3) If the standard deviation of demand is six per week, demand is 50 per week, and the desired service
level is 95%, approximately what is the statistical safety stock?
A) 8 units
B) 10 units
C) 16 units
D) 64 units
E) Cannot be determined without lead time data.
4) A specific product has demand during lead time of 100 units, with a standard deviation during lead
time of 25 units. What safety stock (approximately) provides a 95% service level?
A) 41
B) 55
C) 133
D) 140
E) 165
5) Demand for dishwasher water pumps is 8 per day. The standard deviation of demand is 3 per day, and
the order lead time is four days. The service level is 95%. What should the reorder point be?
A) about 18
B) about 24
C) about 32
D) about 38
E) more than 40
6) The purpose of safety stock is to:
A) replace failed units with good ones.
B) eliminate the possibility of a stockout.
C) eliminate the likelihood of a stockout due to erroneous inventory tally.
D) control the likelihood of a stockout due to variable demand and/or lead time.
E) protect the firm from a sudden decrease in demand.
7) The proper quantity of safety stock is typically determined by:
A) using a single-period model.
B) carrying sufficient safety stock so as to eliminate all stockouts.
C) multiplying the EOQ by the desired service level.
D) setting the level of safety stock so that a given stockout risk is not exceeded.
E) minimizing total costs.
8) If demand is not uniform and constant, then stockout risks can be controlled by:
A) increasing the EOQ.
B) spreading annual demand over more frequent, but smaller, orders.
C) raising the selling price to reduce demand.
D) adding safety stock.
E) reducing the reorder point.
9) If daily demand is normally distributed with a mean of 15 and standard deviation of 5, and lead time is
constant at 4 days, a 90 percent service level will require how much safety stock?
A) 7 units
B) 10 units
C) 13 units
D) 16 units
E) 26 units
10) If daily demand is constant at 10 units per day, and lead time averages 12 days with a standard
deviation of 3 days, 95 percent service requires how much safety stock?
A) 28 units
B) 30 units
C) 49 units
D) 59 units
E) 114 units
11) In a safety stock problem where both demand and lead time are variable, demand averages 150 units
per day with a daily standard deviation of 16, and lead time averages 5 days with a standard deviation of
1 day. What is the standard deviation of demand during lead time?
A) 15 units
B) 100 units
C) 154 units
D) 500 units
E) 13,125 units
12) ________ is the complement of the probability of a stockout.
13) If a safety stock problem includes parameters for average daily demand, standard deviation of
demand, and lead time, then ________ is variable and ________ is constant.
14) When demand is constant and lead time is variable, the safety stock computation requires three
inputs: the value of Z, ________, and the standard deviation of lead time.
15) Define service level.
16) What happens to the cost of safety stock when the service level increases?
17) Thomas’ Bike Shop stocks a high volume item that has a normally distributed demand during lead
time. The average daily demand is 70 units, the lead time is 4 days, and the standard deviation of demand
during lead time is 15.
a. How much safety stock provides a 95% service level to Thomas?
b. What should the reorder point be?
18) The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct
office chair that costs $300. The annual holding cost rate is 40% of the item cost, annual demand is 900
units, and the ordering cost is $20 per order. The lead time is 4 days. Because demand is variable
(standard deviation of daily demand is 2.4 chairs), PCE has decided to establish a customer service level
of 90%. The store is open 300 days per year.
a. What is the optimal order quantity?
b. What is the safety stock?
c. What is the reorder point?
19) Huckaby Motor Services, Inc. rebuilds small electrical items such as motors, alternators, and
transformers, all using a certain type of copper wire. The firm’s demand for this wire is approximately
normal, averaging 20 spools per week, with a standard deviation of 6 spools per week. Cost per spool is
$24; ordering costs are $25 per order; inventory handling cost is $4.00 per spool per year. Acquisition lead
time is four weeks. The company works 50, 5-day weeks per year.
a. What is the optimal size of an order, if minimization of inventory system cost is the objective?
b. What are the safety stock and reorder point if the desired service level is 90%?
20) Demand for ice cream at the Ouachita Dairy can be approximated by a normal distribution with a
mean of 47 gallons per day and a standard deviation of 8 gallons per day. The new management desires a
service level of 95%. Lead time is four days; the dairy is open seven days a week. What reorder point
would be consistent with the desired service level?
21) The Winfield Distributing Company has maintained an 80% service level policy for inventory of
string trimmers. Mean demand during lead time is 170 trimmers, and the standard deviation during lead
time is 60 trimmers. The annual cost of carrying one trimmer in inventory is $6. The area sales people
have recently told Winfield’s management that they could expect a $400 improvement in profit (based on
current figures of cost per trimmer) if the service level were increased to 99%. Is it worthwhile for
Winfield to make this change?
22) Daily demand for a product is normally distributed with a mean of 150 units and a standard deviation
of 15 units. The firm currently uses a reorder point system, and it seeks a 75% service level during the
lead time of 6 days.
a. What safety stock is appropriate for the firm?
b. What is the reorder point?
23) Daily demand for a product is normally distributed with a mean of 200 units and a standard deviation
of 20 units. The firm currently uses a reorder point system, with a lead time of 4 days.
a. What safety stock provides a 50% service level?
b. What safety stock provides a 90% service level?
c. What safety stock provides a 99% service level?
24) Average daily demand for a product is normally distributed with a mean of 5 units and a standard
deviation of 1 unit. Lead time is fixed at four days.
(a) What is the reorder point if there is no safety stock?
(b) What is the reorder point if the service level is 80 percent?
(c) How much more safety stock is required if the service level is raised from 80 percent to 90 percent?
25) Average daily demand for a product is normally distributed with a mean of 20 units and a standard
deviation of 3 units. Lead time is fixed at 25 days. What reorder point provides for a service level of 95
percent?
26) A product has a reorder point of 110 units, and is ordered four times a year on average. The following
table shows the historical distribution of demand values observed during lead time.
Demand
Probability
100
.3
110
.4
120
.2
130
.1
Managers have noted that stockouts occur 30 percent of the time with this policy, and they question
whether a change in inventory policy, to include some safety stock, might be an improvement. The
managers realize that any safety stock would increase the service level, but they are worried about the
increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per
occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher
levels of safety stock add to total costs, or not? What level of safety stock is best?
27) Demand for a product is approximately normal, averaging 5 units per day with a standard deviation
of 1 unit per day. Lead time for this product is approximately normal, averaging 10 days with a standard
deviation of 3 days. What reorder point provides a service level of 90 percent?
28) A product has a reorder point of 260 units, and is ordered ten times a year on average. The following
table shows the historical distribution of demand values observed during lead time.
Demand
Probability
240
.1
250
.2
260
.4
270
.2
280
.1
Currently, stockouts are valued at $5 per unit per occurrence, while inventory carrying costs are $2 per
unit per year. Should the firm add safety stock? If so, how much safety stock should be added?
29) Demand for a product is relatively constant at five units per day. Lead time for this product is
normally distributed with a mean of ten days and a standard deviation of three days.
(a) What reorder point provides a 50 percent service level?
(b) What reorder point provides a 90 percent service level?
(c) If the lead time standard deviation can be reduced from 3 days to 1, what reorder point now provides
90 percent service? How much is safety stock reduced by this change?
Section 6 Single-Period Model
1) Which of the following items is mostly likely managed using a single-period order model?
A) Christmas trees
B) canned food at the grocery store
C) automobiles at a dealership
D) metal for a manufacturing process
E) gas sold to a gas station
2) The main trait of a single-period model is that:
A) inventory has limited value after a certain period of time.
B) it has the largest EOQ sizes.
C) the order quantity should usually equal the expected value of demand.
D) supply is limited.
E) the cost of a shortage cannot be determined accurately.
3) A local club is selling Christmas trees and deciding how many to stock for the month of December. If
demand is normally distributed with a mean of 100 and standard deviation of 20, trees have no salvage
value at the end of the month, trees cost $20, and trees sell for $50 what is the service level?
A) .60
B) .20
C) .84
D) .40
E) unable to determine given the above information
4) Suppose that papers for a newspaper stand cost $0.40 and sell for $0.80. They currently have no salvage
value. If the stand owner is able to find an outlet that would provide a salvage value of $0.10, what would
be the increase in service level?
A) .5
B) 0
C) .07
D) 1
E) unable to determine given only the above information
5) Service level is:
A) the probability of stocking out.
B) the probability of not stocking out.
C) something that should be minimized in retail.
D) calculated as the cost of a shortage divided by (the cost of shortage + the cost of overage) for single–
period models.
E) B and D
6) A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is
normal with a mean of 5 trays and standard deviation of 1 tray. If the owner wants a service level of at
least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts
have no salvage value after the day is complete.
A) 5
B) 4
C) 6
D) 7
E) unable to determine with the above information
7) Consider a local club selling Christmas trees. If trees cost $15 and sell for $60 with no salvage value,
what is the ideal service level? If salvage value is increased to $5, what is the change in service level?
8) Consider a local club selling Christmas trees. If demand is normal with a mean of 200 and a standard
deviation of 50, how many trees should the club stock if service level must be greater than 95%?
9) Demand for gallons of milk (a perishable item) is normally distributed with a weekly mean of 50 and
standard deviation of 15. How many additional gallons of milk must be stocked to increase the service
level from 50% to 80%?
10) Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price
by 70% and always sells for this lower price instantly. If weekly demand for milk is normally distributed
with a mean of 200 gallons and standard deviation of 25 gallons, find the price for which a fresh gallon of
milk sells. Assume a service level of 95% and that the store purchases milk for $2 per gallon.
11) A newspaper boy is trying to perfect his business in order to maximize the money he can save for a
new car. Daily paper sales are normally distributed, with a mean of 100 and standard deviation of 10. He
sells papers for $0.50 and pays $0.30 for them. Unsold papers are trashed with no salvage value. How
many papers should he order each day and what % of the time will he experience a stockout? Are there
any drawbacks to the order size proposed and how could the boy address such issues?
Section 7 Fixed-Period (P) Systems
1) The fixed-period inventory model can have a stockout during the review period as well as during the
lead time, which is why fixed-period systems require more safety stock than fixed–quantity systems.
2) The fixed-period inventory system requires more safety stock than a fixed-quantity system because:
A) a stockout can occur during the review period as well as during the lead time.
B) this model is used for products that have large standard deviations of demand.
C) this model is used for products that require very high service levels.
D) replenishment is not instantaneous.
E) setup costs and holding costs are large.
3) A disadvantage of the fixed-period inventory system is that:
A) it involves higher ordering costs than the fixed quantity inventory system.
B) additional inventory records are required.
C) the average inventory level is decreased.
D) since there is no count of inventory during the review period, a stockout is possible.
E) orders usually are for larger quantities.
4) What is the difference between P and Q inventory systems?
A) order size
B) order spacing
C) maximum service level
D) lead time length
E) A and B
5) Which of the following is a requirement of Q systems?
A) perpetual inventory system
B) constant order spacing
C) variable lead time
D) constant demand
E) all of the above
6) Q is to ________ systems as P is to ________ systems.
A) fixed quantity, fixed period
B) variable demand, constant demand
C) variable lead time, variable demand
D) variable quantity, variable period
E) quality, price
7) Which of the following should be higher in P systems than Q systems?
A) lead time
B) demand
C) order size
D) order spacing
E) safety stock
8) An advantage of the fixed-period inventory system is that:
A) safety stock will be lower than it would be under a fixed-quantity inventory system.
B) there is no physical count of inventory items when an item is withdrawn.
C) no inventory records are required.
D) orders usually are for smaller order quantities.
E) the average inventory level is reduced.
9) A(n) ________ system triggers inventory ordering on a uniform time frequency.
10) What is a fixed-period system?
11) Describe the difference between a fixed-quantity and a fixed-period inventory system?