Practice Problems: Chapter 12, Inventory Management
Problem 1: ABC Analysis
Item
Annual
Demand
Unit value
A104
80
40.25
D205
120
80.75
X104
150
10.00
U404
150
40.50
L205
50
60.70
S104
20
80.20
X205
20
80.15
L104
100
20.05
Item
Annual $
Usage
% of $ usage
Annual
$ Usage
Cum. % of $
Cum. % no. of items
Class
Problem 2:
A firm has 1,000 “A” items (which it counts every week, i.e., 5 days), 4,000 “B” items (counted
every 40 days), and 8,000 “C” items (counted every 100 days). How many items should be counted
per day?
Item Class
No. of items
Policy
A
1000
Every 5 days
B
4000
Every 40 days
C
8000
Every 100 days
Count/day
Problem 3: Given, Demand = 360, Holding cost = $0.80/unit/year, Ordering cost = $100 per
order. What is the EOQ?
Problem 4: Given the data from Problem 3, and assuming a 250-day work year; how many orders
should be processed per year? What is the expected time between orders?
Problem 5: What is the total cost for the inventory policy used in Problem 3?
Problem 6: Assume that the demand was actually higher than estimated (i.e., 500 units instead of
360 units). What will be the actual annual total cost?
Problem 7: If demand for an item is 3 units per day, and delivery lead-time is 15 days, what should
we use for a re-order point?
Problem 8: Assume that our firm produces type C fire extinguishers. We make 30,000 of these fire
extinguishers per year. Each extinguisher requires one handle (assume a 300 day work year for
daily usage rate purposes). Assume an annual carrying cost of $1.50 per handle; production setup
cost of $150, and a daily production rate of 300.
a.
What is the optimal production order quantity?
b.
Determine (i) Imax, (ii) average inventory, (iii) annual total cost, (iv) number of batches per
year, (v) time between orders and (vi) duration of production run.
Problem 9:
We need 5,000 special valve units per year. The ordering cost for these is $100 per order and the
carrying cost is assumed to be 25% of the cost per unit. Price schedule is as given below.
Quantity range
1 - 149
150 - 399
400 and above
What should be the order quantity?
Price/unit
80.00
70.00
68.00
Problem 10: Litely Corp sells 1,350 of its special decorator light switch per year, and places orders
for 300 of these switches at a time. Litely estimates discrete probability distribution for demand
during lead time as follows:
Demand
60
70
75
80
85
Probability
0.20
0.30
0.20
0.15
0.15
The carrying cost per unit per year is calculated as $5 and the stock-out cost is estimated at $6 ($3
lost profit per switch and another $3 lost in goodwill, or future sales loss). What level of safety
stock should Litely use for this product? Assume that the ROP with no safety stock is equal to 75
units.
Problem 11: Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular.
The anticipated demand during lead time can be approximated by a normal curve having a mean of
180 units and a standard deviation of 40 units. What safety stock should Litely carry to achieve a
95% service level?
Problem 12: Grey Wolf lodge is a popular 500-room hotel in the North Woods. Managers need to
keep close tabs on all of the room service items, including a special pint-scented bar soap. The
daily demand for the soap is 275 bars, with a standard deviation of 30 bars. Ordering cost is $10
and the inventory holding cost is $0.30/bar/year. The lead time from the supplier is 5 days. The
lodge is open 365 days a year. The management wants to have a 99 percent cycle-service level.
a. What should the reorder point be for the bar of soap?
b. If the lead time is also variable with a standard deviation of 1 day, what should be the reorder
point?
Problem 13: A small town monthly news magazine circulation averages 2000 copies with a
standard deviation of 250. The cost per copy is $1.25 and sells for $3.99 per copy. Any unsold
copy is recycled, the value of which 0.20 per copy.
a.
What is the cost of stock out per copy?
b.
What is the cost of overstocking per copy?
c.
How many copies of the magazine must be printed?
d.
What is the stock out risk?