CHAPTER 8
INVENTORY MODELS
TRUE/FALSE QUESTIONS
1. Inclusion of quantity discounts may influence both the order
2. In the continuous review system, order quantity tends to be
fixed, and order time is variable. This is reversed in a periodic
3. In the planned shortage model, you cannot recommend a maximum
4. The closer the unit salvage value is to the per unit item
cost, the higher the optimal order quantity will be when using the
5. In the single period inventory model, the optimal service
level is the proportion of total customer demand that will be
6. Excess inventory should be avoided if at all possible, since
it must be either sold at a discount, sold for salvage, or dumped.
7. Insufficient inventory should be avoided if at all possible
8. An inventory policy has two components: the order quantity
9. Holding costs and procurement/manufacturing costs are both
10. In the calculation of economic order quantity, manufacturing
costs for items produced in-house include the costs of setting up
11. The economic order quantity model assumes the item has little
12. The inventory holding cost is proportional to the order
quantity, but the annual ordering cost is inversely proportional to
the order quantity. Annual procurement costs do not depend on the
13. Quantity discounts reduce the unit price. Inventory costs are
14. Economic order quantity for production is optimal for a single
product. The solution for several products sharing a production
line requires computing an economic order quantity for each product.
MULTIPLE CHOICE QUESTIONS
1. Which of the following is not a main category of cost in
inventory models?
a. Customer satisfaction.
b. Production/procurement.
c. Quality/inspection.
d. Holding/carrying.
2. The strongest factor influencing the choice of inventory model
is the:
a. pattern of demand.
b. value of the inventoried item.
c. presence or absence of quantity discounts.
d. presence or absence of safety stocks.
3. “Shrinkage” of inventory includes:
a. reduced unit value.
b. theft.
c. obsolescence.
d. misplacement.
4. In the ABC classification system, “C” items typically account
for:
a. roughly half the annual production value.
b. around half the number of inventory SKU’s.
c. approximately one-third of annual inventory usage.
d. the smallest share of the total inventory.
5. In the economic order quantity (EOQ) model, if the holding
cost and the ordering cost both double, the value of Q* will:
a. decrease by 50%.
b. remain unchanged.
c. double.
d. quadruple.
6. When compared with the maximum inventory level of the economic
order quantity (EOQ) model, the maximum inventory level of the
production lot size model is:
a. smaller.
b. greater.
c. roughly equal.
d. unrelated.
7. In the basic economic order quantity (EOQ) model, at Q* the
estimated total annual holding cost:
a. is less than the estimated total annual ordering cost.
b. equals the estimated total annual ordering cost.
c. is greater then the estimated total annual ordering
cost.
d. bears no necessary relationship to estimated total
annual ordering cost.
8. In the basic economic order quantity (EOQ) model, if monthly
demand is a constant 430 units, the order quantity is 144 (12
dozen), and the firm operates during fifty five-day weeks a year,
the cycle time will be approximately:
a. 7 working days.
b. 7 calendar days.
c. 84 working days.
d. cannot be determined with the data provided.
9. For the production lot size model to be appropriate, the
relationship between D, annual demand, and P, maximum annual
production rate, must be:
a. D > P.
b. D = P.
c. D < P.
d. no necessary relationship exists.
10. In the basic economic order quantity (EOQ) model, a doubling
of estimated annual demand would lead to what change in Q*?
a. A doubling.
b. No change.
c. More than a 50% decrease.
d. Less than a 50% increase.
11. In the production lot size model:
a. the maximum inventory position, M, equals Q*.
b. additions to, and withdrawals from, inventory occur at
equal rates.
c. at Q*, annual production setup costs equal annual
holding costs.
d. at Q*, annual production setup costs exceed annual
holding costs.
12. In the planned shortage model, a zero value for R, the reorder
point, means:
a. reorder only when a customer appears.
b. instantaneous inventory replenishment.
c. reorder when the back-order position is zero.
d. reorder in a quantity equal to the back-order position.
13. When comparing the safety stock of the cycle service level
(SSc) approach with the safety stock level of the unit service level
(SSu) approach, other things being equal:
a. SSc > SSu.
b. SSc = SSu.
c. SSc < SSu.
d. no necessary relationship exists.
14. In the single period inventory model:
a. salvage value is always positive.
b. goodwill (shortage) costs are always less than the item
cost.
c. goodwill (shortage) costs are always less than the
salvage value.
d. salvage value is always less than the selling price.
15. In the single period inventory model, if the unit salvage
value equals the unit cost of the good, the optimal service level
will be:
a. 0.
b. 50%.
c. 100%.
d. unknown.
16. In the single period inventory model, customer demand is
always assumed to be:
a. normally distributed.
b. uniformly distributed.
c. of unknown distribution.
d. stochastic.
17. In the single period inventory model, when the goodwill cost
increases:
a. the optimal order quantity will decrease.
b. the optimal order quantity will increase.
c. the mean demand will increase.
d. the mean demand will decrease.
18. In the single period inventory model, the probability
distribution for customer demand:
a. must be discrete.
b. is directly derived from sales data.
c. may be continuous.
d. is generally assumed to be uniform.
19. Opportunity cost (or shrinkage or obsolescence) is an example
of:
a. holding cost.
b. order/setup cost.
c. customer satisfaction cost.
d. procurement/manufacturing cost.
20. A two bin system is an example of a:
a. (R,M) policy.
b. (R,Q) policy.
c. (T,M) policy.
d. (T,R,M) policy.
SHORT ANSWER QUESTIONS
1. What are the three typical types of inventory process
classifications?
2. By what amount does adding safety stock increase annual
inventory costs?
3. If sales data differs from demand, what constitutes the
difference?
4. In the production lot size model, the maximum inventory level
(M) is lower than in the EOQ model. Why? By how much?
(EOQ reaches M at delivery time. In the production lot size model,
inventory increases gradually until production pauses.
5. If you compare EOQ with the production lot size model, the
optimal order quantity and the holding costs differ by the factor
1 – (demand rate / production rate). Explain.
6. Your major competitor, Grause’s Sofa Factory, just went out of
business with a large number of unfilled backorders. Many Grause’s
customers have lost their deposits. Your sales staff is creating a
marketing campaign targeting Grause’s customer base. How might you
temporarily modify the numbers used in your own planned shortage
model?
7. In the planned shortage model, what is the difference between
annual time-dependent shortage cost and annual time-independent
shortage cost?
8. When employing A,B,C inventory classification, would you use
EOQ models for type C items? Explain.
9. What advantage does an (R,M) model have over an (R,Q) model?
10. Why is there no (T,Q) policy?
FORMULATION/SOLUTION/ANALYSIS QUESTIONS
1. Consider a basic economic order quantity (EOQ) model with the
following characteristics:
Item cost: $15.
Item selling price: $20.
Monthly demand: 500 units (constant)
Annual holding cost: 9% of purchase cost
Cost per order: $18.
Order lead time: 5 days
Firm’s work year: 300 days (50 weeks @ 6 days per week)
Safety stock: 15% of monthly demand
For this problem, determine the values of:
2. Garner is your sole supplier of gremmels, a key component in
the Farfel unit your company produces and sells. Formerly, you
ordered from Garner 800 units monthly, to meet an annual need
(demand) for 9600 units. Purchase cost was $3.00 per unit. Now,
however, Garner is offering discounts of 7% on orders of 1500 or
more, and 15% on orders of 3000 units or more. Orders are placed and
filled at a cost of $32 per order. Inventory holding cost is
estimated at 20% of purchase cost, per item, per year. Under the new
discount plan, what is your best strategy?
3. The annual demand for inventory item 67J is 6000 SKU’s. Order
lead time is 6 workdays, and the firm’s “year” is 300 days (6
workdays weekly, times 50 weeks). Empirical analysis indicates that
the daily standard deviation of SKU demand is 4 units. If the firm
desires only a 5% chance of a stockout, during any inventory cycle:
A. What is the corresponding safety stock level?
B. What is the corresponding reorder point, R?
C. Suppose Q* = 400. Now if the firm is willing to be out of stock
of 67J, an average of no more than two inventory cycles per year,
what should be the safety stock level?
4. A distributor of consumer appliances wants to calculate the
reorder point for a popular model of microwave oven. It operates 365
days a year, and wishes to maintain a 98% unit service level. Other
relevant factors are:
Annual demand: 300 units
Lead time: 5 days
Standard deviation of demand during lead time: 7 units
Order quantity (Q*): 25
A. What is the reorder point, R?
B. What major assumption underlies the application of this
technique?
C. Is the safety stock suggested here different than it would be for
a cycle service level of 98%?
5. Anderson Supply Company sells windows and French doors. Its
most popular French door model is a six foot unit, which it
purchases from Marvel doors. The units cost Anderson $500 each and
sell for $700 each. Anderson uses a 22% annual holding cost rate and
the cost of placing an order with Marvel for the doors is $200. If
Anderson runs out of stock of doors it estimates that it incurs a
goodwill cost of $15 per unit for each week a customer must wait for
the door. The fixed administrative cost to process a backorder is
estimated to be $5. Anderson sells an average of 30 units per week
and the lead time for delivery of the doors is approximately two
weeks.
A. Determine the optimal order quantity and reorder point for the
doors.
B. Approximately what percentage of customers will have to wait for
their units?
6. Flavin Cosmetics produces 80,000 tubes of lipstick monthly. It
currently purchases the cases used in its lipsticks from McGraw
Metals. The cases cost Flavin $.045 each and the cost to place an
order with McGraw is estimated to be $150. Approximately a half
percent of all cases delivered by McGraw are defective so that
Flavin must order 80,402 (80,000/.995) cases to support its
production.
Flavin is considering producing the cases in-house. It can do this
by leasing a casing machine at a cost of $9,000 per year which is
capable of producing 200,000 tubes per month. The production set up
cost to use this machine is $200 and the incremental production cost
of cases is $.038. In this case, there will be no defective cases.
Flavin estimates its holding cost rate for cases is 20% whether they
are purchased or produced in-house.
A. Determine whether Flavin should continue to purchase cases from
McGraw or begin in-house production if their objective is to
minimize the cost of lipstick production.
B. What is Flavin’s optimal purchase or production quantity?
7. A convenience store retailer wants to determine the number of
bags of Easter Beans to order from his wholesaler for the upcoming
holiday season (Easter Beans are similar to jelly beans, but are
larger and more egg-shaped.)
The bags cost the retailer $.49 each and sell for $1.09. Bags
remaining unsold as of the Monday following Easter are placed on
sale for $.25 each and, in the past, have always sold out. If the
store runs out of Easter Beans before Easter Sunday, the goodwill
loss is estimated to be $.60 per bag. The bags come ten to a carton
and the demand in cartons is estimated to be distributed as follows:
x P(x) ´
50 .10
60 .15
70 .30
80 .30
90 .10
100 .05
A. How many cartons should the retailer order?
B. What is the retailer’s expected profit or loss if he orders
optimally?
8. Monthly sales of Better House magazine at Smith’s Foods follow
a normal distribution with a mean of 140 copies and a standard
deviation of 15 copies. The magazine sells at Smith’s for $1.25 a
copy and costs Smith’s $.50 per copy. Unsold copies are repurchased
by the publisher for $.10 per copy. Smith’s management estimates
that if it runs out of Better House magazine it suffers a goodwill
loss of approximately $.80 for each unsatisfied customer.
A. Determine Smith’s optimal order quantity each month for Better
House magazine.
B. Determine Smith’s expected monthly profit from Better House
magazine if it orders optimally.
C. The publisher of Better House magazine is offering Smith’s the
following option. It will increase its selling price from $.50 to
$.55, but will also increase the amount it credits returned
magazines from $.10 to $.25. Should Smith’s take this deal? Give
your reasons.
9. Below is the published all units discount schedule for cases
of Brightall lightbulbs, with breakpoints at 100, 250, and 500.
< 100 cases
$5.00/case
100-250 cases
$4.50/case
251-500 cases
$4.00/case
> 500 cases
$3.80/case
Obviously, no one would buy 99 cases at a cost of $495 since you can
get 110 cases at the same price. What are the real breakpoints?
10. Annual demand = 2000 units.
Cost of order = $100
Holding cost = $10
Cost of backorder = $5
Cost of item = $50
Goodwill cost = $10
Should you use a planned shortage model or EOQ?