HW-cycle&safety-stock NM
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Apr 3, 2024
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SEL
ECT THE
APP
ROP
RIA
TE LAB
EL FRO
M THE
"SE
NSI
TIVI
TY" TAB
ON THE
HO
ME TO
OL BAR
Homework Assignment Solution – Cycle & Safety Stock
1.
Revisit the ImportHome.com case study. Assume that the costs of the GM soymilk
maker and GM cooker are $35 per unit, and the annual inventory holding cost is 18%
of the product cost. All shipping data (shipping quantity, cost per shipment, and lead
time) and service level remain the same as the in-class example. Answer the
following questions based on the demand data of these two products provided in the
Excel file (round the mean and standard deviation of the demand to the nearest
integers; assume that one year has 53 weeks in all calculations).
(a)
(10 points)
For GM soymilk maker, calculate the annual shipping and inventory
carrying costs under both full container and half container. Which is better: full
container vs. half container? Solution:
When we look at the data, the mean is 25 units while the standard deviation is 8
units. Below you will see a chart for full and half containers.
Full Container
Half Container
Shipping quantity
(units)
1400
700
Cost per shipment ($)
3300
2600
Lead time (weeks)
13
15
For full container: Annual shipping cost: 25
×
53
÷
1400
×$
3300
=
$
3123.21
Safety stock: s
¿
=
z
α
σ
√
τ
=
normsinv
(
0.95
)
×
8
×
√
13
=
47
Average on-hand inventory: s
¿
+
Q
2
=
47
+
1400
2
=
747
Annual inventory cost: 747
×
(
$
35
×
0.18
)
=
$
4708.90
Total annual ops cost: $
3123.21
+
$
4708.90
=
$
7832.11
For half container:
Annual shipping cost: 25
×
53
÷
700
×$
2600
=
$
4921.43
Safety stock: s
¿
=
z
α
σ
√
τ
=
normsinv
(
0.95
)
×
8
×
√
15
=
51
SEL
ECT THE
APP
ROP
RIA
TE LAB
EL FRO
M THE
"SE
NSI
TIVI
TY" TAB
ON THE
HO
ME TO
OL BAR
Average on-hand inventory: s
¿
+
Q
2
=
51
+
700
2
=
401
Annual inventory cost: 401
×
(
$
35
×
0.18
)
=
$
2526.07
Total annual ops cost: $
4921.43
+
$
2526.07
=
$
7447.50
After reviewing the numbers we see that half containers are better overall.
(b)
(10 points)
For GM cooker, calculate the annual shipping and inventory
carrying costs under both full container and half container. Which is better: full
container vs. half container?
Solution:
When we look at the data, the mean is 35 units and standard deviation is 10
units. For full container: Annual shipping cost: 3
5
×
53
÷
1400
×$
3300
=
$
4372.50
Safety stock: s
¿
=
z
α
σ
√
τ
=
normsinv
(
0.95
)
×
10
×
√
13
=
59
Average on-hand inventory: s
¿
+
Q
2
=
59
+
1400
2
=
759
Annual inventory cost: 759
×
(
$
35
×
0.18
)
=
$
4783.63
Total annual ops cost: $
4372.50
+
$
4783.63
=
$
9156.13
For half container:
Annual shipping cost: 35
×
53
÷
700
×$
2600
=
$
6890.00
Safety stock: s
¿
=
z
α
σ
√
τ
=
normsinv
(
0.95
)
×
10
×
√
15
=
64
Average on-hand inventory: s
¿
+
Q
2
=
64
+
700
2
=
414
Annual inventory cost: 414
×
(
$
35
×
0.18
)
=
$
2606.34
Total annual ops cost: $
6890.00
+
$
2606.34
=
$
9496.34
After reviewing the data we see that the full container is a better option.
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