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11 Dependent Demand: The Case for Material Requirements Planning

11 Dependent Demand: The Case for Material Requirements Planning

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6.11

The material structure tree
shows how many units are
needed at every level of
production.

DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNING

227

Note that the number in the parentheses in Figure 6.12 indicates how many units of that particular item are needed to make the item immediately above it. Thus, B(2) means that it takes
2 units of B for every unit of A, and F(2) means that it takes 2 units of F for every unit of C.
After the material structure tree has been developed, the number of units of each item
required to satisfy demand can be determined. This information can be displayed as follows:
Part B:
Part C:
Part D:
Part E:
Part F:

2 * number of A’s = 2 * 50 = 100
3 * number of A’s = 3 * 50 = 150
2 * number of B’s = 2 * 100 = 200
3 * number of B’s + 1 * number of C’s = 3 * 100 + 1 * 150 = 450
2 * number of C’s = 2 * 150 = 300

Thus, for 50 units of A we need 100 units of B, 150 units of C, 200 units of D, 450 units of
E, and 300 units of F. Of course, the numbers in this table could have been determined directly
from the material structure tree by multiplying the numbers along the branches times the
demand for A, which is 50 units for this problem. For example, the number of units of D needed
is simply 2 * 2 * 50 = 200 units.

Gross and Net Material Requirements Plan
Once the materials structure tree has been developed, we construct a gross material requirements
plan. This is a time schedule that shows when an item must be ordered from suppliers when there
is no inventory on hand, or when the production of an item must be started in order to satisfy the
demand for the finished product at a particular date. Let’s assume that all of the items are produced
or manufactured by the same company. It takes one week to make A, two weeks to make B, one
week to make C, one week to make D, two weeks to make E, and three weeks to make F. With this
information, the gross material requirements plan can be constructed to reveal the production
schedule needed to satisfy the demand of 50 units of A at a future date. (Refer to Figure 6.13.)
The interpretation of the material in Figure 6.13 is as follows: If you want 50 units of A at
week 6, you must start the manufacturing process in week 5. Thus, in week 5 you need 100 units
of B and 150 units of C. These two items take 2 weeks and 1 week to produce. (See the lead

FIGURE 6.13
Gross Material
Requirements Plan for 50
Units of A

Week
1

2

3

4

5

50

Required Date
A

Order Release

50

Required Date

100

B

100

Order Release

150

Required Date
C
150

Order Release

200

Required Date
200

Order Release

300 150

Required Date
E
300

Order Release

150

300

Required Date
F
300

Lead Time ϭ 1 Week

Lead Time ϭ 2 Weeks

Lead Time ϭ 1 Week

Lead Time ϭ 1 Week

D

Order Release

6

Lead Time ϭ 2 Weeks

Lead Time ϭ 3 Weeks

228

CHAPTER 6 • INVENTORY CONTROL MODELS

TABLE 6.9
On-Hand Inventory

Using on-hand inventory to
compute net requirements.

FIGURE 6.14
Net Material
Requirements Plan for
50 units of A.

ITEM

ON-HAND INVENTORY

A

10

B

15

C

20

D

10

E

10

F

5

times.) Production of B should be started in week 3, and C should be started in week 4. (See the
order release for these items.) Working backward, the same computations can be made for all
the other items. The material requirements plan graphically reveals when each item should be
started and completed in order to have 50 units of A at week 6. Now, a net requirements plan
can be developed given the on-hand inventory in Table 6.9; here is how it is done.
Using these data, we can develop a net material requirements plan that includes gross requirements, on-hand inventory, net requirements, planned-order receipts, and planned-order releases for each item. It is developed by beginning with A and working backward through the
other items. Figure 6.14 shows a net material requirements plan for product A.

Week
Item
A

B

C

D

E

F

1

2

3

4

5

50
10
40
40

Gross
On-Hand 10
Net
Order Receipt
Order Release

80
15
65
65

1

A

2

65
120
20
100
100

Gross
On-Hand 20
Net
Order Receipt
Order Release

A

1

100

Gross
On-Hand 10
Net
Order Receipt
Order Release

Gross
On-Hand 5
Net
Order Receipt
Order Release

Lead
Time

40

Gross
On-Hand 15
Net
Order Receipt
Order Release

Gross
On-Hand 10
Net
Order Receipt
Order Release

6

130
10
120
120

B

1

120
195
10
185
185
185

B

100
0
100
100

2

100
200
5
195
195

195

C

C

3

6.11

DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNING

229

The net requirements plan is constructed like the gross requirements plan. Starting with
item A, we work backward determining net requirements for all items. These computations are
done by referring constantly to the structure tree and lead times. The gross requirements for A
are 50 units in week 6. Ten items are on hand, and thus the net requirements and planned-order
receipt are both 40 items in week 6. Because of the one-week lead time, the planned-order
release is 40 items in week 5. (See the arrow connecting the order receipt and order release.)
Look down column 5 and refer to the structure tree in Figure 6.13. Eighty 12 * 402 items of B
and 120 = 3 * 40 items of C are required in week 5 in order to have a total of 50 items of A in
week 6. The letter A in the upper-right corner for items B and C means that this demand for B
and C was generated as a result of the demand for the parent, A. Now the same type of analysis
is done for B and C to determine the net requirements for D, E, and F.

Two or More End Products
So far, we have considered only one end product. For most manufacturing companies, there are
normally two or more end products that use some of the same parts or components. All of the
end products must be incorporated into a single net material requirements plan.
In the MRP example just discussed, we developed a net material requirements plan for
product A. Now, we show how to modify the net material requirements plan when a second end
product is introduced. Let’s call the second end product AA. The material structure tree for
product AA is as follows:
AA

D(3)

F(2)

Let’s assume that we need 10 units of AA. With this information we can compute the gross
requirements for AA:
Part D:
Part F:

3 * number of AA’s = 3 * 10 = 30
2 * number of AA’s = 2 * 10 = 20

To develop a net material requirements plan, we need to know the lead time for AA. Let’s
assume that it is one week. We also assume that we need 10 units of AA in week 6 and that we
have no units of AA on hand.
Now, we are in a position to modify the net material requirements plan for product A to include AA. This is done in Figure 6.15.
Look at the top row of the figure. As you can see, we have a gross requirement of 10 units
of AA in week 6. We don’t have any units of AA on hand, so the net requirement is also 10 units
of AA. Because it takes one week to make AA, the order release of 10 units of AA is in week 5.
This means that we start making AA in week 5 and have the finished units in week 6.
Because we start making AA in week 5, we must have 30 units of D and 20 units of F in
week 5. See the rows for D and F in Figure 6.15. The lead time for D is one week. Thus, we must
give the order release in week 4 to have the finished units of D in week 5. Note that there was no
inventory on hand for D in week 5. The original 10 units of inventory of D were used in week 5
to make B, which was subsequently used to make A. We also need to have 20 units of F in week
5 to produce 10 units of AA by week 6. Again, we have no on-hand inventory of F in week 5.
The original 5 units were used in week 4 to make C, which was subsequently used to make A.
The lead time for F is three weeks. Thus, the order release for 20 units of F must be in week 2.
(See the F row in Figure 6.15.)
This example shows how the inventory requirements of two products can be reflected in the
same net material requirements plan. Some manufacturing companies can have more than 100
end products that must be coordinated in the same net material requirements plan. Although
such a situation can be very complicated, the same principles we used in this example are

230

CHAPTER 6 • INVENTORY CONTROL MODELS

FIGURE 6.15
Net Material
Requirements Plan,
Including AA

Week
Item

Inventory

AA

Gross
On-Hand: 0
Net
Order Receipt
Order Release

A

B

C

D

E

F

1

2

3

4

5

10
0
10
10

1 Week

50
10
40
40

1 Week

40

Gross
On-Hand: 15
Net
Order Receipt
Order Release

80
15
65
65

A

2 Weeks

65
120
20
100
100

Gross
On-Hand: 20
Net
Order Receipt
Order Release

A

1 Week

100
130
10
120
120

Gross
On-Hand: 10
Net
Order Receipt
Order Release

Gross
On-Hand: 5
Net
Order Receipt
Order Release

Lead
Time

10

Gross
On-Hand: 10
Net
Order Receipt
Order Release

Gross
On-Hand: 10
Net
Order Receipt
Order Release

6

B

120
B

100
0
100
100

1 Week

C

2 Weeks

100
200
5
195
195

195

AA

30
195
10
185
185

185

30
0
30
30

C

20
0
20
20

AA

3 Weeks

20

employed. Remember that computer programs have been developed to handle large and complex manufacturing operations.
In addition to using MRP to handle end products and finished goods, MRP can also be used
to handle spare parts and components. This is important because most manufacturing companies sell spare parts and components for maintenance. A net material requirements plan should
also reflect these spare parts and components.

6.12

Just-in-Time Inventory Control

With JIT, inventory arrives just
before it is needed.

During the past two decades, there has been a trend to make the manufacturing process more efficient. One objective is to have less in-process inventory on hand. This is known as JIT inventory. With this approach, inventory arrives just in time to be used during the manufacturing
process to produce subparts, assemblies, or finished goods. One technique of implementing JIT
is a manual procedure called kanban. Kanban in Japanese means “card.” With a dual-card

6.12

FIGURE 6.16
The Kanban System

JUST-IN-TIME INVENTORY CONTROL

231

C-kanban
and
Container

P-kanban
and
Container
4

1

Producer
Area

Storage
Area
3

User
Area
2

kanban system, there is a conveyance kanban, or C-kanban, and a production kanban, or Pkanban. The kanban system is very simple. Here is how it works:
Four Steps of Kanban
1. A user takes a container of parts or inventory along with its accompanying C-kanban to his
or her work area. When there are no more parts or the container is empty, the user returns
the empty container along with the C-kanban to the producer area.
2. At the producer area, there is a full container of parts along with a P-kanban. The user
detaches the P-kanban from the full container of parts. Then the user takes the full container
of parts along with the original C-kanban back to his or her area for immediate use.
3. The detached P-kanban goes back to the producer area along with the empty container. The
P-kanban is a signal that new parts are to be manufactured or that new parts are to be placed
into the container. When the container is filled, the P-kanban is attached to the container.
4. This process repeats itself during the typical workday. The dual-card kanban system is
shown in Figure 6.16.
As shown in Figure 6.16, full containers along with their C-kanban go from the storage area
to a user area, typically on a manufacturing line. During the production process, parts in the
container are used up. When the container is empty, the empty container along with the same
C-kanban goes back to the storage area. Here, the user picks up a new full container. The P-kanban
from the full container is removed and sent back to the production area along with the empty
container to be refilled.
At a minimum, two containers are required using the kanban system. One container is used
at the user area, and another container is being refilled for future use. In reality, there are usually
more than two containers. This is how inventory control is accomplished. Inventory managers
can introduce additional containers and their associated P-kanbans into the system. In a similar
fashion, the inventory manager can remove containers and the P-kanbans to have tighter control
over inventory buildups.
In addition to being a simple, easy-to-implement system, the kanban system can also be
very effective in controlling inventory costs and in uncovering production bottlenecks. Inventory arrives at the user area or on the manufacturing line just when it is needed. Inventory does
not build up unnecessarily, cluttering the production line or adding to unnecessary inventory
expense. The kanban system reduces inventory levels and makes for a more effective operation.
It is like putting the production line on an inventory diet. Like any diet, the inventory diet imposed by the kanban system makes the production operation more streamlined. Furthermore,
production bottlenecks and problems can be uncovered. Many production managers remove
containers and their associated P-kanban from the kanban system in order to “starve” the production line to uncover bottlenecks and potential problems.
In implementing a kanban system, a number of work rules or kanban rules are normally
implemented. One typical kanban rule is that no containers are filled without the appropriate
P-kanban. Another rule is that each container must hold exactly the specified number of parts or
inventory items. These and similar rules make the production process more efficient. Only those
parts that are actually needed are produced. The production department does not produce inventory just to keep busy. It produces inventory or parts only when they are needed in the user area
or on an actual manufacturing line.

232

6.13

CHAPTER 6 • INVENTORY CONTROL MODELS

Enterprise Resource Planning
Over the years, MRP has evolved to include not only the materials required in production, but
also the labor hours, material cost, and other resources related to production. When approached
in this fashion, the term MRP II is often used, and the word resource replaces the word
requirements. As this concept evolved and sophisticated computer software programs were developed, these systems were called enterprise resource planning (ERP) systems.
The objective of an ERP system is to reduce costs by integrating all of the operations of a
firm. This starts with the supplier of the materials needed and flows through the organization to
include invoicing the customer of the final product. Data are entered once into a database, and
then these data can be quickly and easily accessed by anyone in the organization. This benefits
not only the functions related to planning and managing inventory, but also other business
processes such as accounting, finance, and human resources.
The benefits of a well-developed ERP system are reduced transaction costs and increased
speed and accuracy of information. However, there are drawbacks as well. The software is expensive to buy and costly to customize. The implementation of an ERP system may require a
company to change its normal operations, and employees are often resistant to change. Also,
training employees on the use of the new software can be expensive.
There are many ERP systems available. The most common ones are from the firms SAP,
Oracle, People Soft, Baan, and JD Edwards. Even small systems can cost hundreds of thousands
of dollars. The larger systems can cost hundreds of millions of dollars.

Summary
This chapter introduces the fundamentals of inventory control
theory. We show that the two most important problems are (1)
how much to order and (2) when to order.
We investigate the economic order quantity, which determines how much to order, and the reorder point, which determines when to order. In addition, we explore the use of
sensitivity analysis to determine what happens to computations
when one or more of the values used in one of the equations
changes.
The basic EOQ inventory model presented in this chapter
makes a number of assumptions: (1) known and constant demand and lead times, (2) instantaneous receipt of inventory, (3)
no quantity discounts, (4) no stockouts or shortages, and (5) the
only variable costs are ordering costs and carrying costs. If
these assumptions are valid, the EOQ inventory model provides optimal solutions. On the other hand, if these assumptions do not hold, the basic EOQ model does not apply. In these

cases, more complex models are needed, including the production run, quantity discount, and safety stock models. When the
inventory item is for use in a single time period, the marginal
analysis approach is used. ABC analysis is used to determine
which items represent the greatest potential inventory cost so
these items can be more carefully managed.
When the demand for inventory is not independent of the
demand for another product, a technique such as MRP is
needed. MRP can be used to determine the gross and net material requirements for products. Computer software is necessary
to implement major inventory systems including MRP systems
successfully. Today, many companies are using ERP software
to integrate all of the operations within a firm, including inventory, accounting, finance, and human resources.
JIT can lower inventory levels, reduce costs, and make a
manufacturing process more efficient. Kanban, a Japanese word
meaning “card,” is one way to implement the JIT approach.

Glossary
ABC Analysis An analysis that divides inventory into three
groups. Group A is more important than group B, which is
more important than group C.
Annual Setup Cost The cost to set up the manufacturing or
production process for the production run model.
Average Inventory The average inventory on hand. In this
chapter the average inventory is Q>2 for the EOQ model.

Bill of Materials (BOM) A list of the components in a product, with a description and the quantity required to make
one unit of that product.
Economic Order Quantity (EOQ) The amount of inventory
ordered that will minimize the total inventory cost. It is also
called the optimal order quantity, or Q*.

KEY EQUATIONS

Enterprise Resource Planning (ERP) A computerized information system that integrates and coordinates the operations of a firm.
Instantaneous Inventory Receipt A system in which inventory is received or obtained at one point in time and not
over a period of time.
Inventory Position The amount of inventory on hand plus
the amount in any orders that have been placed but not yet
received.
Just-in-Time (JIT) Inventory An approach whereby inventory arrives just in time to be used in the manufacturing
process.
Kanban A manual JIT system developed by the Japanese.
Kanban means “card” in Japanese.
Lead Time The time it takes to receive an order after it is
placed (called L in the chapter).
Marginal Analysis A decision-making technique that uses
marginal profit and marginal loss in determining optimal
decision policies. Marginal analysis is used when the number of alternatives and states of nature is large.
Marginal Loss The loss that would be incurred by stocking
and not selling an additional unit.
Marginal Profit The additional profit that would be realized
by stocking and selling one more unit.
Material Requirements Planning (MRP) An inventory
model that can handle dependent demand.

233

Production Run Model An inventory model in which inventory is produced or manufactured instead of being ordered
or purchased. This model eliminates the instantaneous
receipt assumption.
Quantity Discount The cost per unit when large orders of
an inventory item are placed.
Reorder Point (ROP) The number of units on hand when an
order for more inventory is placed.
Safety Stock Extra inventory that is used to help avoid
stockouts.
Safety Stock with Known Stockout Costs An inventory
model in which the probability of demand during lead time
and the stockout cost per unit are known.
Safety Stock with Unknown Stockout Costs An inventory
model in which the probability of demand during lead time
is known. The stockout cost is not known.
Sensitivity Analysis The process of determining how sensitive the optimal solution is to changes in the values used in
the equations.
Service Level The chance, expressed as a percent, that there
will not be a stockout. Service level = 1 - Probability
of a stockout.
Stockout A situation that occurs when there is no inventory
on hand.

Key Equations
Equations 6-1 through 6-6 are associated with the economic
order quantity (EOQ).
(6-1) Average inventory level =
(6-2) Annual ordering cost =
(6-3) Annual holding cost =
(6-4) EOQ = Q * =

Q
2

D
C
Q o
Q
C
2 h

2DCo
A Ch

(6-9) Average inventory =

Q
d
a1 - b
p
2

(6-10) Annual holding cost =
(6-11) Annual setup cost =

Q
D
Co + Ch
Q
2
Total relevant inventory cost.

1CQ2
2

2DCo
B IC
EOQ with Ch expressed as percentage of unit cost.

(6-7) Q =

(6-8) ROP = d * L
Reorder point: d is the daily demand and L is the lead
time in days.

(6-13) Q * =

Q
d
a1 - bCh
p
2

D
C
Q s

(6-12) Annual ordering cost =

(6-5) TC =

(6-6) Average dollar level =

Equations 6-9 through 6-13 are associated with the production
run model.

D
Co
Q

2DCs

d
Ch a1 - b
p
Q
Optimal production quantity.

Equation 6-14 is used for the quantity discount model.
Q
D
C + Ch
Q o
2
Total inventory cost (including purchase cost).

(6-14) Total cost = DC +

234

CHAPTER 6 • INVENTORY CONTROL MODELS

stant daily demand, and ␴L is the standard deviation of
lead time.

Equations 6-15 to 6-20 are used when safety stock is required.
(6-15) ROP = 1Average demand during lead time2 + SS
General reorder point formula for determining when
safety stock (SS) is carried.

(6-19) ROP = d L + Z12Ls2d + d 2s2L2
Formula for determining reorder point when both daily
demand and lead time are normally distributed; where d
is the average daily demand, L is the average lead time
in days, and ␴L is the standard deviation of lead time,
and ␴d is the standard deviation of daily demand.

(6-16) ROP = 1Average demand during lead time2 + ZsdLT
Reorder point formula when demand during lead time is
normally distributed with a standard deviation of ZsdLT.
(6-17) ROP = dL + Z1sd 2L2
Formula for determining the reorder point when daily
demand is normally distributed but lead time is constant,
where d is the average daily demand, L is the constant
lead time in days, and ␴d is the standard deviation of
daily demand.

Q
Ch + 1SS2Ch
2
Total annual holding cost formula when safety stock is
carried.

(6-20) THC =

ML
ML + MP
Decision rule in marginal analysis for stocking additional units.

(6-21) P Ú

(6-18) ROP = dL + Z1dsL2
Formula for determining the reorder point when daily
demand is constant but lead time is normally distributed,
where L is the average lead time in days, d is the con-

Solved Problems
Solved Problem 6-1
Patterson 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 the ordering cost is not $20, and Patterson has been ordering 150 units each time an
order is placed. For this order policy to be optimal, what would the ordering cost have to be?

Solutions
a. The EOQ assumptions are met, so the optimal order quantity is
EOQ = Q* =
b. Number of orders per year =

21250220
2DCo
=
= 100 units
B Ch
B
1

250
D
=
= 2.5 orders per year
Q
100

Note that this would mean in one year the company places 3 orders and in the next year it would
only need 2 orders, since some inventory would be carried over from the previous year. It averages
2.5 orders per year.
Q
100
c. Average Inventory =
=
= 500 units
2
2
d. Given an annual demand of 250, a carrying cost of $1, and an order quantity of 150, Patterson
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 EOQ

SOLVED PROBLEMS

235

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.
Q =

2DCo
A Ch

Co = Q 2
=
=

Ch
2D

115022112
212502
22,500
= $45
500

Solved Problem 6-2
Flemming Accessories produces paper slicers used in offices and in art stores. The minislicer has been
one of its most popular items: Annual demand is 6,750 units and is constant throughout the year.
Kristen Flemming, owner of the firm, produces the minislicers in batches. On average, Kristen can manufacture 125 minislicers per day. Demand for these slicers during the production process is 30 per day.
The setup cost for the equipment necessary to produce the minislicers is $150. Carrying costs are $1 per
minislicer per year. How many minislicers should Kristen manufacture in each batch?

Solution
The data for Flemming Accessories are summarized as follows:
D = 6,750 units
Cs = $150
Ch = $1
d = 30 units
p = 125 units
This is a production run problem that involves a daily production rate and a daily demand rate. The
appropriate calculations are shown here:
Q* =
=

2DCs
B Ch11 - d>p2
216,750211502
B 111 - 30>1252

= 1,632

Solved Problem 6-3
Dorsey Distributors has an annual demand for a metal detector of 1,400. The cost of a typical detector
to Dorsey is $400. Carrying cost is estimated to be 20% of the unit cost, and the ordering cost is $25 per
order. If Dorsey orders in quantities of 300 or more, it can get a 5% discount on the cost of the detectors. Should Dorsey take the quantity discount? Assume the demand is constant.

Solution
The solution to any quantity discount model involves determining the total cost of each alternative after
quantities have been computed and adjusted for the original problem and every discount. We start the
analysis with no discount:
EOQ 1no discount2 =

211,40021252
B

0.214002

= 29.6 units

236

CHAPTER 6 • INVENTORY CONTROL MODELS

Total cost 1no discount2 = Material cost + Ordering cost + Carrying cost
= $40011,4002 +

1,4001$252
29.6

+

29.61$400210.22
2

= $560,000 + $1,183 + $1,183 = $562,366
The next step is to compute the total cost for the discount:
EOQ 1with discount2 =

211,40021252

B 0.21$3802
= 30.3 units
Q1adjusted2 = 300 units

Because this last economic order quantity is below the discounted price, we must adjust the order quantity to 300 units. The next step is to compute total cost:
Total cost 1with discount2 = Material cost + Ordering cost + Carrying cost
= $38011,4002 +

1,4001252
300

+

3001$380210.22
2

= $532,000 + $117 + $11,400 = $543,517
The optimal strategy is to order 300 units at a total cost of $543,517.

Solved Problem 6-4
The F. W. Harris Company sells an industrial cleaner to a large number of manufacturing plants in the
Houston area. An analysis of the demand and costs has resulted in a policy of ordering 300 units of this
product every time an order is placed. The demand is constant, at 25 units per day. In an agreement with
the supplier, F. W. Harris is willing to accept a lead time of 20 days since the supplier has provided an
excellent price. What is the reorder point? How many units are actually in inventory when an order
should be placed?

Solution
The reorder point is
ROP = dxL = 251202 = 500 units
This means that an order should be placed when the inventory position is 500. Since the ROP is greater
than the order quantity, Q = 300, an order must have been placed already but not yet delivered. So the
inventory position must be
Inventory position = 1Inventory on hand2 + 1Inventory on order2
500 = 200 + 300
There would be 200 units on hand and an order of 300 units in transit.

Solved Problem 6-5
The B. N. Thayer and D. N. Thaht Computer Company sells a desktop computer that is popular among
gaming enthusiasts. In the past few months, demand has been relatively consistent, although it does
fluctuate from day to day. The company orders the computer cases from a supplier. It places an order
for 5,000 cases at the appropriate time to avoid stockouts. The demand during the lead time is normally
distributed, with a mean of 1,000 units and a standard deviation of 200 units. The holding cost per unit
per year is estimated to be $4. How much safety stock should the company carry to maintain a 96%
service level? What is the reorder point? What would the total annual holding cost be if this policy is
followed?

SELF-TEST

237

Solution
Using the table for the normal distribution, the Z value for a 96% service level is about 1.75. The standard deviation is 200. The safety stock is calculated as
SS = zs = 1.7512002 = 375 units
For a normal distribution with a mean of 1,000, the reorder point is
ROP = 1Average demand during lead time2 + SS
= 1000 + 350 = 1,350 units
The total annual holding cost is
THC =

Q
5000
Ch + 1SS2Ch =
4 + 135024 = $11,400
2
2

Self-Test





Before taking the self-test, refer to the learning objectives at the beginning of the chapter, the notes in the margins, and the
glossary at the end of the chapter.
Use the key at the back of the book to correct your answers.
Restudy pages that correspond to any questions that you answered incorrectly or material you feel uncertain about.

1. Which of the following is a basic component of an inventory control system?
a. planning what inventory to stock and how to acquire it
b. forecasting the demand for parts and products
c. controlling inventory levels
d. developing and implementing feedback measurements
for revising plans and forecasts
e. all of the above are components of an inventory
control system
2. Which of the following is a valid use of inventory?
a. the decoupling function
b. to take advantage of quantity discounts
c. to avoid shortages and stockouts
d. to smooth out irregular supply and demand
e. all of the above are valid uses of inventory
3. One assumption necessary for the EOQ model is instantaneous replenishment. This means
a. the lead time is zero.
b. the production time is assumed to be zero.
c. the entire order is delivered at one time.
d. replenishment cannot occur until the on-hand
inventory is zero.
4. If the EOQ assumptions are met and a company orders
the EOQ each time an order is placed, then the
a. total annual holding costs are minimized.
b. total annual ordering costs are minimized.
c. total of all inventory costs are minimized.
d. order quantity will always be less than the average
inventory.

5. If the EOQ assumptions are met and a company orders
more than the economic order quantity, then
a. total annual holding cost will be greater than the total
annual ordering cost.
b. total annual holding cost will be less than the total
annual ordering cost.
c. total annual holding cost will be equal to the total
annual ordering cost.
d. total annual holding cost will be equal to the total
annual purchase cost.
6. The reorder point is
a. the quantity that is reordered each time an order is
placed.
b. the amount of inventory that would be needed to meet
demand during the lead time.
c. equal to the average inventory when the EOQ assumptions are met.
d. assumed to be zero if there is instantaneous
replenishment.
7. If the EOQ assumptions are met, then
a. annual stockout cost will be zero.
b. total annual holding cost will equal total annual ordering cost.
c. average inventory will be one-half the order quantity.
d. all of the above are true.
8. In the production run model, the maximum inventory
level will be
a. greater than the production quantity.
b. equal to the production quantity.