Practice Problems for Inventory Management
Note: For assignment 4, you may focus only on questions 12.6, 12.7, 12.8, 12.9, 12.10, 12.12, 12.13, 12.15.
12.6 If D=8000 per month, S=$45 per order, H=$2 per unit per month,
a. What is the economic order quantity?
b. How does your answer change if the holding cost doubles?
c. What if the holding cost drops to half?
12.7 Henry Crouch’s law office has traditionally ordered ink refills 60 units at a time. The firm
estimates that carrying cost is 40% of the $10 unit cost and that annual demand is about 240 units
per year. The assumptions of the basic EOQ model are thought to apply.
a. For what value of ordering cost would its action be optimal?
b. If the true ordering cost turns out to be much greater than your answer to part (a), what
is the impact on the firm’s ordering policy?
12.8 Madeline Thimmes’s Dream Store sells waterbeds and assorted supplies. Her best-selling bed
has an annual demand of 400 units. Ordering cost is $40; holding cost is $5 per unit per year.
a. To minimize the total cost, how many units should be ordered each time an order is
placed?
b. If the holding cost per unit was $6 instead of $5, what would be the optimal order
quantity?
12.9 Bell Canada stocks a certain switch connector at its central warehouse for supplying field service
offices. The yearly demand for these connectors is 15 000 units. Bell estimates its annual holding cost
for this item to be $25 per unit. The cost to place and process an order from the supplier is $75. The
company operates 300 days per year, and the lead time to receive an order from the supplier is two
working days.
a.
b.
c.
d.
Find the economic order quantity.
Find the annual holding costs.
Find the annual ordering costs.
What is the reorder point?
12.10 Lead time for one of your fastest-moving products is 21 days. Demand during this period
averages 100 units per day.
a. What would be an appropriate reorder point?
b. How does your answer change if demand during lead time doubles?
c. How does your answer change if demand during lead time drops to half?
12.12 Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company
chain with a central inventory operation. Thomas’s fastest-moving inventory item has a demand of
6000 units per year. The cost of each unit is $100, and the inventory carrying cost is $10 per unit per
year. The average ordering cost is $30 per order. It takes about five days for an order to arrive, and
the demand for one week is 120 units. (This is a corporate operation, and there are 250 working days
per year.)
a.
b.
c.
d.
e.
f.
What is the EOQ?
What is the average inventory if the EOQ is used?
What is the optimal number of orders per year?
What is the optimal number of days between any two orders?
What is the annual cost of ordering and holding inventory?
What is the total annual inventory cost, including cost of the 6000 units?
12.13 Joe Henry’s machine shop uses 2500 brackets during the course of a year. These brackets are
purchased from a supplier 90 kilometres away. The following information is known about the
brackets:
Annual demand:
2500
Holding cost per bracket per year:
$1.50
Order cost per order:
$18.75
Lead time:
2 days
Working days per year:
250
a. Given the above information, what would be the economic order quantity (EOQ)?
b. Given the EOQ, what would be the average inventory? What would be the annual
inventory holding cost?
c. Given the EOQ, how many orders would be made each year? What would be the annual
order cost?
d. Given the EOQ, what is the total annual cost of managing the inventory?
e. What is the time between orders?
f. What is the reorder point (ROP)?
12.15 M. Cotteleer Electronics supplies microcomputer circuitry to a company that incorporates
microprocessors into refrigerators and other home appliances. One of the components has an annual
demand of 250 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per
unit per year, and the ordering cost is $20 per order.
a.
b.
c.
d.
To minimize cost, how many units should be ordered each time an order is placed?
How many orders per year are needed with the optimal policy?
What is the average inventory if costs are minimized?
Suppose that the ordering cost is not $20, and Cotteleer has been ordering 150 units
each time an order is placed. For this order policy (of Q=150Q=150) to be optimal,
determine what the ordering cost would have to be.
12.27 Barbara Flynn is in charge of maintaining hospital supplies at General Hospital. During the past
year, the mean lead time demand for bandage BX-5 was 60 (and was normally distributed).
Furthermore, the standard deviation for BX-5 was seven. Ms. Flynn would like to maintain a 90%
service level.
a. What safety stock level do you recommend for BX-5?
b. What is the appropriate reorder point?
12.28 Based on available information, lead time demand for PC jump drives averages 50 units
(normally distributed), with a standard deviation of five drives. Management wants a 97% service level.
a. What value of Z should be applied?
b. How many drives should be carried as safety stock?
c. What is the appropriate reorder point?
12.40 A gourmet coffee shop in downtown Vancouver is open 200 days a year and sells an average of
75 pounds of Kona coffee beans a day. (Demand can be assumed to be distributed normally with a
standard deviation of 15 pounds per day.) After ordering (fixed cost 5 $16 per order), beans are
always shipped from Hawaii within exactly four days. Per-pound annual holding costs for the beans
are $3.
a. What is the economic order quantity (EOQ) for Kona coffee beans?
b. What are the total annual holding costs of stock for Kona coffee beans? (Assuming no
safety stock.)
c. What are the total annual ordering costs for Kona coffee beans?
d. Assume that management has specified that no more than a 1% risk of stockout is
acceptable. What should the reorder point (ROP) be?
e. What is the safety stock needed to attain a 1% risk of stockout during lead time?
f. What is the annual holding cost of maintaining the level of safety stock needed to support
a 1% risk?
g. If management specified that a 2% risk of stockout during lead time would be acceptable,
would the safety stock holding costs decrease or increase?
Solutions.
12.6
2(8,000)(45)
 600 units
2
(b) If H doubles, from $2 to $4/unit/month,
(a) EOQ 
2  8,000 45
= 424.26 units
4
(c) If H drops to half, from $2 to $1/unit/month,
EOQ =
2 8,000  45
EOQ 
12.7 (a)
1
 848.53 units
This problem reverses the unknown of a standard EOQ
60 
2  240  S
; or 60 
0.4  10
480 S
, or
4
60  120 S , so solving for S results in S 
3,600
 $30.
120
(b) If S were $30, then the EOQ would be 60. If the true
ordering too little at a time.
12.8
ordering cost turns out to be much greater than $30, then
(a) Economic Order Quantity (Holding cost  $5 per year):
Q
2 DS

H
2  400  40
 80 units
5
where D  annual demand, S  setup or order cost,
H  holding cost
(b) Economic Order Quantity (Holding cost  $6 per year):
Q
2 DS

H
2  400  40
 73 units
6
where D  annual demand, S  setup or order cost,
H  holding cost
12.9
D  15,000, H  $25/unit/year, S  $75
(a) EOQ 
2 DS

H
2  15,000  75
 300 units
25
(b) Annual holding costs  (Q/2)  H  (300/2)
 25  $3,750
(c) Annual ordering costs  (D/Q)  S  (15,000/300)
 75  $3,750
 15,000 units 
(d) ROP = d  L  
  2 days  100 units
 300 days 
12.10 (a) Reorder point  Demand during lead time
 100 units/day  21 days  2,100 units
(b) If demand during lead time doubles to 200 units/day,
ROP = 200 units/day × 21 days = 4,200 units.
(c) If demand during lead time drops to 50 units/day,
ROP = 50 units/day × 21 days = 1,050 units.
12.12
(a) EOQ =
2 DS
=
H
problem to solve for S.
2(6,000)(30)
= 189.74 units
10
(b) Average inventory = 94.87
(c) Optimal number of orders/year= 6000/189.74 = 31.62
the firm’s order policy is
(d) Optimal days between orders =
250
 7.91
31.62
(e) Cost of inventory management, excluding cost of goods = (31.62  30) + (94.87  10) ≈ $1,897.30
(f) Total annual inventory cost = $601,897.30 (including the $600,000 cost of goods)
Note: Rounding occurs in answers.
12.13
2 DS
2(2500)18.75

H
1.50
 250 brackets per order
Q 250
Average inventory  
 125 units
2
2
Q
Annual holding cost  H  125(1.50)  $187.50
2
D 2500
Number of orders 

 10 orders /year
Q
250
D
Annual order cost  S  10(18.75)  $187.50
Q
Q
D
TC  H  S  187.50  187.50  $375/ year
2
Q
Working days
Time between orders 
(D/Q)
250

 25 days
10
ROP  dL  10(2)  20 units (where 10  daily demand)
(a) Q 
(b)
(c)
(d)
(e)
(f)
d
12.15
2500
 10
250
(a) The EOQ assumptions are met, so the optimal order quantity is
EOQ 
2 DS

H
2(250)20
 100 units
1
(b) Number
of
 2.5 orders per year.
orders
per
year

D/Q

250/100
Note that this would mean in one year the company places 3 orders and in the next it would only need
2 orders since some inventory would be carried over from the previous year. It averages 2.5 orders per year.
(c) Average inventory  Q/2  100/2  50 units
(d) Given
an
annual
demand
of
250,
a
carrying
cost
of $1, and an order quantity of 150, M. Cotteleer Electronics must determine what the ordering cost would have to be for the order policy
of 150 units to be optimal. To find the answer to this problem, we must solve the traditional economic order quantity equation for the
ordering cost. As you can see in the calculations that follow, an ordering cost of $45 is needed for the order quantity of 150 units to be
optimal.
2 DS
H
2 H
SQ
2D
Q
(150)2 (1)
2(250)
22,500
=
 $45
500
=
12.27
(a)   60;   7
Safety stock for 90% service level  Z(at 0.90)
 7  1.28  8.96  9
(b) ROP  60  9  69 BX-5 bandages.
12.28
(a) Z  1.88
(b) Safety stock  Z  1.88(5)  9.4 drives
(c) ROP  50  9.4  59.4 drives
12.40 (a) d  75 lbs/day 200 days per year
D  15,000 lb/year
H  $3/lb/year S  $16/order
Q  400 lb of beans 
2(15,000)(16)
3
(b) Total annual holding cost =
Q
H = (200)($3) = $600
2
(c) Total annual order cost =
D
S = (37.5)(16) = $600
Q
(d) LT  4 days with   15
Stockout risk  1%
  2.33
ROP  Lead time demand  SS
where SS  ( )(dLT) and lead time demand  (d)(LT)
 dLT 


LT (15) 
ROP  369.99
 4  (15)  30
where ROP  (d)(LT)  SS
(e) SS  69.99 from part (d)
(f) Annual safety stock holding cost  $209.97
(g) 2% stockout level  Z = 2.054
SS  (Z)(dLT)  61.61
The lower we make our target service level, the less SS we need.