Transcript Document

Solved Problems
Chapter 12: Inventory
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Solved Problem
The data shows projected
annual dollar usage for 20
items. Exhibit 12.3 shows the
data sorted, and indicates that
about 70% of total dollar usage
is accounted for by the first 5
items.
Exhibit 12.2
Usage-Cost Data for
20 Inventoried Items
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Exhibit 12.3 ABC Analysis Calculations
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Exhibit 12.4 ABC Histogram for the Results from Exhibit 12.3
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Solved Problem: Merkle Pharmacies, P. 245
D = 24,000 cases per year.
Co = $38.00 per order.
I = 18 percent.
C = $12.00 per case.
Ch = IC = $2.16.
24,000
1
TC = Q ($2.16) +
($38.00)
Q
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EOQ =
√
2(24,000)(38) = 919 cases rounded
2.16
to a whole number.
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Solved Problem: Southern Office, p. 247
Southern Office Supplies, Inc. distributes laser printer
paper.
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Ordering costs are $45.00 per order.
One ream of paper costs $3.80.
Annual inventory-holding cost rate is 20%.
The average annual demand is 15,000 reams, or about
15,000/52 = 288.5 per week.
The standard deviation of weekly demand is about 71.
The lead time from the manufacturer is two weeks.
Inventory-holding cost is Ch = IC = 0.20($3.80) =
$0.76 per ream per year.
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Solved Problem
• The average demand during the lead time is
(288.5)(2) = 577 reams.
• The standard deviation of demand during the
lead time is approximately 71√2 = 100
reams.
• The EOQ model results in an order quantity of
1333, reorder point of 577, and total annual
cost of $1,012.92.
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Solved Problem
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Desired service level of 95%, which results in a stockout of roughly once
every 2 years. For a normal distribution, this corresponds to a standard
normal z-value of 1.645.
r = mL + zsL = 577 + 1.645(100) = 742 reams
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This policy increases the reorder point by 742 – 577 = 165 reams, which
represents the safety stock.
The cost of the additional safety stock is Ch times the amount of safety
stock, or ($0.76/ream)(165 reams) = $125.40.
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Solved Problem: Southern Office, p. 249, Fixed
Period Inventory Systems
Managing Fixed Period Inventory Systems
Economic time interval:
T = Q*/D
[12.12]
Optimal replenishment level without safety stock:
M = d (T + L)
[12.13]
Where:
d = Average demand per time period.
L = Lead time in the same time units.
M = Demand during the lead time plus review period.
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Managing Fixed Period Inventory Systems
Uncertain Demand
• Compute safety stock over the period T + L.
• The replenishment level is computed as:
M = mT+L + zσT+L
[12.14]
mT+L = mt (T + L)
[12.15]
σT+L = σt √T + L
[12.16]
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Solved Problem: p. 250
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A buyer orders fashion swimwear about six months
before the summer season.
Each piece costs $40 and sells for $60.
At the sale price of $30, it is expected that any
remaining stock can be sold during the August sale.
The cost per item of overestimating demand is equal to
the purchase cost per item minus the August sale price
per item: cs = $40 – $30 = $10.
The per-item cost of underestimating demand is the
difference between the regular selling price per item
and the purchase cost per item; that is, cu = $60 – $40
= $20.
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Solved Problem
Assume that a uniform probability distribution ranging
from 350 to 650 items describes the demand.
Exhibit 12.12 Probability Distribution for Single Period Model
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Solved Problem
The optimal order size Q must satisfy:
P (demand ≤ Q*) = cu /(cu + cs)
= 20/(20+10) = 2/3
Because the demand distribution is uniform, the
value of Q* is two-thirds of the way from 350 to
650. This results in Q* = 550.
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