Day27 In-class Exercise copy
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School
Pennsylvania State University *
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Course
404
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
Pages
2
Uploaded by DUL596
SCM 404 Day 27 In-class Exercise Solution
Name: _______________
A manufacturer of medical equipment is located in Madison, Wisconsin. The medical equipment
is sold directly to cardiologists all over North America. The manufacturer currently divides the
U.S into
24
territories, each with its own sales force. All product inventories are maintained
locally
in each territory
.
o
HighVal product: weekly demand in each territory
μ
H
=
2,
σ
H
=
5
, weight
0.1
pounds, cost
$
200
each
o
LowVal product: weekly demand in each territory
μ
L
=
20,
σ
L
=
5
, weight
0.04
pounds, cost
$
30
each
o
Desired customer service level is CSL=
0.997
, holding cost is calculated based on
annual interest rate of
25%
o
Option A: Replenish inventory once a week using UPS
at each territory
o
UPS has a lead time of one week
o
The shipping cost is calculated using
$
0.66
+
0.26
x
,
x
is the quantity
shipped in pounds
o
Option B: Eliminate inventories in the territories,
aggregate all inventories in a finished-
goods warehouse at Madison, and replenish the warehouse once a week using FedEx.
The shipment size is for
1
unit of HighVal and
10
Units of LowVal
o
FedEx has a lead time of one week
o
The shipping cost is calculated using
$
5.53
+
0.53
x
,
x
is the quantity
shipped in pounds
o
Which option generates lower cost?
Ø
System cost
Ø
Inventory cost: HighVal product, LowVal product
Ø
Transportation cost: HighVal product, LowVal product
Ø
Replenishment lead time
L
=
1
week
Ø
Reorder interval
T
=
1
weeks (periodically replenishment)
Ø
CSL =
0.997
Ø
Average lot size:
Q
H
=
¿
expected demand during T weeks
Ø
Q
H
=
T μ
H
=
1
∗
2
=
2
units
Ø
Safety inventory
s s
H
Ø
Find the wanted z-value,
Pr
(
Z≤ z
)
=
CSL, Z
N
(
0,1
)
Ø
CSL
=
0.997,
z
=
2.75
Ø
σ
T
+
L
is the demand standard deviation during the reorder interval and lead
time:
σ
T
+
L
=
√
T
+
L
σ
H
=
¿
√
1
+
1
∗
5
=
7.07
Ø
s s
H
=
z
∗
¿
σ
T
+
L
=
19.4
units
Ø
Total HighVal holding inventory in each territory =
Q
H
2
+
s s
H
=
20.4
units
Ø
Total HighVal holding inventory across 24 territories:
24
∗
20.4
=
489.6
units
Ø
Average lot size:
Q
L
=
¿
expected demand during T weeks
Ø
Q
L
=
T μ
L
=
1
∗
20
=
20
units
Ø
Safety inventory
s s
L
Ø
Find the wanted z-value,
Pr
(
Z≤ z
)
=
CSL, Z
N
(
0,1
)
Ø
CSL
=
0.997,
z
=
2.75
Ø
σ
T
+
L
is the demand standard deviation during the reorder interval and lead
time:
σ
T
+
L
=
√
T
+
L
σ
L
=
¿
√
1
+
1
∗
5
=
7.07
Ø
s s
L
=
z
∗
¿
σ
T
+
L
=
19.4
units
Ø
Total LowVal holding inventory in each territory =
Q
L
2
+
ss
L
=
29.4
units
Ø
Total LowVal holding inventory across 24 territories:
24
∗
29.4
=
705.6
units
Ø
Holding cost for HighVal
Ø
$
200
∗
0.25
=
$
50
per unit per year
Ø
Holding cost for LowVal
Ø
$
30
∗
0.25
=
$
7.5
per unit per year
Ø
Annual inventory holding cost:
489.6
∗
$
50
+
705.6
∗
$
7.5
=
$
29,772
Since the inventory in each territory is replenished once a week:
Ø
The average replenishment order from each territory consists of
Q
H
=
2
units of
HighVal products,
Q
L
=
20
units of LowVal products.
Ø
Average weight of each replenishment order
Ø
0.1
∗
Q
H
+
0.04
∗
Q
L
=
0.1
∗
2
+
0.04
∗
20
=
1
pounds
Ø
Shipping cost per shipment order
Ø
$
0.66
+
0.26
∗
1
=
$
0.92
Ø
Each territory has 52 replenishment per year (1 year = 52 weeks) and there are 24
territories, the annual transportation cost
Ø
52
∗
24
∗
0.92
=
$
1148.16
Ø
Total cost = inventory cost + transportation cost
Total cost
¿
$
29,772
+
$
1148.16
=
$
30920.16
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