfficesOffices
StockroomStockroom
Locker Locker roomroom
ToolroomToolroom
Shipping Shipping and and
receivingreceiving
ProductionProduction Key:Key: AAEEIIOOUUXX
Relationship Diagrams: Example (cont.)Relationship Diagrams: Example (cont.)
Computerized layout Computerized layout SolutionsSolutions
CRAFT Computerized Relative Allocation of Facilities
Technique CORELAP
Computerized Relationship Layout Planning PROMODEL and EXTEND
visual feedback allow user to quickly test a variety of scenarios
Three-D modeling and CAD integrated layout analysis available in VisFactory and similar software
Designing Service Layouts
Must be both attractive and functional Types
Free flow layouts encourage browsing, increase impulse purchasing, are flexible
and visually appealing Grid layouts
encourage customer familiarity, are low cost, easy to clean and secure, and good for repeat customers
Loop and Spine layouts both increase customer sightlines and exposure to products,
while encouraging customer to circulate through the entire store
Types of Store LayoutsTypes of Store Layouts
Designing Product Layouts
Objective Balance the assembly line
Line balancing tries to equalize the amount of work at each
workstation Precedence requirements
physical restrictions on the order in which operations are performed
Cycle time maximum amount of time a product is allowed to
spend at each workstation
Cycle Time ExampleCycle Time Example
Cd = production time available
desired units of output
Cd = (8 hours x 60 minutes / hour)
(120 units)
Cd = = 4 minutes480
120
Flow Time vs Cycle TimeFlow Time vs Cycle Time
Cycle time = max time spent at any station Cycle time = max time spent at any station Flow time = time to complete all stationsFlow time = time to complete all stations
1 2 3
4 minutes4 minutes 4 minutes4 minutes 4 minutes4 minutes
Flow time = 4 + 4 + 4 = 12 minutesFlow time = 4 + 4 + 4 = 12 minutesCycle time = max (4, 4, 4) = 4 minutesCycle time = max (4, 4, 4) = 4 minutes
Efficiency of Line and Balance Delay
ii
ii = 1= 1
ttii
nCnCaaEE = =
ii
ii = 1= 1
ttii
CCddNN = =
EfficiencyEfficiency Minimum number Minimum number of workstationsof workstations
wherewhere
ttii = completion time for element = completion time for element ii
jj = number of work elements= number of work elementsnn = actual number of workstations= actual number of workstations
CCaa = actual cycle time= actual cycle time
CCdd = desired cycle time= desired cycle time
Balance Balance delaydelay total idle total idle
time of linetime of line calculated calculated
as (1 - as (1 - efficiency)efficiency)
Line Balancing ProcedureLine Balancing Procedure
1. Draw and label a precedence diagram2. Calculate desired cycle time required for line3. Calculate theoretical minimum number of workstations4. Group elements into workstations, recognizing cycle
time and precedence constraints5. Calculate efficiency of line6. Determine if theoretical minimum number of
workstations or an acceptable efficiency level has been reached. If not, go back to step 4.
Station 1
Minutes per Unit 6
Station 2
7
Station 3
3
Assembly Lines Balancing ConceptsAssembly Lines Balancing Concepts
Question: Suppose you load work into the three work stations below such that each will take the corresponding number of minutes as shown. What is the cycle time of this line?
Question: Suppose you load work into the three work stations below such that each will take the corresponding number of minutes as shown. What is the cycle time of this line?
Answer: The cycle time of the line is always determined by the work station taking the longest time. In this problem, the cycle time of the line is 7 minutes. There is also going to be idle time at the other two work stations.
Answer: The cycle time of the line is always determined by the work station taking the longest time. In this problem, the cycle time of the line is 7 minutes. There is also going to be idle time at the other two work stations.
Example of Line BalancingExample of Line Balancing
You’ve just been assigned the job a setting up an You’ve just been assigned the job a setting up an electric fan assembly line with the following tasks:electric fan assembly line with the following tasks:
Task Time (Mins) Description PredecessorsA 2 Assemble frame NoneB 1 Mount switch AC 3.25 Assemble motor housing NoneD 1.2 Mount motor housing in frame A, CE 0.5 Attach blade DF 1 Assemble and attach safety grill EG 1 Attach cord BH 1.4 Test F, G
Example of Line Balancing: Example of Line Balancing: Structuring the Precedence DiagramStructuring the Precedence Diagram
Task PredecessorsA None
A
B A
B
C None
C
D A, C
D
Task PredecessorsE D
E
F E
F
G B
G
H E, G
H
Example of Line Balancing: Precedence DiagramExample of Line Balancing: Precedence Diagram
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
Question: Which process step defines the maximum Question: Which process step defines the maximum rate of production?rate of production?
Question: Which process step defines the maximum Question: Which process step defines the maximum rate of production?rate of production?
Answer: Task C is the cycle time of the line and therefore, the maximum rate of production.
Answer: Task C is the cycle time of the line and therefore, the maximum rate of production.
Example of Line BalancingExample of Line Balancing: Determine Cycle : Determine Cycle TimeTime
Required Cycle Time, C = Production time per period
Required output per periodRequired Cycle Time, C =
Production time per period
Required output per period
C = 420 mins / day
100 units / day= 4.2 mins / unitC =
420 mins / day
100 units / day= 4.2 mins / unit
Question: Suppose we want to assemble 100 Question: Suppose we want to assemble 100 fans per day. What would our cycle time fans per day. What would our cycle time have to be? have to be?
Question: Suppose we want to assemble 100 Question: Suppose we want to assemble 100 fans per day. What would our cycle time fans per day. What would our cycle time have to be? have to be?
Answer: Answer:
Example of Line Balancing: Determine Theoretical Example of Line Balancing: Determine Theoretical Minimum Number of WorkstationsMinimum Number of Workstations
Question: What is the theoretical minimum number of Question: What is the theoretical minimum number of workstations for this problem?workstations for this problem?
Question: What is the theoretical minimum number of Question: What is the theoretical minimum number of workstations for this problem?workstations for this problem?
Answer: Answer: Theoretical Min. Number of Workstations, N
N = Sum of task times (T)
Cycle time (C)
t
t
Theoretical Min. Number of Workstations, N
N = Sum of task times (T)
Cycle time (C)
t
t
N = 11.35 mins / unit
4.2 mins / unit= 2.702, or 3t
N = 11.35 mins / unit
4.2 mins / unit= 2.702, or 3t
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
Station 1 Station 2 Station 3
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
Station 1 Station 2 Station 3
A (4.2-2=2.2)
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
Station 1 Station 2 Station 3
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
C (4.2-3.25)=.95
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Station 1 Station 2 Station 3
C (4.2-3.25)=.95
Idle = .95
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Station 1 Station 2 Station 3
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
C (4.2-3.25)=.95
Idle = .95
D (4.2-1.2)=3E (3-.5)=2.5
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Station 1 Station 2 Station 3
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
C (4.2-3.25)=.95
Idle = .95
D (4.2-1.2)=3E (3-.5)=2.5F (2.5-1)=1.5
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Station 1 Station 2 Station 3
A
C
B
D E F
GH
2
3.25
1
1.2 .5
11.4
1
C (4.2-3.25)=.95
Idle = .95
D (4.2-1.2)=3E (3-.5)=2.5F (2.5-1)=1.5H (1.5-1.4)=.1Idle = .1
Task Followers Time (Mins)A 6 2C 4 3.25D 3 1.2B 2 1E 2 0.5F 1 1G 1 1H 0 1.4
A (4.2-2=2.2)B (2.2-1=1.2)G (1.2-1= .2)
Idle= .2
Station 1 Station 2 Station 3
Example of Line Balancing: Determine the Efficiency of Example of Line Balancing: Determine the Efficiency of the Assembly Linethe Assembly Line
Efficiency =Sum of task times (T)
Actual number of workstations (Na) x Cycle time (C)Efficiency =
Sum of task times (T)
Actual number of workstations (Na) x Cycle time (C)
Efficiency =11.35 mins / unit
(3)(4.2mins / unit)=.901Efficiency =
11.35 mins / unit
(3)(4.2mins / unit)=.901
Line Balancing: ExampleLine Balancing: ExampleWORK ELEMENTWORK ELEMENT PRECEDENCEPRECEDENCE TIME (MIN)TIME (MIN)
AA Press out sheet of fruitPress out sheet of fruit —— 0.10.1
BB Cut into stripsCut into strips AA 0.20.2
CC Outline fun shapesOutline fun shapes AA 0.40.4
DD Roll up and packageRoll up and package B, CB, C 0.30.3
0.10.1
0.20.2
0.40.4
0.30.3D
B
C
A
Line Balancing: Example (cont.)Line Balancing: Example (cont.)WORK ELEMENTWORK ELEMENT PRECEDENCEPRECEDENCE TIME (MIN)TIME (MIN)
AA Press out sheet of fruitPress out sheet of fruit —— 0.10.1
BB Cut into stripsCut into strips AA 0.20.2
CC Outline fun shapesOutline fun shapes AA 0.40.4
DD Roll up and packageRoll up and package B, CB, C 0.30.3
Cd = = = 0.4 minute40 hours x 60 minutes / hour
6,000 units
2400
6000
N = = = 2.5 3 workstations1.0
0.4
0.1 + 0.2 + 0.3 + 0.4
0.4
Line Balancing: Example (cont.)Line Balancing: Example (cont.)
CCdd = 0.4 = 0.4
NN = 2.5 = 2.5
REMAINING REMAININGWORKSTATION ELEMENT TIME ELEMENTS
1 A 0.3 B, CB 0.1 C, D
2 C 0.0 D3 D 0.1 none
0.10.1
0.20.2
0.40.4
0.30.3D
B
C
A
A, B C D
Work station 1
Work station 2
Work station 3
0.3 minute
0.4 minute
0.3 minute
CCdd = 0.4 = 0.4
NN = 2.5 = 2.5
E = = = 0.833 = 83.3%0.1 + 0.2 + 0.3 + 0.4
3(0.4)
1.0
1.2
Line Balancing: Example (cont.)Line Balancing: Example (cont.)
Computerized Line Computerized Line BalancingBalancing
Use heuristics to assign tasks to Use heuristics to assign tasks to workstationsworkstations Longest operation timeLongest operation time Shortest operation timeShortest operation time Most number of following tasksMost number of following tasks Least number of following tasksLeast number of following tasks Ranked positional weightRanked positional weight
Hybrid LayoutsHybrid Layouts
Cellular layouts group dissimilar machines into work centers (called cells)
that process families of parts with similar shapes or processing requirements
Production flow analysis (PFA) reorders part routing matrices to identify families of parts
with similar processing requirements Flexible manufacturing system
automated machining and material handling systemsautomated machining and material handling systems which can produce an enormous variety of items
Mixed-model assembly line processes more than one product model in one line
Cellular Layouts
1.1. Identify families of parts with similar Identify families of parts with similar flow pathsflow paths
2.2. Group machines into cells based on Group machines into cells based on part familiespart families
3.3. Arrange cells so material movement Arrange cells so material movement is minimizedis minimized
4.4. Locate large shared machines at Locate large shared machines at point of usepoint of use
Original Process LayoutOriginal Process Layout
CA B Raw materials
Assembly
1
2
3
4
5
6 7
8
9
10
11
12
Part Routing MatrixPart Routing Matrix
MachinesParts 1 2 3 4 5 6 7 8 9 10 11 12
A x x x x xB x x x xC x x xD x x x x xE x x xF x x xG x x x xH x x x
Figure 5.8Figure 5.8
Revised Cellular LayoutRevised Cellular Layout
3
6
9
Assembly
12
4
8 10
5
7
11
12
A B CRaw materials
Cell 1 Cell 2 Cell 3
Reordered Routing MatrixReordered Routing Matrix
MachinesParts 1 2 4 8 10 3 6 9 5 7 11 12
A x x x x xD x x x x xF x x xC x x xG x x x xB x x x xH x x xE x x x
Advantages and Disadvantages Advantages and Disadvantages of Cellular Layoutsof Cellular Layouts
AdvantagesAdvantages Reduced material Reduced material
handling and transit timehandling and transit time Reduced setup timeReduced setup time Reduced work-in- Reduced work-in-
process inventoryprocess inventory Better use of human Better use of human
resourcesresources Easier to controlEasier to control Easier to automateEasier to automate
DisadvantagesDisadvantages Inadequate part familiesInadequate part families Poorly balanced cellsPoorly balanced cells Expanded training and Expanded training and
scheduling of workersscheduling of workers Increased capital Increased capital
investmentinvestment
Automated Manufacturing CellAutomated Manufacturing Cell
Source: J. T. Black, “Cellular Manufacturing Systems Reduce Setup Time, Make Small LotProduction Economical.” Industrial Engineering (November 1983)
Flexible Manufacturing Flexible Manufacturing Systems (FMS)Systems (FMS)
FMS consists of numerous programmable machine tools connected by an automated material handling system and controlled by a common computer network
FMS combines flexibility with efficiency FMS layouts differ based on
variety of parts that the system can process size of parts processed average processing time required for part
completion
Full-Blown FMS
Mixed Model Mixed Model Assembly LinesAssembly Lines
Produce multiple models in any order Produce multiple models in any order on one assembly lineon one assembly line
Issues in mixed model linesIssues in mixed model lines Line balancingLine balancing U-shaped linesU-shaped lines Flexible workforceFlexible workforce Model sequencingModel sequencing
Balancing U-Shaped LinesBalancing U-Shaped Lines
A B C
D E
Precedence diagram:Precedence diagram:
Cycle time = 12 minCycle time = 12 min
A,B C,D E
(a) Balanced for a straight line(a) Balanced for a straight line
9 min9 min 12 min12 min 3 min3 min
Efficiency = = = .6666 = 66.7 %Efficiency = = = .6666 = 66.7 %24243636
24243(12)3(12)
12 min12 min 12 min12 min
C,D
A,B
E
(b) Balanced for a U-shaped line(b) Balanced for a U-shaped line
Efficiency = = = 100 %Efficiency = = = 100 %24242424
24242(12)2(12)