Supplement E -Supplement E -
Special Inventory ModelsSpecial Inventory Models
Special Inventory ModelsSpecial Inventory Models
Production quantity
Demand during production interval
Maximum inventory
Production and demand
Demand only
TBO
On-
hand
inve
ntor
y Q
Time
IImaxmax
p – d
Figure E.1
Special Inventory ModelsSpecial Inventory Models
Production and demand
Demand only
TBO
Production quantity
Demand during production interval
Maximum inventory
On-
hand
inve
ntor
y Q
Time
IImaxmax
p – d
Imax = (p – d) = Q( )Qp
p – dp
Special Inventory ModelsSpecial Inventory Models
Production and demand
Demand only
TBO
Production quantity
Demand during production interval
Maximum inventory
On-
hand
inve
ntor
y Q
Time
IImaxmax
p – d
C = (H) + (S)Imax
2DQ
Special Inventory ModelsSpecial Inventory Models
Production and demand
Demand only
TBO
Production quantity
Demand during production interval
Maximum inventory
On-
hand
inve
ntor
y Q
Time
IImaxmax
p – dC = ( ) + (S)D
QQ p – d2 p
Special Inventory ModelsSpecial Inventory Models
Production and demand
Demand only
TBO
Production quantity
Demand during production interval
Maximum inventory
On-
hand
inve
ntor
y Q
Time
IImaxmax
p – d
Figure E.1
ELS =p
p – d2DS
H
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 190190 – 30
2(10,500)($200)$0.21
Example E.1
ELS = 4873.4 barrels
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = ( )(H) + (S)DQ
Q p – d2 p
Example E.1
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = ( ) ($0.21) + ($200)10,5004873.4
4873.4 190 – 30 2 190
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = $430.91 + $430.91
Example E.1
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = $861.82
TBOELS = (350 days/year)ELSD
Example E.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.
Special Inventory Special Inventory ModelsModels
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = $861.82
TBOELS = 162.4, or 162 daysExample E.1
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = $861.82
TBOELS = 162.4, or 162 days
Production time = ELSp
Example E.1
Special Inventory ModelsSpecial Inventory Models
Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year
Economic Production Lot SizeEconomic Production Lot Size
ELS = 4873.4 barrels
C = $861.82
TBOELS = 162.4, or 162 days
Production time = 25.6, or 26 days
Example E.1
Special Inventory ModelsSpecial Inventory ModelsEconomic Production Lot SizeEconomic Production Lot Size
Figure E.2
C for P = $4.00C for P = $3.50C for P = $3.00
PD forP = $4.00 PD for
P = $3.50 PD forP = $3.00
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ 4.00
EOQ 3.50
EOQ 3.00
First price break
Second price break
Tota
l cos
t (do
llars
)
Tota
l cos
t (do
llars
)
Purchase quantity (Q)0 100 200 300
Purchase quantity (Q)0 100 200 300
First price break
Second price break
(a) Total cost curves with purchased materials added (b) EOQs and price break quantities
Figure E.3
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 =2DS
H
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
Example E.2
EOQ57.00 =2(936)(45)0.25(57.00)
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
Example E.2
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ57.00 = 77 units EOQ58.80 = 76 units EOQ60.00 = 75 units
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
Example E.2
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C = (H) + (S) + PDQ2
DQ
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
Example E.2
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = [(0.25)($60.00)] + ($45) + $60.00(936)752
93675
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
Example E.2
C75 = $57,284
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = $57,284
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
C300 = [(0.25)($58.80)] + ($45) + $58.80(936)3002
936300
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = $57,284
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
C300 = $57,382
Example E.2
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = $57,284
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
C300 = $57,382
C500 = [(0.25)($57.00)] + ($45) + $57.00(936)5002
936500 Example E.2
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.
Special Inventory Special Inventory ModelsModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = $57,284
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
C300 = $57,382
C500 = $56,999Example E.2
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ57.00 = 77 units
Annual demand = 936 unitsOrdering cost = $45
Holding cost = 25% of unit price
EOQ58.80 = 76 units EOQ60.00 = 75 units
C75 = $57,284
Order Quantity Price per Unit
0 – 299 $60.00300 – 499 $58.80500 or more $57.00
C300 = $57,382
C500 = $56,999Example E.2
Special Inventory ModelsSpecial Inventory Models
Figure E.4
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020304050
DQ 10 20 30 40 50
For Q ≤ DPayoff = pQ
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 200 200 200 20030 300 300 30040 400 40050 500
DQ 10 20 30 40 50
For Q ≤ DPayoff = pQ
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 200 200 200 20030 300 300 30040 400 40050 500
DQ 10 20 30 40 50
For Q > DPayoff = pD – I(Q – D)
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 200 200 200 20030 300 300 30040 400 40050 500
DQ 10 20 30 40 50
For Q > DPayoff = ($10)(30) – ($5)(40 – 30)
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 200 200 200 20030 300 300 30040 250 400 40050 500
DQ 10 20 30 40 50
For Q > DPayoff = $250
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 50 200 200 200 20030 0 150 300 300 30040 –50 100 250 400 40050 –100 50 200 350 500
DQ 10 20 30 40 50
For Q > DPayoff = pD – I(Q – D)
Example E.3
Special Inventory ModelsSpecial Inventory Models
Figure E.5
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 50 200 200 200 20030 0 150 300 300 30040 –50 100 250 400 40050 –100 50 200 350 500
DQ 10 20 30 40 50
Expected payoff30 =
Example E.3
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.
Special Inventory Special Inventory ModelsModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 50 200 200 200 20030 0 150 300 300 30040 –50 100 250 400 40050 –100 50 200 350 500
DQ 10 20 30 40 50
Expected payoff30 = 0.2($0) + 0.3($150) + 0.3($300) + 0.1($300) + 0.1($300)
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $10020 50 200 200 200 20030 0 150 300 300 300 19540 –50 100 250 400 40050 –100 50 200 350 500
DQ 10 20 30 40 50 Expected Payoff
Expected payoff30 = $195
Example E.3
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $100 $10020 50 200 200 200 200 17030 0 150 300 300 300 19540 –50 100 250 400 400 17550 –100 50 200 350 500 140
DQ 10 20 30 40 50 Expected Payoff
Figure E.6
Special Inventory ModelsSpecial Inventory ModelsOne-Period DecisionsOne-Period DecisionsDemand 10 20 30 40 50
Demand Probability 0.2 0.3 0.3 0.1 0.1
Profit per ornament during season = $10Loss per ornament after season = $5
10 $100 $100 $100 $100 $100 $10020 50 200 200 200 200 17030 0 150 300 300 300 19540 –50 100 250 400 400 17550 –100 50 200 350 500 140
DQ 10 20 30 40 50 Expected Payoff
Figure E.6
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