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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.



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