Chapter 13 – Inventory Management
16. Given:
D = 800 * 12 = 9,600
S = $40
H = 25% of purchase cost
Price Schedule Supplier A:
Range
Price per Unit (P)
1-199
$14.00
200-499
$13.80
500+
$13.60
1-149
$14.10
350+
$13.70
Chapter 13 – Inventory Management
Supplier B:
Step 1:
Beginning with the lowest unit price, compute minimum points for each price range until you find
a feasible minimum point.
Minimum point P = $13.70:
47453.473
)70.13(25.
40)600,9(22
H
DS
Feasible
Step 2:
Compute total cost for Q = 474.
17. Given:
D = 3,600 boxes per year
Q = 800 boxes (recommended)
S = $80/order
H = $10/box/year
Chapter 13 – Inventory Management
13–34
Education.
Step 2:
Determine total cost for the common minimum point and for the price breaks of all lower unit
costs.
Chapter 13 – Inventory Management
13–35
Education.
18. Given:
Daily usage = 800 feet/day & lead time = 6 days.
19. Given:
EDDLT = 300 units
dLT = 30 units
a. Determine ROP for 1% risk of stockout:
20. Given:
EDDLT = 600 lb.
dLT = 52 lb.
Stockout risk = 4%
a. Determine SS for 4% risk of stockout.
Using Appendix B, Table B, we look for the z value corresponding to 1.00 – .04 = 0.96.
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Education.
21. Given:
d = 21 gallons/week
d = 3.5 gallons/week
LT = 2 days & the dairy is open 7 days a week
Service level= 90%
Hint: Work in terms of weeks
a. Determine ROP and days of supply on hand:
Using Appendix B, Table B, we look for the z value corresponding to .90.
The closest probability is .8997, which corresponds to z = 1.28.
b. OI = 10 days & 8 gallons are on hand at the order time:
3487.3387/12)5.3(28.1
7
2
7
10
21)(
ALTOIzLTOIdQ d
(round up)
Determine the probability of experiencing a stockout before this order arrives:
Risk of a stockout at the end of the initial lead time:
Using Formula 13-13, set the ROP equal to the quantity on hand when the order is placed and
solve for z:
LTzdROP d)((LT)
Chapter 13 – Inventory Management
c. The manager is using the ROP model described in part a. One day after placing an order with
the supplier, the manager receives a call that the order will be delayed and will arrive 3 days
from the initial order date. Two gallons have been sold since the order was placed (one day
ago).
Determine the probability of a stockout:
ROP = 9 gallons.
Determine the probability of experiencing a stockout before this order arrives (in 2 days):
Risk of a stockout at the end of the initial lead time:
Using Formula 13-13, set the ROP equal to the quantity on hand 1 day after the order was
placed and solve for z:
LTzdROP d)((LT)
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22. Given:
d = 30 gallons/day
ROP = 170 gallons
SS = 50 gallons and provides a stockout risk of 9%
Step 1:
Solve for the standard deviation of demand during the lead time.
We know that SS = 50.
Using Appendix B, Table B, we look for the z value corresponding to 1.00 – .09 = .91.
Step 2:
Determine the SS.
Stockout risk = 3%.
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Education.
23. Given:
d = 85 boards/day
ROP = 625 boards
LT
= 6 days
LT = 1.1 days
Determine the probability of a stockout:
625 = (85 x 6) + z (85) (1.1)
24. Given:
Service level = 96%
d
= 12 units/day
d = 2 units/day
LT
= 4 days
LT = 1 day
a. Determine the ROP:
Using Appendix B, Table B, we look for the z value corresponding to .96.
The closest probability is .9599, which corresponds to z = 1.75.
b. The model might not be appropriate if seasonality were present because during the busy times
of the year, the ROP would be set too low (causing stockouts) and during the slow times of
the year, the ROP would be set too high (causing excess inventory).
Chapter 13 – Inventory Management
25. Given:
LT = 4 x (1 – 0.25) = 4 x 0.75 = 3 days
S = $30
D = 4,500 gallons
H = $3