Quantitative Review II. Taguchi Loss Function Design the product or service so that it will not be...
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![Page 1: Quantitative Review II. Taguchi Loss Function Design the product or service so that it will not be sensitive to variations during the manufacturing or.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e535503460f94b48a3e/html5/thumbnails/1.jpg)
ISQS 3344 Introduction to Production and
Operations Management
Spring 2014
Quantitative Review II
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Taguchi Loss Function
• Design the product or service so that it will not be sensitive to variations during the manufacturing or delivery process
• For example, design a manufactured good with a smaller design tolerance = better quality
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2)()( TxkxL where
L(x) = the monetary value of the loss
associated with deviating from the
target limit “T” k = the constant that translates the
deviation into dollars x = the actual value of the dimension T = target limits
Taguchi Loss Function
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A quality characteristic has a specification (in inches) of 0.200 0.020. If the value of the quality characteristic exceeds 0.200 by the tolerance of 0.020 on either side, the product will require a repair of $150. Develop the appropriate Taguchi loss function (k).
000,375
)020.0(150
)020.0()200.0180.0220.0(150
)()(
2
22
2
k
k
kork
TxkxL
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A quality engineer has a manufacturing specification (in cm) of 0.200 plus or minus 0.050. Historical data indicates that if the quality characteristic takes on values larger than .250 cm or smaller than .150 cm, the product fails and a cost of $75 is incurred. Determine the Taguchi Loss Function and estimate the loss for a dimension of 0.135 cm.
000,30
)050.0/()75(
050.0)200.0150.0250.0()(
75$)(
2
k
k
orTx
xL
2)(000,30)( TxxL
75.126$)200.0135.0(000,30)135.0( 2 L
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Reliability Management
• Series product components
• Parallel product components
)).......()()(( 321 ns ppppR
)1)........(1)(1)(1(1321 npppppR
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The manufacturing of compact disks requires four sequential steps. The reliability of each of the steps is 0.96, 0.87, 0.92, and 0.88 respectively. What is the reliability of the process?
)).......()()(( 321 ns ppppR
0.6762 .88)7)(0.92)(0(0.96)(0.8 sR
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Parallel/Redundancy
A
B
C
B
.98
.91
.91
.97
9919.0)91.01)(91.01(1 BR
%29.949429.0)97.0)(9919.0)(98.0( orRS
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Given the diagram below, determine the system reliability if the individual component reliabilities are: A = 0.94, B = 0.92, C = 0.97, and D = 0.93.
A
D
C
B
RaRb = 1 - (1 - 0.94)(1 - 0.92) = 0.9952RcRd = 1 - (1 - 0.97)(1 - 0.93) =
0.9979
RabRcd = (0.9952)(0.9979) = 0.9931
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The system reliability for a two-component parallel system is 0.99968. If the reliability of the first component is 0.99, determine the reliability of the second component.
)1)........(31)(21)(11(1 npppppR
0.99968 = 1 – (1 – 0.99)(1 – p2)0.99968 = 1 – (0.01 – 0.01p2)0.99968–1 = -0.01 + 0.01p2
p2 = 0.968
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More Reliability QuestionWhat is the reliability of this system?If you could add one process (must be one of the existing processes) to best improve reliability what would be the improved reliability?
A0.987
B0.895
C0.947
D0.918
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More Reliability Question -- Solution
Reliability = 0.987*0.895*0.947*0.918= 0.768
A0.987
B0.895
C0.947
D0.918
A0.987
B0.895
C0.947
D0.918
B0.895
Parallel B Reliability = 1-(1-0.895)*(1-0.895) = 0.989
System Reliability = 0.987*0.989*0.947*0.918 = 0.849
Improvement = 0.849 – 0.768 = 0.08
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Kanban
where:K = the number of Kanban cardsd = the average production rate OR demand of
productp = the processing timew = the waiting time of Kanban cardsα = safety stock as a %, usually ranging from 0 to
1C = the capacity of a standard container
C
wpdK
)1)((
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Computing the number of kanbans: An aspirin manufacturer has converted to JIT manufacturing using Kanban containers. They wish to determine the number of containers at the bottle filling operation which fills at a rate of 400 per hour. Each container holds 35 bottles, it takes 30 minutes to receive more bottles (processing plus delivery time) and safety stock is set at 10%.
d = 400 bottles per hour p+w = 30 minutes or 0.5 hour C = 35 bottles per container α = 0.10
kanbansC
wpdK 29.6
35
220
35
)1.1)(5.0(400)1)((
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Location Analysis Methods
Factor Rating Method:Σ (Factor Weighti * Factor Scorei)
5*10=4*20=2*30=5*10=3*30=
2*10=2*20=5*30=3*10=5*30=
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Location Analysis MethodsCenter-of-Gravity Method:
where dix = x-coordinate of location i
diy = y-coordinate of location i
Qi = Quantity of goods moved to or from location i
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Where would be the best place to put the warehouse?
Location X coordinate
Ycoordinate
Number of Containers Shipped per Week
Chicago 30 120 2,000
Pittsburgh 90 110 1,000
New York 130 130 1,000
Atlanta 60 40 2,000
Center-of-Gravity Method
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Question 3A Plus Logistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are Chicago, Pittsburgh, and New York.Which town would be the best place to put the warehouse?
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Question 3 (Continued)
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Question 3 -- Solution
Therefore, the best place to put warehouse is Insanity!
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Location Analysis Methods
Load Distance Model:
Find load distance score by: Calculate the rectilinear distance and multiply by the
number of loads
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Load Distance ModelCalculate Rectilinear Distance
Identify Loads, i.e., 4 loads from A to B
Load Distance Score for AB = 45*4 = 180
milesD
D
D
YYXXD
AB
AB
AB
BABAAB
45
2520
15401030
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TT Logistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are A, B, and C. The two potential sites for the warehouse are D and E. The total quantity to be delivered to each destination is: 200 to A, 100 to B, and 300 to C. The x, y coordinates for the delivery locations and warehouses are as follows:
Where to locatewarehouse, D or E?
Location X coordinate
Ycoordinate
Location A 92 42
Location B 80 40
Location C 90 35
Warehouse D 90 45
Warehouse E 90 40
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Load Distance Score
Warehouse DDistance Loads Score
Location A 2+3=5 200 1000Location B 10+5=15 100 1500Location C 0+10=10 300 3000
5500Warehouse E
Distance Loads ScoreLocation A 2+2=4 200 800Location B 10+0=10 100 1000Location C 0+5=5 300 1500
3300
Location X coordinate
Ycoordinate
Location A 92 42
Location B 80 40
Location C 90 35
Warehouse D 90 45
Warehouse E 90 40
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Designing Process LayoutsStep 1: Gather information
Space needed, space available, importance of proximity between various units
Step 2: Develop alternative block plansUsing trial-and-error or decision support tools
Step 3: Develop a detailed layoutConsider exact sizes and shapes of
departments and work centers including aisles and stairways
Tools like drawing, 3-D models, and CAD software are available to facilitate this process.
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Process Layout (Step 1: Gather information)
Recovery First Sports Medicine Clinic Layout(total space 3750 sq.ft.)A
400 sq.ft.B
300 sq.ft.C
300 sq.ft.D
800 sq.ft.E
900 sq.ft.F
1050 sq.ft.
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Process Layout (Step 2: Develop a block layout)Current Proposed
A400
sq.ft.
B300
sq.ft.
C300
sq.ft.
D800
sq.ft.
E900
sq.ft.
F1050 sq.ft.
A400
sq.ft.
D800
sq.ft.
C300
sq.ft.
E900
sq.ft.
B300
sq.ft.
F1050 sq.ft.
Proposed layout would require less walking.
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What is the load distance for this layout?
Trips between departments
B A D
C E F
Dept.
A B C D E F
A 10 30 10 0 10B 30 15 15C 20 15 5E 25
Load Distance Problem
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Load Distance Problem
Depts.
Trips Distance
Score
AB 10 1 10
AC 30 2 60
AD 10 1 10
AF 10 2 20
BD 30 2 60
BE 15 2 30
BF 15 3 45
CD 20 3 60
CE 15 1 15
CF 5 2 10
EF 25 1 25
345
B A D
C E F
Dept.
A B C D E F
A 10 30 10 0 10
B 30 15 15
C 20 15 5
E 25
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Assembly Line BalancingStep 1: Identify task & immediate
predecessorsStep 2: Calculate the cycle timeStep 3: Determine the output rateStep 4: Compute the theoretical minimum
number of workstationsStep 5: Assign tasks to workstations (balance
the line)Step 6: Compute efficiency, idle time &
balance delay
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Assembly Line Balancing(Step 1: Identify tasks & immediate predecessors)
Example 10.4 Vicki's Pizzeria and the Precedence DiagramImmediate Task Time
Work Element Task Description Predecessor (secondsA Roll dough None 50B Place on cardboard backing A 5C Sprinkle cheese B 25D Spread Sauce C 15E Add pepperoni D 12F Add sausage D 10G Add mushrooms D 15H Shrinkwrap pizza E,F,G 18I Pack in box H 15
Total task time 165
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Layout CalculationStep 2: Determine cycle time (The amount of
time each workstation is allowed to complete its tasks.)Cycle time = Station A (50 seconds) -- the
bottleneckStep 3: Determine output rate
Step 4: Compute the theoretical minimum number of workstations (number of station needed to achieve 100% efficiency)
hourPizzasunit
hour
Bottleneck
imeAvailableTputMaximumOut /72
sec/50
sec/3600
StationsCycleTime
imesTotalTaskTTM 30.3
sec50
sec165
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Assembly Line Balancing(Step 5: Balance the line)
3 Work Stations(A,B), (C,D,G), (E,F,H,I)
55 sec
55 sec55 sec
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Assembly Line Balancing(Step 6: Compute efficiency, idle time & balance delay)
Efficiency
Balance DelayBalance Delay = 1 – Assembly Line Efficiency
%)100())((
(%)meNewCycleTiationsNumberOfSt
imesTotalTaskTEfficiency
%100165
165
55*3
sec165(%) Efficiency
IdleTimeayBalanceDel 011
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What is the bottleneck?What is the maximum production per hour?What is efficiency and balance delay?How to minimize work stations?How should they be groups?New efficiency?
A
B
C
4.1 mins
D
1.6 mins
E
2.7 mins
F
3.3 mins
G
2.6 mins
2.3 mins
3.4 mins
Line Balancing Problem
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Line Balancing ProblemWhat is the bottleneck?
4.1 minutesWhat is the maximum production per hour?
60/4.1 = 14.63 units/hourWhat is efficiency and balance delay?
Efficiency = 20/(7*4.1) = 69.69%Balance Delay = 1-.6969 = 30.31%
How to minimize work stations?
Should we use 4 or 5 work stations?
nsWorkStatioCycleTime
imesTotalTaskTTM 88.4
1.4
20
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4 Work Stations
A
B
C
4.1 mins
D
1.6 mins
E
2.7 mins
F
3.3 mins
G
2.6 mins
2.3 mins
3.4 mins5.7
mins
5.7 mins
6 mins
2.6 mins
Efficiency = 20/(4*6) = 20/24 = 83.3%Balance delay = 1-.833 = 16.7%Maximum production/hour = 60/6 = 10 units/hour
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5 Work Stations
A
B
C
4.1 mins
D
1.6 mins
E
2.7 mins
F
3.3 mins
G
2.6 mins
2.3 mins
3.4 mins5.7
mins
4.9 mins
2.7 mins
2.6 mins
Efficiency = 20/(5*5.7) = 20/28.5 = 70.18%Balance delay = 1-.7018 = 29.82%Maximum production/hour = 60/5.7 = 10.52 units/hour
4.1 mins
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Should we use 4 or 5 or 7 work stations?4 Work Stations
Efficiency = 83.3%Balance delay = 16.7%Maximum production/hour = 10 units/hour
5 Work StationsEfficiency = 70.18%Balance delay = 29.82%Maximum production/hour = 10.52 units/hour
7 Work StationsEfficiency = 69.69%Balance delay = 30.31%Maximum production/hour = 14.63 units/hour
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Supply Chain EfficiencyMeasuring Cash to Conversion Cycle
Inventory Turnover (IT)Inventory Days’ Supply (IDS)Accounts Receivable Turnover (ART)Accounts Receivable Days’ Supply (ARDS)Accounts Payable Turnover (APT)Accounts Payable Days’ Supply (APDS)
Cash-to-Cash Conversion Cycle = IDS + ARDS - APDS
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Inventory Ratios Inventory Turnover (IT):
# of times you turn your inventory annually
Inventory Days’ Supply (IDS):how many days inventory you keep
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Accounts Receivable Ratios Accounts Receivable Turnover (ART):
# of times you turn your accts. rec. annually
Accounts Receivable Days’ Supply (ARDS):how long it takes to get $ owed paid to you
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Accounts Payable Ratios Accounts Payable Turnover (APT):
# of times you turn your accts. payable annually
Accounts Payable Days’ Supply (APDS):how long you take to pay your bills
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Dell’s Financial dataRevenue $35.40
billionsCost of goods sold $29.10
billionsAverage Inventory Value $0.306
billionsAverage Accounts Receivable $2.586
billionsAverage Accounts Payable $5.989
billions
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Dell’s ExampleDell’s Inventory Turnover
Dell’s Inventory Days’ Supply
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Dell’s ExampleDell’s Accounts Receivable Turnover
Dell’s Accounts Receivable Days’ Supply
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Dell’s ExampleDell’s Accounts Payable Turnover
Dell’s Accounts Payable Days’ Supply
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Dell’s ExampleDell’s Cash-to-Cash Conversion Cycle
= IDS + ARDS – APDS= 3.84 days + 26.66 days – 61.76 days= -31.26 days
The negative value means that Dell receives customers’ payments (accounts receivable) 31.26 days, on average, before Dell has to pay its suppliers (accounts payable).
This means that Dell’s value chain is a self-funding cash model.
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Dell’s Negative Cash-to-Cash Conversion Cycle
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Breakeven Analysis (Make/Buy Decision)
Total Cost of Outsourcing:
Total Cost of Insourcing:
Indifference Point:
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The Bagel Shop ProblemJim & John plan to open a small bagel shop.
The local baker has offered to sell them bagels at 50 cents each. However, they will need to invest $2,000 in bread racks to transport the bagels back and forth from the bakery to their store.
Alternatively, they can bake the bagels at their store for 20 cents each if they invest $20,000 in kitchen equipment.
They expect to sell 80,000 bagels each year.
What should they do?
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The Bagel Shop ProblemIndifference Point Calculation:
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The Bagel Shop Problem
Make vs Buy Decision at 80,000 bagels Outsource (Buy) In House (Make)
$2,000+($.5*80,000) $20,000+($.2*80,000)= $42,000 = $36,000
Make vs Buy Decision at 50,000 bagels Outsource (Buy) In House (Make)$2,000+($.5*50,000) $20,000+($.2*50,000)= $27,000 = $30,000
If the demand is lower than the indifference point, outsourcing is a cheaper alternative, and vice versa.
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That’s all, folks!
Good Luck!