+1443 776-2705 panelessays@gmail.com

due in 20 hours

attached

Alliance Supermarket and Point-of-Sale (POS) Systems

Read the “Alliance Supermarket” case study in Chapter 10 of your text.

Alliance Supermarkets has been using a point-of-sale (POS) system for some time to track its inventory. The system uses a laser scanner to read the universal product code (UPC) on each item at the checkout container. The UPC is a number that uniquely identifies the product on which it appears. Currently, Alliance is using the UPC information to update inventory records for each item. Although the system has greatly improved the company’s ability to replenish inventory promptly, the company still has some problems. For example, sudden changes in demand for a particular item can catch the company by surprise as it bases inventory replenishment on historical demand patterns. Further, demand patterns and preferences may vary from one store to another depending on the customers served by each, but the inventory system groups all demand information together and treats each store equally. Finally, the manufacturers that make the products stocked by Alliance Supermarkets are always pressuring Alliance to help them target appropriate customers for special promotions and sales.

The chief information officer (CIO) of Alliance realizes that much more could probably be done with the data collected from its POS system. For example, the company could analyze the relationship between each product’s sales and weather patterns. It is even possible to analyze an individual customer’s buying habits and identify instances in which a customer may be persuaded to try a different brand of a certain product.

For this assignment be sure to address the following points:

· Study this situation and formulate new and innovative uses of the information from the POS system. Ideally, these ideas should help Alliance better serve its customers by ensuring that adequate quantities of each item are available, that costs are kept low, and that customers are made aware of new products that may interest them.

· Describe any information that may help Alliance reduce costs while providing better service.

· Propose a new approach that could be used by Alliance by using the purchase information that can be obtained on individual customers.

· Assess ethical and privacy considerations of information gathered from the POS system or purchased items.

Your paper should be in paragraph form (avoid the use of bullet points) and supported with the concepts outlined in your text and additional scholarly sources.

Submit your three- to four-page paper (not including the title and reference pages). Your paper must be formatted according to APA style as outlined in the Writing Center and must cite at least three scholarly sources in addition to the textbook.

Required Resources

Text

Vonderembse, M. A., & White, G. P. (2013). 
Operations management
. Bridgepoint Education.

· Chapter 7: Facility Location and Process Selection

· Chapter 8: Capacity Decisions

 

Recommended Resources

Multimedia

July, E. (Producer) & Rodrigo, J. M. (Director). (2003). 
Business is blooming: The international floral industry (Links to an external site.)
 [Video file]. Retrieved from the Films On Demand database.

· Watch the following segments:

· Anticipating Flower Market Demand

· Ecuador: King in the Flower World

· Ecuador’s Flower Production

· Exporting Flowers from Ecuador

Websites

American Society for Quality. (n.d). Pareto chart (Links to an external site.). Retrieved from http://asq.org/learn-about-quality/cause-analysis-tools/overview/pareto.html

American Society for Quality. (n.d). Six sigma (Links to an external site.). Retrieved from http://asq.org/sixsigma/

Learning Objectives

After completing this chapter, you should be able to:

• Define capacity as a measure of an organization’s ability to provide customers with
the requested service or good.

• Explain that capacity estimation is difficult because many management decisions
affect capacity.

• Describe how overall capacity of the system is dependent on the capacities of the
departments and machines that form the production system.

• Determine the bottleneck in a system and demonstrate how that information can
be used.

• Describe key capacity decisions, such as how much capacity to add; when, where,
and what type (process) of capacity to add; when to reduce capacity and by how
much.

8 ©Fotosearch/SuperStock

Capacity Decisions

von70154_08_c08_223-256.indd 223 2/22/13 3:34 PM

CHAPTER 8Section 8.1 Capacity Defined

8.1 Capacity Defined

Capacity is a measure of an organization’s ability to provide customers with the demanded services or goods in the amount requested and in a timely manner. Capacity is also the maximum rate of production. An organization marketing and
selling rotisserie chicken should be able to produce and deliver chicken in sufficient quan-
tities to satisfy consumer demand during lunch and dinner times when demand peaks.
Meeting customer demand requires the acquisition of physical facilities, the hiring and
training of qualified people, and the acquisition of materials to achieve the desired pro-
duction level. The following important questions about capacity planning are addressed
in this chapter:

• How can management estimate capacity?
• What is system capacity, and why is it important?
• How can capacity decisions be made to gain a competitive advantage for the

organization?

Role of Capacity Planning
Capacity planning is very important because significant capital is usually required to
build the facilities and purchase the equipment to build capacity. Creating a series of large
server farms to support the Internet and data communications requires substantial invest-
ment. Millions of dollars are required to build a brewery, a hospital, or a knitting produc-
tion line to make sweaters. These expenditures are for fixed assets that are expensive to
maintain and even more expensive to change. Capacity decisions require careful consid-
eration of an organization’s long-term objectives and the market demand. Capacity deci-
sions must be consistent with current and anticipated demand.

Organizations should be flexible in order to meet future as well as present capacity require-
ments. Flexibility can allow managers to:

• Adjust production volume to respond to changes in customer demand.
• Produce different products on the same equipment (product mix) to respond to

changing customer needs.
• Alter product technology and process technology to maintain or improve an

organization’s competitive position.

von70154_08_c08_223-256.indd 224 2/22/13 3:34 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

8.2 Estimating and Altering Capacity

Before estimating capacity, it is necessary to recognize the difference between
theoretical or ideal capacity and
achievable capacity. Theoretical
capacity is what a service firm
or a manufacturer can produce
under ideal conditions for a
short period of time. Under
ideal conditions there are no
equipment breakdowns, main-
tenance requirements, mate-
rial problems, or worker errors.
While organizations strive to
eliminate these unproductive
delays, allowances for these ele-
ments must be made in order
to develop realistic estimates of
capacity.

Real World Scenarios: Meijer Superstores

Meijer superstores provide consumers with a full range of food products as well as a diverse range
of other products, such as sporting goods, automotive supplies, clothes, and lawn care equipment.
Meijer’s concept is twofold: 1) build big stores that have high sales; and 2) aggressively expand the
number of stores. In addition to the advantage of one-stop shopping, Meijer’s large capacity stores
offer other advantages.

The average purchase made by each customer should be higher because of the wide product variety.
Although most traditional grocery items such as bread, rice, and milk have very low profit margins,
products like microwaveable hamburgers, organic products, free-range chicken, and in-store bakery
goods have higher margins and these boost profits.

Larger capacity allows Meijer to spread the fixed cost of a store over a greater sales volume, thereby
reducing costs and increasing profits. For example, when more customers shop at Meijer, the cost of
floor space, food display racks, and checkout facilities remain unchanged. These are simply utilized
at a higher level. Heating and lighting costs are also unaffected by these additional shoppers, for the
most part. Meijer is creating economies of scale by serving more customers with the same facilities
and equipment. Examples of variable costs for Meijer include staffing levels for checkout counters
and spending for items such as eggs and milk when customers buy more. Meijer also has installed
self-checkout facilities that take less space and reduce labor costs at checkout to increase facility
utilization and to enhance productivity.

Meijer is also spreading the fixed costs of corporate operations over more stores by rapidly expand-
ing the number of new stores. In addition to cutting the per-store share of these corporate-level fixed
costs, expansion gives Meijer more buying power, which enables it to negotiate better prices and
delivery schedules from suppliers.

.Thinkstock

To estimate capacity, managers must first select a way to
measure it. Hospitals often use beds as a measure of capacity.

von70154_08_c08_223-256.indd 225 2/22/13 3:34 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

To estimate capacity, managers must first select a way to measure it. In some cases, the
choice is obvious, for example, tons per hour of steel or kilowatt-hours of electricity. A
hospital can use beds as a measure of capacity. Thus, a hospital with 100 beds that are
available 365 days per year has a capacity of 36,500 patient-days each year. Hospitals
measure the number of patients admitted and how long each stays so they can calculate
patient-days consumed. A comparison of patient-days consumed and patient-days avail-
able gives the operating ratio shown below.

Hospital’s operating ratio 5
24,000 patient-days consumed
36,500 patient-days available

3 100

5 65.8%

In general, the operating ratio is calculated according to the following equation:

Operating ratio 5
capacity consumed

capacity available
3 100

Finding a yardstick to estimate capacity is more difficult in a restaurant than in a hospital
because there is no uniform product on which the measurement can be based. Capacity
could be measured in terms of people served, meals prepared, or the ability to gener-
ate sales dollars. It is management’s responsibility to select the appropriate measure and
apply it.

Once the measure has been selected, estimating capacity involves the following steps:

1. Determine the maximum rate per hour of the production equipment.
2. Determine the number of hours worked in a given time period.
3. Multiply those two numbers.

Capacity/period 5 (maximum production rate/hour) 3 (number of
hours worked/period)

Production rate 5
number of units produced

amount of time

Capacity can be changed by changing the number of hours worked in a time period, or
by changing the production rate. The number of hours worked per time period is affected
by several factors, including overtime, multiple shifts, downtime for preventive mainte-
nance, and allowances for unplanned equipment failure.

von70154_08_c08_223-256.indd 226 2/22/13 3:34 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

Several management decisions
affect capacity. For example,
increases in the amount and
quality of preventive mainte-
nance could increase capacity
by reducing unexpected equip-
ment failure. Other decisions
affect capacity by changing the
production rate. The following
decisions are examined in this
section:

• Changing the mix of
products produced by
the facility.

• Adding people to the
production process.

• Increasing the moti-
vation of production
employees.

• Increasing the machine
production rate.

• Improving the quality of the raw materials and the work in process.
• Increasing product yield.

Product Mix
An organization’s product mix is the percentage of total output devoted to each prod-
uct. For example, an agency may sell life, house, and automobile insurance. How does

.Associated Press/AP Images

An organization’s product mix is the percentage of total
output devoted to each product. Johnson & Johnson is a large
corporation with an expansive product mix including consumer
and pharmaceutical products such as Tylenol and BAND-AIDs.

Problem

Given the following information on maximum production rate and hours worked for an oven that
cooks pizzas, determine the capacity per week.

Maximum production rate 5 40 pizzas/hour

Number of hours 5 84 hours/week

Overtime 5 0 hours/week

Preventive maintenance 5 0 (because it is performed after closing)

Equipment failure 5 2% of planned hours

(Unplanned downtime)

Capacity/week 5 (40 pizzas/hour)(84 1 0 2 0 hours/week)(1 2 0.02)

5 3,292.8 pizzas/week

The hours worked per week is reduced from 100% to 98% of the available hours because of the 2%
downtime anticipated for equipment failure.

von70154_08_c08_223-256.indd 227 2/22/13 3:35 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

Problem

Assume that each contact for life insurance takes three hours, house insurance takes two hours, and
automobile insurance requires one hour. What are the capacities of an agent who works 40 hours
per week under Mix 1 and Mix 2?

Type Mix 1 Mix 2

Life insurance 0.20 0.40

House insurance 0.30 0.40

Automobile insurance 0.50 0.20

Begin by calculating the production rate for each type of insurance. These production rates represent
what an agent could do if he or she sold only that type of insurance.

Production Rate 5 (hours worked per week)/(hour required per unit)

Production RateLife 5 (40 hrs./wk.)/(3 hrs./unit) 5 13.33 contacts per week

Production RateHouse 5 (40 hrs./wk.)/(2 hrs./unit) 5 20 contacts per week

Production RateAuto 5 (40 hrs./wk.)/(1 hr./unit) 5 40 contacts per week

Now calculate the capacity for one week if Mix 1 is assumed. Now, the agent’s time is divided among
the various types according to the mix.

PR 5 (13.3 contacts/wk.)(0.2) 1 (20 contact/wk.)(0.3) 1 (40 contacts/wk.)(0.5)

5 28.67 contacts/wk.

As an exercise, calculate the capacity if Mix 2 is assumed. (The answer should be 21.33 contacts per
week.) Thus, as the mix shifts away from automobile insurance to life and house insurance, which
require more time per contact, the capacity of an agent as measured by the number of contacts
declines. If an average selling price for each type of contract can be determined, it would be possible to
calculate the capacity of a sales person when generating revenue on a daily, weekly, or monthly basis.

product mix effect capacity? It may take more of an agent’s time to sell life insurance
than automobile insurance. Consequently, a shift in demand toward life insurance poli-
cies reduces an agent’s selling capacity. In theory, the agent should earn more money sell-
ing life insurance to compensate for the extra time. Otherwise, the agent will favor house
and auto insurance.

Product mix issues are also relevant in manufacturing. A steel company produces steel
of many alloys, shapes, and sizes, and these differences require different production pro-
cesses and times. For example, the sheet steel that forms the body of an automobile or
an appliance is produced in many widths. A 60-inch piece may be needed for the hood,
and a 40-inch piece may be needed for a door panel. The mill that rolls these widths takes
about the same amount of time per foot regardless of width. Therefore, a mill with a heavy
mix of 40-inch pieces will be able to produce fewer tons per hour than a mill with many
60-inch pieces. What is the capacity of the processing equipment, and what are the units of

von70154_08_c08_223-256.indd 228 2/22/13 3:35 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

Problem

Assume that a company uses steel that is 1/8-inch thick and has a density of 0.2833 pounds per cubic
inch. The machines roll steel for 80 hours per week at an average speed of 30 inches per second. The
company produces both 40- and 60-inch widths of steel and wants to determine the capacity of each
of the following product mixes.

Size Mix 1 Mix 2

40 inches 80% 50%

60 inches 20% 50%

The company’s production rate can be calculated as follows:

Production rate (PR) 5 (production rate for 40-inch)(mix for 40-inch) + (production rate for 60-inch)
(mix for 60-inch)

The production rate for the 40-inch size (PR40) can be determined as follows:

PR40 5 (width)(thickness)(processing rate inches/hour)(density)

5 (40 in)(1/8 in)(30 in/sec)(3,600 sec/hr)(0.2833 Ibs/cubic in)

5 152,982 Ibs/hr

This would be the production rate if only the 40-inch size were produced. Calculate the production
rate for the 60-inch size, which is 229,473 pounds per hour.

Now calculate the overall production rate if Mix 1 is assumed.

PR 5 (152,982 Ibs/hr)(0.8) 1 (229,473 lbs/hr)(0.2)

5 122,385.6 lbs/hr 1 45,894.6 lbs/hr

5 168,280.2 Ibs/hr

Convert this figure to tons per hour.

PR 5
168,280.0 lbs/hr

2,000 lbs/ton

5 84.14 tons/hr

Next, convert the production rate into an estimate of capacity for a week.

Capacity for Mix 1 5 (PR of mix 1)(hours worked)

5 (84.14 tons/hr)(80 hrs/week)

5 6,731.2 tons/week

Calculate the capacity if Mix 2 is assumed, which is 7,649.1 tons per week. Thus, as the mix shifts
from 40-inch to 60-inch steel, the capacity increases. Capacity is influenced by product mix.

capacity? Steel is measured in tons per hour, but those who estimate capacity realize that
capacity changes as the mix of steel changes because different products have different pro-
duction rates. Therefore, product mix must be estimated before capacity can be estimated.

von70154_08_c08_223-256.indd 229 2/22/13 3:35 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

Adding People
Adding people to an operation may increase the maximum production rate. This increase
occurs when the operation is constrained by the amount of labor assigned to the job. The
capacity of both service operations and manufacturing operations is affected by adding or
eliminating people. Organizations that are successful need to be willing and able to adapt
to change. Part of being able to adapt is having flexibility to meet changes in demand. The
following example illustrates the flexibility available to an organization in meeting vary-
ing levels of demand.

Problem

To assemble the frames for 25 rocker/recliner chairs, each assembler takes his or her work order to
the inventory clerk to pick the parts required to make the chairs. This takes about 30 minutes. After
returning to the work area, each assembler completes 25 chair frames in 3 1/2 hours. To increase the
capacity to assemble chair frames, a separate stock picker could be hired to gather inventory for all
the assemblers. Then each assembler would be able to increase production by 1/7 because the 30
minutes consumed in stock picking could now be used to assemble chairs. Therefore, each assembler
could assemble for 4 hours rather than 3 1/2 hours. One stock picker could serve eight assemblers.
The capacity improvement is calculated here.

Capacity per assembler before stock picker 5 (25 chairs/4 hrs.)(8 hrs./shift)

5 50 chairs/shift

Capacity per assembler after stock picker 5 (25 chairs/3.5 hrs.)(8 hrs./shift)

5 57.14 chairs/shift

% Increase in Capacity 5
New Capacity 2 Old Capacity

Old Capacity
3 100

5
57.14 2 50

50
3 100

5 14.28%

Increasing Motivation
Another way to increase the production rate for an operation with labor constraints is to
increase motivation. Substantial increases in production rates can be achieved when work-
ers feel they are an important part of the operation. These productivity increases do not
require additional labor costs or extra investment in equipment. The people work harder
to accomplish more when they have an emotional or financial stake in the organization.

There has been a growing awareness among both management and labor that communi-
cation and cooperation offer better opportunities for success than sharp-tongued rheto-
ric, lockouts, and strikes. Evidence of this willingness to cooperate exists in almost every
industry as organizations fight for market share and workers fight for jobs in the increas-
ingly global environment. In the automotive industry, labor has agreed to liberalize work
rules so that productivity can be increased. For example, some facilities have reduced the
number of job classifications from 100 to only a few, making it possible to perform simple

von70154_08_c08_223-256.indd 230 2/22/13 3:35 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

.iStockphoto/Thinkstock

A pizza oven is an example of a machine constraint. To
increase capacity, new machines must be purchased or existing
machines must be operated more efficiently.

maintenance tasks with one or two employees rather than five or six. Management has
agreed to profit sharing, which allows the workforce to share in the benefits of these sim-
plified work rules. Management has also begun to recognize the talents of its labor force
and has encouraged employee involvement in what used to be exclusively management
domain: decision making.

Labor is learning to accept efforts to improve automation because workers see that cutting
costs and enhancing quality can lead to the best kind of job security, that is, increasing
sales. Shared decision-making has not only caused increased cooperation, but it has cre-
ated more motivated employees, thus providing the following benefits to organizations:

• Organizations can tap into talent that already exists in their workforce.
• Workforces are more receptive to training and new ideas.
• People work harder and smarter.

Increasing Machine Production Rate
In an operation that is machine
constrained, adding people will
not increase capacity. Machine
constrained means that the
equipment is operating for all
the available time at its best
speed, while the operators have
some idle time. For example, if a
pizza oven can bake 40 pies per
hour, and the staff can assemble
60 pies per hour, then the pro-
cess is machine constrained. To
increase capacity, either new
machines should be purchased
or existing machines should be
operated more efficiently.

One possibility that was men-
tioned earlier is to increase pre-
ventive maintenance so that
downtime due to machine fail-
ure will be reduced or eliminated. Another approach is to develop procedures that more
efficiently utilize existing machines. With continuing process improvements there is usu-
ally a way to improve a machine’s production rate. A procedure could be as simple as
finding a faster and better way to load pizzas into the oven or increasing the heat in the
oven to cook pizzas faster.

Improving Quality
Improving quality can often increase the capacity of operations. Simply stated, if an oper-
ation produces a product of inferior quality and the product is rejected, the capacity used
to produce that product is wasted. Poor quality gives the organization’s customers a bad

von70154_08_c08_223-256.indd 231 2/22/13 3:35 PM

CHAPTER 8Section 8.2 Estimating and Altering Capacity

impression of its product, and also robs operations of needed capacity. Consider the fol-
lowing case.

Real World Scenarios: Downey Carpet Cleaning

Downey Carpet Cleaning is a family-owned business that cleans carpets, furniture, and drapery. It
also performs general housekeeping services. For several years, Downey has offered a carpet service
that thoroughly cleans high-traffic areas at one low price although some competitors charge extra for
high-traffic areas. Why should Downey charge the lower rate? According to the owner, who is also
the manager, it is a sound business decision.

A callback to clean a carpet a second time for a dissatisfied customer takes as much time as making
two regular carpet-cleaning stops because regular stops are scheduled to avoid as much nonproduc-
tive travel time as possible. Callbacks often require much longer drives. Each callback robs Downey of
capacity and additional potential revenue. Comparatively, the extra time and money for the chemi-
cals needed to clean the high-traffic areas right the first time are small.

The typical carpet-cleaning worker can perform 10 jobs per day with an average revenue of $43 per
job. One callback for which the company receives no additional revenue causes Downey to lose $86
in revenue. The company misses out on two regular jobs at $43 per job. Plus, the out-of-pocket costs
for the chemicals to clean the carpet a second time, and the costs of operating the truck for the
return trip are incurred. In one day, the extra costs of the chemicals, and the time for the worker to
complete all 10 jobs correctly the first time is less than $20. By avoiding callbacks, Downey is able to
increase its capacity. In addition to a sound financial policy, customers also like the policy and fre-
quently have Downey return for other services as well as for their next carpet cleaning.

Increasing Product Yield
In many operations, the quantity
of output is less than the quan-
tity of input. In other words,
some inputs are lost during the
production of a good or service.
Yield is the ratio of the quantity
of output to the input quantity.

Yield 5
quantity of output

quantity of input

Yield is a function of the charac-
teristics of the process for pro-
ducing the product. For exam-
ple, an oil refinery begins with
one barrel of crude oil, but when
it is finished, there is less than
one barrel of finished product.
Small amounts evaporate, are
spilled, or are otherwise lost in

Comstock Images/Thinkstock

When filming a movie, a director often shoots excess footage
and then edits it, removing scenes to create the final version of
the film. An increase in yield would mean shooting less “extra”
footage.

von70154_08_c08_223-256.indd 232 2/22/13 3:35 PM

CHAPTER 8Section 8.3 Determining System Capacity

Points to Consider
Capacity estimation is a necessary prerequisite to capacity planning. Without knowledge
of the existing limits on capacity, meaningful capacity planning or production planning
cannot take place. As the earlier section indicates, capacity is not a fixed number. Capacity
is a function of management ingenuity. It can be influenced by good planning, good oper-
ating procedures, effective maintenance programs, and other management decisions. One
of the important responsibilities of operations managers is to investigate ways to increase
capacity before investing substantial capital in new facilities.

8.3 Determining System Capacity

Until this point, the discussion of estimating and improving capacity has focused on only one machine or one operation within a company. The reality is that operations are a combination of different machines, equipment, and processes that make fin-
ished products. To plan effectively, management must know the capacity of the entire pro-
duction system, not just the capacity of individual parts. System capacity is the ability of the
organization to produce a sufficient number of goods and services to meet the demands of
customers. The capacity of an insurance company is not dependent only on the capacity of
its sales personnel, the capacity of a hospital is not set only by the number of surgery rooms,
and the capacity of a pizza parlor is not determined only by the capacity of its ovens.

For convenience, the term department is used when referring to a portion of the produc-
tion system. To analyze system capacity, it is important to determine how departments are
related. The two basic arrangements, product layout and process layout, are discussed in
Chapter 7 and are also used here.

the production process. Some is burned as waste gas. The yield is the percentage of the
output that is a useful product. A 96% yield means 96 of every 100 barrels of input are
made into useful products. If a refinery’s engineers find methods to increase the yield by
1%, the refinery will have more product to sell, which increases effective capacity. Making
movies follows a similar process. A director may shoot eight hours of film but may edit
the film so that the final movie is two hours or less. The extra time used to shoot the movie
costs money and prevents using the actors, sound stage, locations, cameras, and equip-
ment to make other movies. Increasing yield would mean shooting less than eight hours
of film to make the two-hour movie.

Highlight: Intel and Computer Chips

After Intel introduces new computer chips, it usually experiences a dramatic improvement in yield
during production. Initially, the number of chips that meet standards may be only 60%. As the com-
pany learns more about the process, the yield may increase to 90% or more. This 30-point increase in
yield leads to 50% more product to sell. (Previously only 60 of 100 chips could be sold. Now 90 chips,
that is, 30 more, are available.) Thus, capacity is increased. Because these 30 additional chips add no
production cost, most of the revenue from their sale contributes directly to the company’s bottom
line. For Intel, moving up the yield curve as quickly as possible has a substantial impact on meeting
customer demand and on increasing profitability.

von70154_08_c08_223-256.indd 233 2/22/13 3:35 PM

CHAPTER 8Section 8.3 Determining System Capacity

Product Layout
Product-oriented layout is characterized by high demand for the same or similar prod-
ucts. Examples include refining steel, making paper, and processing checks in a bank. In
this arrangement, there are few, if any, product variations, and the layout fits the domi-
nant flow of the product—thus, the name “product layout.”

For example, to make paper, wooden logs are ground and chemically treated to produce
a watery mixture called pulp. The pulp is pumped to the papermaking machine where
excess water is gradually squeezed out, leaving a thin sheet of wet paper. The wet paper
passes through a series of dryers that remove most of the remaining moisture. The paper
is then rolled into logs that can be 30 feet wide and several feet in diameter. These huge
logs are later cut into many different widths. Most types of paper are made using the same
process and follow the same flow (see Figure 8.1).

Figure 8.1: Product-oriented layout of paper mill

Pulp
preparation Papermaking Drying

Process Layout
Process-oriented layout is characterized by the production of many different products
with the same equipment and low volume of any individual product. No single prod-
uct has enough volume to support a dedicated set of machines. Each product has differ-
ent production requirements that place different demands on the equipment. Examples
include a machine shop that produces specialty automotive parts for racing engines, a
hospital emergency room, and an automotive repair shop that offers a wide variety of ser-
vices. In this arrangement, the layout is grouped by similar machine types because there
is no dominant product flow—thus the name “process layout.”

An automotive center contains the equipment to analyze a variety of mechanical prob-
lems. As seen in the following list, different customers desire a different set of services.
The facilities are arranged by process because there is no dominant flow (see Figure 8.2).

Figure 8.2: Process-oriented layout of an automotive service center

Liftwork:
Shock absorbers

and exhaust
systems

Batteries
and electrical

Tires

Tune-upsBrakes
Wheel

alignment

von70154_08_c08_223-256.indd 234 2/22/13 3:35 PM

CHAPTER 8Section 8.3 Determining System Capacity

Customer Services Requested

A Tires, shock absorbers, wheel alignment

B Tires, brakes, tune-up

C Brakes, tune-up, exhaust system

D Tires, brakes, shock absorbers, muffler

E Shock absorbers

The capacity of the product-oriented and process-oriented layouts is determined by ana-
lyzing the capacity of individual departments. Approaches to determining the capacity of
both layouts are discussed next.

Product Layout and System Capacity
The capacity of a product-oriented system can be visualized as a series of pipes of varying
capacity, with the smallest diameter or capacity holding back the entire system. Figure
8.3 shows five pipes (departments or machines) with different diameters (capacities). The
output from one pipe becomes the input to the next until the finished product exits pipe
number five. In Figure 8.3, pipe number two cannot handle all the flow that pipe number
one can deliver and, therefore, it restricts the flow. Because of pipe number two’s lim-
ited capacity, it restricts the flow from upstream pipes and starves the downstream pipes.
Pipes three, four, and five can work on only what pipe two can …

Learning Objectives

After completing this chapter, you should be able to:

• Describe the relationships among forecasting, aggregate planning, master schedul-
ing, MRP, and capacity planning.

• Show how a master schedule is developed from an aggregate plan.

• Use the method of overall factors to estimate capacity requirements based on a
master schedule.

• Explain the difference between independent and dependent demand, and indicate
the type of demand for which MRP is appropriate.

• Use MRP to develop planned order releases for items at all levels of the bill of
materials.

• Develop a load report and load profile based on MRP output, routings, and labor
standards.

• Describe the characteristics of MRP II.

9 .iStockphoto/Thinkstock

Planning for Material
and Resource Requirements

von70154_09_c09_257-302.indd 257 2/22/13 3:30 PM

CHAPTER 9Section 9.1 Role of Planning

9.1 Role of Planning

Planning is one of the most important, yet least understood, jobs that a manager per-forms. Poor planning can hinder a company’s ability to handle unexpected occur-rences. Good planning can place a company in an extremely strong competitive
position, one that prepares the organization to deal with any event. All parts of the orga-
nization—marketing, operations, finance—must work together in the planning process to
ensure that they are moving in harmony with one another.

The start of the planning activity is the development of a competitive strategy. In today’s
extremely competitive global marketplace, organizations cannot afford to go forward
without a well-planned strategy, which includes the operations function as well as every
other part of the organization. The strategy is then converted into a business plan—a blue-
print for implementing the strategic plan. Based on a forecast and the business plan, each
part of an organization must then develop its own plans that describe how the various
parts will work to implement the business and strategic plans. Forecasts of demand and
other important business factors, such as costs, are vital if an organization wants to create
an effective plan. This series of planning stages is shown in Figure 9.1.

Figure 9.1: Operations planning activities

Organization
strategic plan

Business
plan

Demand
forecast

Financial
plan

Operations
plan

Aggregate
plan

Sales
plan

von70154_09_c09_257-302.indd 258 2/22/13 3:30 PM

CHAPTER 9Section 9.1 Role of Planning

As part of this overall planning
effort, firms develop operational
plans that extrapolate across dif-
ferent time periods. Long-range
operations planning addresses
facilities and resources includ-
ing the number of facilities to
build, the location(s), the capac-
ity, and the type of process tech-
nologies. Long-range planning
is often considered to be five
years, but could be longer or
shorter depending on the indus-
try, For example, if an industry
such as electric power genera-
tion requires 10 years to build
a facility, a 5-year plan would
be too short. The industry must
be able to plan far enough into
the future so it can make the
changes needed to respond to
growth in demand.

Medium-range operations planning develops ways to utilize resources to meet customer
demand. The time horizon for medium-range planning is generally from 6 to 18 months
in the future, but may vary outside of this range. The decisions that are usually made as
part of medium-range operations planning include the following:

• Workforce size
• Operating hours of the facilities
• Levels of inventory that will be maintained
• Output rates for the processes

Medium-range operations plans must be well coordinated with the marketing plans and
the financial plans created by the organization, because these help the firm to develop the
aggregate plan. See Figure 9.1.

Aggregate planning is the combining of individual end items into groups or families of
parts for planning purposes. For instance, an appliance manufacturer may begin medium-
range planning by determining production rates for each broad product family, such as
refrigerators, stoves, and dishwashers. The aggregated plan is a statement of planned
output by product groups on a monthly basis. It provides enough information to make
decisions about important operating decisions such as setting contracts for materials, hir-
ing and training employees, and inventory.

.Thinkstock

The planning process begins with the creation of a competitive
strategy, which is then converted into a business plan—a
blueprint for implementing the strategic plan.

von70154_09_c09_257-302.indd 259 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

Highlight: PC Manufacturing

An aggregate plan for a PC manufacturer will state the number of units it intends to produce, but it
will not provide the number of each model or type the firm intends to produce. The aggregate plan
will not identify the amount of memory each unit will have or the type of video card. The aggregate
plan helps the company and its suppliers to plan for production over the next few weeks, months,
or possibly one year. As each time period, say one month, passes, the aggregate plan is refreshed
to account for more recent information about demand. A functional short-term aggregate plan will
ensure that the firm and its suppliers have enough flexibility to respond to customer demand as it
is reported in the very short term so that each PC has the features that customer wants. This final
step involves scheduling so that the right material and the right employees with the right skills come
together at the right place and time with the right equipment to make the product. This is the final,
essential step when creating and executing an operational plan. It involves the creation of a master
production schedule.

There must be enough flexibility in the contracts with suppliers as well as the capabili-
ties of the employees and facilities so the firm can produce what the customer demands
because the aggregate plan does not provide sufficient details. When actual production
takes place, the appliance company must specify the number of each model to be pro-
duced. For a refrigerator, the model would identify the size in cubic feet, energy efficiency,
and layout (side-by-side or over-under). This more detailed plan, called the master pro-
duction schedule, is based on the aggregate plan.

If sufficient quantities of required resources and materials are not available when needed,
customer service will suffer. When developing a master production schedule, a company
must ensure that the schedule is realistic in terms of its resource and material require-
ments. This chapter explains how to develop a master production schedule, and how an
organization can determine the resource and material requirements to produce the goods
and services for that master production schedule. This leads to a plan that will ensure the
appropriate quantity of materials and resources available at the right time and place.

9.2 Master Production Schedule

The master schedule—or master production schedule (MPS)—is based on the “aggregated” plan. The master production schedule “disaggregates the aggregate plan” because it is a specific statement of exactly what will be produced and a spe-
cific date for production. The master production schedule usually states individual end
items or product models. The master schedule is, therefore, a detailed extension of the
medium-range operations plan, or aggregate plan.

Planning Horizons
The aggregate plan is often developed for one year into the future. The master sched-
ule, however, does not need to extend that far, especially because it becomes more dif-
ficult to manage as time increases. As a general rule, companies use six months or less for
their master schedule. However, an important rule is that the master scheduling horizon

von70154_09_c09_257-302.indd 260 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

should be at least equal to the longest cumulative lead time of any product and its compo-
nent parts. In other words, enough time must be allowed from the time a master schedule
quantity is entered for all parts and raw materials to be ordered from suppliers, compo-
nent parts to be manufactured, and the final product to be assembled and shipped. Oth-
erwise, the master schedule will not be able to satisfy the demand for those products with
long cumulative lead times.

MPS Development Process
The master schedule is a statement of exactly what will be produced. It must simultane-
ously satisfy the needs of sales and marketing and be feasible in terms of operations.
Developing a master schedule that is close to the aggregate plan, yet still satisfies mar-
keting and operations, is not an easy task. The aggregate plan was developed based on a
strategy that maintained acceptable inventory and workforce levels. The master schedule
should still be based on that strategy, but must now do so for individual end items. In
addition, the master schedule must not place more capacity demands on any machine
or work center than can reasonably be met by existing capacity. Due to the difficulties
involved in developing a good master production schedule, the job is usually done by
experienced individuals called master schedulers.

Maine Woods Company produces wooden toys using a labor-intensive production pro-
cess relying heavily on skilled woodworkers to make most of the parts that are used for
the company’s finished products. The company’s aggregate production plan is developed
on a monthly basis for one year into the future. For planning purposes, the company’s
48 different products are grouped by product characteristics into three product families:
wheel goods, blocks, and baby toys. It is these families that are reflected in the aggregate
plan. Table 9.1 shows that plan for the wheel-goods products only.

Table 9.1: Maine Woods Co. aggregate plan, wheel-goods product group

Month Demand
Forecast

Regular-Time
Production

Overtime
Production

Beginning
Inventory

Ending
Inventory

January 1,800 2,000 0 200

February 1,700 2,000 200 500

March 1,800 2,000 500 700

April 1,500 2,000 700 1,200

May 1,800 2,000 1,200 1,400

June 1,900 2,000 1,400 1,500

July 2,000 2,000 1,500 1,500

August 2,500 2,000 1,500 1,000

September 2,500 2,000 1,000 500

October 2,900 2,000 400 500 0

November 2,400 2,000 400 0 0

December 2,000 2,000 0 0

von70154_09_c09_257-302.indd 261 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

The company has developed an aggregate plan that emphasizes maintaining a constant
workforce. Due to the high skill level required of its employees, Maine Woods does not
want to hire or lay off personnel. Instead, inventory is built up in anticipation of high
demand during late summer and fall when the retail stores that sell Maine Woods’ toys
order in preparation for Christmas. Overtime has been planned only as a necessity in
October and November when no inventory will be available.

Matching the Schedule to the Plan
Refer again to the Maine Woods aggregate plan shown in Table 9.1. Production exceeds
demand during the early part of the year, thus increasing inventory. During that time
period, the company’s objectives for the master production schedule will be to:

• Produce quantities that will match the aggregate plan
• Produce each individual product in proportion to its expected demand
• Schedule production so that available capacity is not exceeded

The wheel-goods product group consists of three products: tricycles, toy wagons, and
scooters. Past experience indicates that orders for these items will be divided so that
approximately half are for tricycles and the remaining orders are equally divided between
wagons and scooters. Thus, in January, the planned production of 2,000 units should be
divided so that 1,000 tricycles, 500 toy wagons, and 500 scooters are produced. The same
should also be done for February and March.

Figure 9.2 shows one possible master schedule that satisfies the preceding requirements.
Notice that the total production of all three products in each month matches the aggregate
plan for that month. Further, production of each individual product is distributed evenly
so the production facilities will not be overloaded in some weeks and under loaded in
others.

Figure 9.2: Maine Woods Co. master production schedule, wheel-goods product group:
Constant planned production

Month January February March

Week 1 2 3 4 5 6 7 8 9 10 11 12

Tricycle

Toy Wagon

Scooter

250 250 250 250 250 250 250 250 250 250 250 250

250 250 250 250 250 250

250 250 250 250 250 250

2,000 2,000 2,000Totals

P
ro

d
u

c
t

The master schedule shown in Figure 9.2 could be extended across the first nine months
of the year because planned production during each of those months is the same. But, in
October, planned production increases to 2,400 units. To meet this increase, the difference
can be spread evenly across that month, keeping each product’s proportion of the total the
same as before. Figure 9.3 shows the master schedule with increased output for October.

von70154_09_c09_257-302.indd 262 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

Figure 9.3: Maine Woods Co. master production schedule, wheel-goods product group

Month September October

Week 37 38 39 40 41 42 43 44

Tricycle

Toy Wagon

Scooter

250 250 250 250 300 300 300 300

250 250 300 300

250 250 300 300

2,000 2,400Totals

P
ro

d
u

c
t

Accounting for Customer Orders
The master schedule shown in Figure 9.3 is based on the aggregate plan and historical
information about demand for each product. However, customer orders must become
part of the process; otherwise, the company may be producing based on a plan that is no
longer valid because demand has changed.

To show how a master schedule that takes demand into account can be developed, remove
inventory buildup from the picture by concentrating on the months of November and
December when inventory is not available and demand must be met from current produc-
tion. The example will concentrate on just one product—the toy wagon.

Suppose it is the last week of October, and the forecasts still indicate that 600 toy wag-
ons (one-fourth of 2,400) will be ordered during November and another 500 (one-fourth
of 2,000) during December. We can enter this information in Figure 9.4 in the “Forecast
demand” row. Actual customer orders may, however, differ from the forecast. Therefore,
the next row in Figure 9.4 indicates actual orders booked. Notice how the actual number
of orders received decreases farther into the future because there are fewer known orders.
As the future time periods draw closer to the present, customer orders should increase,
coming closer to the forecast.

Figure 9.4: Maine Woods Co. master production schedule based on demand forecast
and booked customer orders for toy wagons

Month November December

Week 45 46 47 48 49 50 51 52

Forecast demand

Customer orders
booked

Projected on-hand
inventory

150 150 150 150 125 125 125 125

170 140 85 20

230 65 -85

300Master schedule

165 120 45 0

On-hand inventory at end of October = 100

von70154_09_c09_257-302.indd 263 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

Problem

Refer to Figure 9.4 for Maine Woods. The projected on-hand inventory for weeks 45, 46, and 47 is
calculated as follows:

WEEK 45:

1. Actual on-hand inventory from the preceding week (last week of October) is 100 units.
2. The master schedule amount for week 45 is 300.
3. There are 170 customer orders booked during week 45, which is larger than the forecast for

that week (150).

Projected on-hand inventory 5 100 1 300 2 170 5 230

WEEK 46:

1. Projected on-hand inventory from the preceding week (week 45) is 230 units.
2. The master schedule amount in week 46 is 0.
3. There are 165 customer orders booked in week 46, which is larger than the forecast for that

week (150).

Projected on-hand inventory 5 230 1 0 2 165 5 65 (continued)

Projecting On-Hand Inventory
Because Maine Woods produces toy wagons only every other week, a key to meeting
customer orders will be inventory. For example, notice that the company has 100 toy wag-
ons in inventory at the end of October. However, customer orders for the first week of
November are 170. Therefore, unless more wagons are produced, demand cannot be met.
To avoid this problem, Maine Woods has already scheduled another batch of 300 wagons
for production during the first week of November, as shown in Figure 9.4.

To plan additional production of toy wagons, which will be scheduled in the “Master
schedule” row of Figure 9.4, it will be necessary to calculate the projected on-hand inven-
tory. This is referred to as “projected” because it is only based on information currently
available. As new customer orders arrive, the actual on-hand inventory each week may
change.

To determine projected inventory on hand for a specific week, execute the following steps:

1. Determine the amount available to meet demand: Add either actual inventory on
hand from the preceding week or projected on-hand inventory from the preced-
ing week to the quantity shown in the “Master schedule” row for the week being
calculated. If the master production schedule is blank, then the amount is zero.

2. Determine demand: Select the larger of forecast demand or customer orders
booked. This is done for two reasons. First, actual orders may exceed the forecast.
Second, additional orders could be received in the future for periods in which
customer orders booked are currently less than the forecast.

3. Calculate on-hand inventory: Subtract the amount determined in step 2 from the
amount in step 1. The result is the projected on-hand inventory for the week.

von70154_09_c09_257-302.indd 264 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

Amount Available-to-Promise
In addition to scheduling production to meet projected demand, it is essential to prepare
for customer orders to be received at any time. The firm must be able to respond to these
requests, and that is called “available-to-promise.” For example, suppose a customer has
contacted Maine Woods to request 50 toy wagons to be shipped in week 46. Will the com-
pany have enough toy wagons available to meet this new order plus the existing orders
for weeks 45 and 46 (which are 170 and 165, respectively) for a total of 335 toy wagons?

Problem (continued)

WEEK 47:

1. Projected on-hand inventory from the preceding week (week 46) is 65 units.
2. The master schedule amount in week 47 is 0.
3. Forecast demand for week 47 is 150, which is larger than the customer orders booked for that

week (140).

Projected on-hand inventory 5 65 1 0 2 150 5 285

When projected on-hand inventory becomes a negative number, as it has in week 47, the need for
more production is indicated. Thus, a master schedule quantity must be entered for week 47. The
exact quantity to schedule will be determined on the basis of production capacity available, expected
demand, and desired batch sizes. Following its procedure of producing toy wagons every other week,
Maine Woods would plan to produce enough to meet demand for the next two weeks, which would
be 300, based on the demand forecast shown in Figure 9.5. Notice that the projected on-hand inven-
tory balance for week 47 has been recalculated, based on the new master schedule quantity.

Figure 9.5: Calculation of available-to-promise for November and December for
Maine Woods Co.

Week 45 46 47 48 49 50 51 52

Forecast demand

Customer orders
booked

Projected on-hand
inventory

150 150 150 150 125 125 125 125

170 140 85 20

230 65 215

300Master schedule

165 120 45 0

65 190 65 190 65

300 250 250

65
Available-to-

promise
40 120 230

On-hand inventory at end of October = 100

Month November December

von70154_09_c09_257-302.indd 265 2/22/13 3:30 PM

CHAPTER 9Section 9.2 Master Production Schedule

Companies calculate an available-to-promise
quantity to determine whether new orders can be
accepted within a given time period. This quan-
tity represents the number of units that can be
promised for completion any time before the next
master schedule quantity.

The available-to-promise quantity is calculated as
follows:

1. In the first time period of the planning
horizon, add actual on-hand inventory
from the preceding time period to any
master schedule quantity. Then subtract
the sum of customer orders booked
before the next master schedule quantity.

2. For subsequent weeks, calculate available-
to-promise only for those weeks when
a master schedule quantity is indicated.
Subtract the sum of customer orders
booked before the next master sched-
ule quantity from the master schedule
amount for the given week. Do not
include projected on-hand inventory, as
that amount could be used in preceding
weeks if more orders are booked.

Problem

Referring to the Maine Woods example shown in Figure 9.5, we will determine available-to-promise
quantities for November.

WEEK 45:

Actual on-hand inventory from the preceding week (end of October) 5 100. The master schedule
quantity for week 45 5 300. The sum of customer orders booked before the next master schedule
quantity (week 47) 5 170 1 165. The available-to-promise quantity 5 (100 1 300) 2 (170 1 165)
5 65.

WEEK 46:

There is no master schedule quantity in this week, so it is skipped.

WEEK 47:

The master schedule amount 5 300. The sum of customer orders booked before the next master
schedule quantity (week 49) 5 140 1 120. The available-to-promise quantity 5 300 2 (140 1 120)
5 40. (continued)

.Comstock/Thinkstock

A firm must be able to handle customer
orders that may be received at any time. If
a customer requests 50 toy wagons to be
shipped in a specified period of time, the
company must take actions to ensure that
the order is met.

von70154_09_c09_257-302.indd 266 2/22/13 3:30 PM

CHAPTER 9Section 9.3 Master Scheduling in Practice

9.3 Master Scheduling in Practice

The discussion of master production scheduling thus far provides basic information. In actual practice, the job is much more difficult and involved. The next section dis-cusses a few key points that are important to understand.
Integration with Other Functional Areas
Although the master schedule relates primarily to production, it also has significant impli-
cations for marketing and finance. The number of units produced during each time period
determines whether demand can be met for that time period. Further, this production will
generate significant costs for labor and materials, while also determining the inflow that
comes from sales. Consequently, both marketing and finance must not only be aware of
the master schedule, but also must give it their approval.

Marketing and sales may have special promotions or other plans that must be reflected
in the master schedule. If the trial MPS does not satisfy marketing’s requirements, then
it must be redone. Meeting the various internal and external demands with available
resources is what makes master scheduling so difficult.

In the past, developing the MPS was often an iterative process, frequently involving only
marketing and operations. But, with today’s emphasis on elimination of functional barri-
ers, some companies have formed inter-functional teams with representatives from opera-
tions, marketing, and finance. Such a team works together to develop a master schedule
that meets all their needs. As a result, the schedule is completed more quickly. Further,
through face-to-face discussions, each individual on the team can better understand the
challenges and constraints faced by the functional areas other team members represent.

The first version is a “trial” MPS, not necessarily the final one. As Figure 9.6 indicates,
after the trial master schedule is developed, a determination must be made as to whether
sufficient capacity is available.

Problem (continued)

This indicates that Maine Woods can promise another 65 units to its customers for completion in
week 45 or 46. The word “or” is critical because it means that there are only 65 units available across
both weeks. So, Maine Woods cannot promise 65 in week 45 and 65 in week 46. The available-to-
promise for week 47 or 48 is 40. Because the calculation is step two assumes that the 65 available-
to-promise in week 45 or 46 are consumed, these 40 units are in addition to the 65. So, if the 65 units
are used, there are still 40 units available to promise in week 47 or 48. If some of the 65 available-to-
promise in week 45 or 46 are not consumed, the available-to-promise in week 47 or 48 will increase
by the amount that is not used.

von70154_09_c09_257-302.indd 267 2/22/13 3:30 PM

CHAPTER 9Section 9.3 Master Scheduling in Practice

Figure 9.6: Iterative process for developing a master production schedule

No

Yes

Yes

Approved
aggregate

plan

No

Trial
master

schedule

Approved
MPS

Capacity
OK?

Capacity
OK?

Does
marketing
approve?

von70154_09_c09_257-302.indd 268 2/22/13 3:30 PM

CHAPTER 9Section 9.3 Master Scheduling in Practice

Approaches to Change
It is important to understand that these plans are not something a company can do only
once each year. Planning is a continuous process that can be thought of as rolling out a
scroll. As time passes, the scroll keeps getting rolled up on the end closest to the present
time and unrolled at the other end, so that a new planning horizon comes into view. This
concept is called rolling through time.

Forecasts far into the future
are less accurate than nearer
term forecasts. Thus, it may be
necessary to make changes in
planned production as the plan-
ning horizon draws nearer. For
instance, a company might find
that demand for one of its prod-
ucts is far exceeding the compa-
ny’s forecasts. This organization
would be foolish not to alter its
production plans to meet the
increased demand. Thus, both
the aggregate plan and the mas-
ter schedule will change as time
passes. But, too much change
can be disruptive. For example,
a company might have already
hired employees and bought
materials to meet its production
plan. Altering that plan could

mean idle employees or inventories of unused materials. Many companies “freeze” their
master schedule for a certain time into the future to avoid such problems.

Freezing the master schedule means that no further changes can be made after a certain
time. For instance, a company may indicate that the master schedule will be frozen for one
week into the future. Thus, no changes may be made once a plan is within one week of
its execution date. This is depicted in Figure 9.7. The master schedule is commonly frozen
for a few weeks, although longer and shorter periods are used, depending on how easily
a company can change its plans.

.Associated Press

A company may find that demand for one of its products far
exceeds its forecasts. This was the case for the Furby, which
was the “must have” toy for the 1998 holiday season.

von70154_09_c09_257-302.indd 269 2/22/13 3:30 PM

CHAPTER 9Section 9.3 Master Scheduling in Practice

Figure 9.7: Freezing the master schedule

Planned production

Week

1 2 3 4 5 6 7

Present FutureMay be changedFrozen

40 30 40 30
50

50 40

20 20 30 20
30

40 50

30 50 40 50
40 50

30

60 50 50 60 60
50 60

40

20

50 40

60 50

Item 1

Item 2

Item 3

Item 4

Accounting for Demand
When developing a master production schedule for the Maine Woods Company, two
approaches were used. The first was based on producing to inventory, while the second
was based on producing to customer orders. In actual practice, both sources of demand
must be considered. There are also other sources of demand. For example, companies
that operate multiple plants often have one plant producing parts for another plant.
Such orders would be identified as interplant orders. Further, many companies produce
replacement parts for their products, such as starter motors for automobiles or blades for
lawnmowers. These service parts requirements must also be considered. Such a process is
depicted in Figure 9.8.

Figure 9.8: Recognizing all sources of demand through demand management

Interplant orders 25

150

50

200 100

75

Service parts

Bench warehouse
orders

Research &
development orders

5 10 5

50 50 50

5

15Marketing samples

50 50 50

5

125

20 15

100

195Total demand 205 275

75

Week

Customer demand

1 2 3 4 5 6

180 200 225

von70154_09_c09_257-302.indd 270 2/22/13 3:30 PM

CHAPTER 9Section 9.4 Rough-Cut Capacity Planning

Problem

Consider the production plan for Maine Woods’ wheel goods, which is given in Figure 9.2. An aggre-
gate production of 2,000 units has been planned for January. When developing the master schedule
of Figure 9.2, Maine Woods has converted that planned production into the detailed schedule for its
three wheel-goods products—toy wagons, tricycles, and scooters.

Based on historical accounting information, each tricycle required …

Learning Objectives

After completing this chapter, you should be able to:

• List the purposes that inventory serves.

• Describe the different types of inventory.

• Explain the differences between perpetual and periodic inventory systems.

• Use the EOQ model to calculate order size.

• Calculate economic order quantities with quantity discounts.

• Determine the order point.

• Calculate safety stock.

10 ©iStockphoto/Thinkstock

Inventory Management

von70154_10_c10_303-338.indd 303 2/22/13 3:48 PM

CHAPTER 10Section 10.1 Inventory

10.1 Inventory

Inventory represents a sig-nificant investment of work-ing capital for manufactur-
ing companies such as Sony,
wholesale and retail organiza-
tions such as Walmart, and food
service providers such as Red
Lobster. Firms like these should
carefully consider the costs and
benefits of holding inventory.
When firms hold large amounts
of inventory, they increase the
costs associated with holding
inventory including working
capital, storage, and inventory
management. Conversely, when
firms hold small amounts of
inventory, they must make fre-
quent orders and accept the risk
of being unable to satisfy cus-
tomer demand. Making small
and frequent orders tends to increase transaction, transportation, and equipment set-up
costs. This is a fundamental trade-off in managing inventory.

Multiple elements that impact this trade-off are discussed throughout the chapter and
are relevant in the following chapters. This chapter also discusses methods for control-
ling independent demand inventory. The previous chapter addressed dependent demand
items. Different systems for controlling and monitoring independent demand inventory
are discussed and several mathematical models are described in this chapter. These sys-
tems help companies determine how much inventory should be ordered to minimize costs
and also when to order inventory so that the desired level of customer service can be pro-
vided. Determining how much inventory to order and when is key to managing inventory.

Purpose of Inventory
Inventory can help businesses meet demand and work more efficiently. For many items,
it does not make sense to produce them only when there is demand. When a customer
walks into a retail store to buy groceries or cosmetics, they expect to walk out of the store
with the item. When customers walk into a dealer’s showroom to buy a car, they do not
want to wait until the car is produced; they want to drive it away. There are also advan-
tages to maintaining a stable level of production. Employment levels must be changed
and equipment must be activated or shut down to allow production rates to fluctuate.
These changes incur cost. In some cases, there simply is not enough capacity to meet the
high level of demand, therefore, an alternative must be found. During low-demand times,
firms can produce more product than they can currently sell with the unused portion
going to inventory. The inventory can be used when demand accelerates and increasing
the production level is not possible or is not economically feasible.

Many firms keep a cushion or “safety stock” of inventory to protect against unexpected
demand. In this way, they can continue to meet customer demand without delays. Keeping

.John McBride & Company Inc./Getty Images

For manufacturing companies, wholesale and retail
organizations, and food service providers, inventory represents
a significant investment in working capital and a substantial
cost to store and manage.

von70154_10_c10_303-338.indd 304 2/22/13 3:48 PM

CHAPTER 10Section 10.2 Information Systems for Inventory Management

a safety stock of inventory is also useful when shipments from suppliers are delayed. This
allows the firm to meet customer demand even though the supplier cannot meet its lead
time commitment.

When producing goods, it is often important to separate steps in the production process
that operate at different speeds. For example, a manufacturing part may be machined at
one rate—one part in five minutes. The next step is to heat treat the machined parts in a
furnace that operates in a batch mode—the furnace can hold up to 100 parts and take eight
hours for heat treating. Therefore, a inventory of up to 100 parts should be accumulated
before heat treatment.

In many situations, discounts are available to purchase a certain quantity. These can be
quantity discounts or transportation discounts. A firm may need a certain amount of
parts, but it may decide to buy more because a supplier is offering a discount for purchas-
ing the larger amount. This is similar to buying a larger box of laundry detergent because
it cost less per unit than the smaller box. Shipping in a certain amount may substantially
reduce transportation costs. The best known transportation discount involves shipping in
full truck load quantities rather than less than truck load amounts. The same can be said
for shipping a full rail car versus less than a full rail car.

A company may try to hedge against possible price increases. When an increase in the pur-
chase price is anticipated by the company or announced by the supplier, the company may
order additional materials prior to the increase. This is similar to the quantity discount. Other
times, firms may want to hedge against uncertainty in supply. A supplier may announce
down time for its operations, or a supplier may have an upcoming contract negotiation with
its labor union. Maintaining some extra inventory on hand may be prudent.

Types of Inventory
Several common types of inventory are:

1. Raw materials: These parts and materials are obtained from suppliers and are
used in the production process.

2. Work-in-process (WIP): These are partly finished parts, components, subassem-
blies, or modules.

3. Finished goods: Items are ready to ship to the customer. No more work is
required.

4. Replacement parts: These are maintained to replace other parts in machinery or
equipment as those parts wear out.

5. Supplies: Parts or materials are used to support the production process, but not
usually a component of the product. These items, such as lubricant and cutting
tools, are consumed in the production process.

6. Transportation (pipeline): The portion of inventory that is in the process of being
shipped through the distribution system.

10.2 Information Systems for Inventory Management

The purpose of inventory management systems is to provide information so that suf-ficient inventory will exist to meet the company’s objectives. Of course, too much inventory can mean extra costs. Thus, the inventory management system is designed
to ensure that inventory levels are maintained within a desired range for each item.

von70154_10_c10_303-338.indd 305 2/22/13 3:48 PM

CHAPTER 10Section 10.2 Information Systems for Inventory Management

Today’s computer systems and the widespread use of bar codes (as shown in Figure 10.1),
have made inventory control more automated. It is not always be possible, or even desir-
able, to computerize all inventory control. This section describes different systems and
how they can be used, either with or without computers. All these systems focus on help-
ing companies determine what, when, and how much to order.

Figure 10.1: Bar codes used for inventory management

PART NO.
(P)

QUANTITY
(Q)

(0000000000)

DESCRIPTION

SERIAL

COLOR

S U P P L I E R
C A P I T O L P L A S T I C S
3 3 3 V A N C A M P R O A D
B O W L I N G G R E E N , O H . 4 3 4 0 2

50327–MG9–0000

420

00134

BLK
BATTERY CUSHION UPPER
DELIVERY INFORMATION FORM

PART NO.
(P)

QUANTITY
(Q)

(0000000000)

DESCRIPTION

SERIAL
(S)

COLOR

S U P P L I E R
C A P I T O L P L A S T I C S
3 3 3 V A N C A M P R O A D
B O W L I N G G R E E N , O H . 4 3 4 0 2

50328–MG9–0000

120

00134

BLK
BATTERY CUSHION LOWER

DELIVERY INFORMATION FORM

von70154_10_c10_303-338.indd 306 2/22/13 3:48 PM

CHAPTER 10Section 10.2 Information Systems for Inventory Management

.Digital Vision/Thinkstock

To keep track of inventory, retailers use a point-of-sale (POS)
system that records each transaction as the items are read by a
bar code scanner.

Perpetual Inventory Systems
A perpetual inventory system continuously monitors inventory levels. It is also known
as a continuous review system. Under such a system, inventory transactions are recorded
as they occur. If the number of transactions is small, this recording can be done by hand,
which is how inventory was recorded before computerized systems. This non-computer-
ized approach makes sense if there are only a handful of items to inventory. Computers,
however, have made the process much easier and faster for a larger number of items. For
example, grocery stores and retailers such as Walmart use point-of-sale systems that record

the transaction as each item is
read by the bar code scanner. As
at Toys “R” Us, this information
is passed along to the supplier,
so replenishment can take place.
An ATM is another example of a
perpetual inventory system; this
system updates the balance in a
patron’s bank account as with-
drawals are made. Debit cards
are one way for the bank to
move the money from the user’s
account at the time of transac-
tion. These cards also allow the
bank to determine if there is suf-
ficient money to cover the trans-
action, which is good for the
bank and the retailer.

Companies use bar codes for
raw material and work-in-process inventories as a way to computerize these inventory
records. The bar codes shown in Figure 10.1 are used on a component part ordered from
a supplier. Using bar codes or other similar technologies allow the firm to be constantly
aware of inventory levels. When inventory drops to a predetermined level (the order
point) an order for more can be generated. Often, this ordering is completed automati-
cally by the same computer system that maintains the inventory records. The quantity

Real World Scenarios: Toys “R” Us—Dealing with Fads in the Toy Business

A major problem in the toy industry is identifying when fads begin and end. There is a long history of
fads including GI Joes, Smurfs, Furbies, and Transformers, which have recently made a comeback. In
many cases, these items are hot one year and gone the next. Toys “R” Us carries more than 20,000
different items. To maximize profits, the company must be sure it maintains just the right amount
of each item. One way it does this is by using computers to monitor sales data and to order (or stop
ordering) as point-of-sale (POS) demand information indicates. This information is transmitted each
day to the company’s headquarters where it is automatically monitored. Thus, when demand for
scooters picks up, the computers can catch the trend and began placing larger orders. Likewise, drops
in sales when a fad has ended can be caught and replenishment orders halted.

von70154_10_c10_303-338.indd 307 2/22/13 3:48 PM

CHAPTER 10Section 10.2 Information Systems for Inventory Management

ordered is usually a fixed amount, often the economic order quantity, which is discussed
later in this chapter.

Periodic Inventory Systems
For the continuous review system to work, it is necessary to know the inventory level
constantly, and to have a supplier who will replenish inventory at any time. In this way,
when the order point in the continuous review system is reached, an order can be sent and
delivery can take place.

When a company does not know the level of inventory or the supplier will only deliver
at a specific interval such as monthly or weekly, the periodic review system can be used.
A meaningful order cannot be placed if the on-hand level of inventory is unknown. Also,
ordering after the supplier’s order window has closed will not generate an immediate
response. The supplier will not process and deliver the order until the order window is
open.

To be effective, the periodic review system is designed to place an order only when on-
hand inventory information is available and the supplier is willing to deliver, in other
words, when the order window is open. The local concrete plant uses cement, which it
stores in large tanks. It takes a physical inventory only on Monday because it is time con-
suming, so it does not know if or how much it needs to order except on Monday. The stor-
age tanks at most gasoline service stations are refilled on a preset schedule, for example,
once each week on Friday. Monitoring inventory continuously and placing an order on
Saturday does not help because the delivery will not be made until the following Friday.

In these cases, the order point must be set at a level that will allow the company to meet
expected demand until the next order window occurs plus demand during the lead time.
If the on-hand inventory is less than this order point, an order is generated that will push
on-hand inventory back to a predetermined level. The periodic review system, also called
the fixed order interval system, can be run without a computerized system to monitor
inventory levels, but it is more likely to run out of stock because the system is unable to
react quickly to changes in demand because inventory level is not continually monitored.
If the firm wishes to keep the chance of stockouts low, it must increase the level of safety
stock inventory.

Aggregate Performance Measures
Inventory represents a tremendous capital investment. In general, the companies that can
operate with less inventory are the companies that operate more efficiently. Aggregate
performance measures can be used to judge how well a company is utilizing its inven-
tory resources. One of the most common measures is average inventory investment—the
dollar value of a company’s average level of inventory. The primary disadvantage of this
measure is that it makes comparisons between companies difficult. For example, larger
companies will generally have more inventory than smaller companies. Thus, a large mul-
tinational company may have a larger average inventory investment than a small busi-
ness, but the larger company may be using its inventory more efficiently.

von70154_10_c10_303-338.indd 308 2/22/13 3:48 PM

CHAPTER 10Section 10.2 Information Systems for Inventory Management

Inventory turnover ratio is a measure that allows for better comparison among compa-
nies. This ratio is calculated by comparing a company’s sales to its average inventory
investment, as follows:

Inventory turnover 5 annual cost of goods sold/average inventory investment

The inventory turnover ratio indicates how many times the inventory turns over or is sold
during one year. Because this ratio is a relative measure, companies of different sizes can
be more easily compared. In general, a company with a higher turnover ratio will be using
its inventory more efficiently. For example, automobile companies using just-in-time (JIT)
often have very high inventory turnover ratios of 30 or more, while those not using JIT
may be in the range of 6 to 12. JIT is providing only the items that are needed at the time
they are needed. One disadvantage of this ratio is that figures among industries may not
be comparable.

A measure closely related to inventory turnover is days of inventory. The calculation
procedure is as follows:

Days of Inventory 5 average inventory investment/(annual cost of
goods sold/days per year)

The days of inventory indicate approximately
how many days of sales can be supplied solely
from inventory. The lower this value, the more
efficiently inventory is being used. In general,
inventory turnover can be converted to days of
inventory by using the following calculation:

Days of inventory 5 days per year/inventory
turnover rate

ABC Classification
Interestingly, companies do not need to keep accu-
rate track of all inventory items. For instance, cer-
tain parts may have a relatively low value and be
used infrequently; those items can often be moni-
tored very loosely. On the other hand, high-value
and high-usage items must be tracked carefully
and continuously. ABC analysis has been devel-
oped to determine which inventory items should
receive the highest level of control. By multiplying
the dollar value of each item by its annual usage,
a dollar usage value can be obtained. Dollar usage
follows the Pareto Principle (see Chapter 4) in that
typically, only 20% of all the items account for
80% of the total dollar usage, while the remaining
items typically account for only 20% of the dollar

.Stockbyte/Thinkstock

ABC analysis is used to determine which
inventory items should receive the highest
level of control. This method focuses
efforts where the payoff is highest.

von70154_10_c10_303-338.indd 309 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

usage. This principle leads to the ABC classification, which is based on focusing efforts
where the payoff is highest.

After calculating the dollar usage for each inventory item, the items are ranked by dollar
usage, from highest to lowest. The first 20% of the items are assigned to class A, as shown
in Table 10.1. These are the items that warrant closest control and monitoring through a
perpetual inventory system. Accurate inventory records are important, and there is a high
potential for cutting costs through careful buying and close scrutiny of safety stocks.

Table 10.1: ABC classification of inventory items

Item Annual
Demand

Unit Cost Annual Dollar
Usage

% Annual
Dollar Usage

Cumulative %
Annual Dollar
Usage

Classification

1 5,000 $30 $150,000 48.91 48.91 A

2 200 450 90,000 29.34 78.25 A

3 2,000 10 20,000 6.52 84.77 B

4 800 20 16,000 5.22 89.99 B

5 1,000 10 10,000 3.26 93.25 B

6 1,200 5 6,000 1.96 95.21 C

7 1,300 4 5,200 1.69 96.90 C

8 2,500 2 5,000 1.63 98.53 C

9 3,500 1 3,500 1.14 99.67 C

10 500 2 1,000 0.33 100.00 C

306,700

The next 30% of the items are classified as B items. These deserve less attention than A
items. Finally, the last 50% of stocked items are C items. These have the lowest dollar usage
and can be monitored loosely, with larger safety stocks maintained to avoid stockouts.

10.3 Economic Order Quantity Model

Inventory decisions involve trade-offs: Keeping more inventory may decrease the amount of stockouts as well as reduce the ordering and set-up costs, but keeping more inventory requires more investment, storage, and management costs. One model that
seeks to minimize these costs is the economic order quantity (EOQ). The EOQ model is
concerned primarily with the cost of ordering and the cost of holding inventory, but the
basic model can be expanded to address several issues.

von70154_10_c10_303-338.indd 310 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

Costs of Ordering and Holding
One major component of cost associated with inventory is the cost of replenishing it, usu-
ally called ordering cost. If a part or raw material is ordered from outside suppliers, an
ordering cost is incurred. Conversely, parts, subassemblies, or finished products may be
produced in-house. In that case, ordering cost is represented by the costs associated with
changing over equipment from producing one item to producing another, and is referred
to as set-up cost. To simplify, this text will refer to both ordering costs and set-up costs as
ordering costs.

Ordering costs may include many different items. Some of these will be relatively fixed,
and others may vary. It will be important to differentiate between the ordering costs that
do not change much and those that are incurred each time an order is placed. For example,
suppose a company currently places orders for a given part with its supplier five times
per year. If, instead, the company ordered six times per year, which costs would probably
change (variable costs), and which would probably not (fixed costs)? The general break-
down between fixed and variable ordering costs is listed in Table 10.2.

Table 10.2: Fixed costs and variable costs

Fixed Costs Variable Costs

Staffing costs (payroll, benefits, etc.)
Office furniture and equipment

Shipping costs
Cost of placing an order (phone, postage, order forms)
Cost of lost production during set-up
Cost of materials used during set-up
Receiving and inspection costs

Although it costs money to replenish inventory, it also costs money to hold that inventory.
Such inventory holding costs, also called carrying costs, may include costs paid for storage
space, interest paid on borrowed money to finance the inventory, and any losses incurred
due to damage or obsolescence. Once again, it is important to differentiate between fixed
and variable costs of holding inventory. To understand this difference, consider this ques-
tion: What happens if an inventory level is increased by one unit? Which costs would not
change (fixed costs), and which costs would change (variable costs)? The general break-
down for inventory holding is shown in Table 10.3.

Table 10.3: Inventory holding

Fixed Costs Variable Costs

Capital costs of warehouse
Taxes on warehouse and property
Costs of operating warehouse
Personnel costs

Cost of capital in inventory
Insurance on inventory value
Losses due to obsolescence, theft, spoilage
Taxes on inventory value
Cost of renting warehouse space

von70154_10_c10_303-338.indd 311 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

In the next section, the most basic approach to determining order quantity, called the eco-
nomic order quantity (EOQ) model, is discussed. The goal of firms using the EOQ model is
to minimize the total annual costs of ordering and holding inventory by varying the order
quantity. Only variable costs are considered because fixed costs are not affected by short-
term variation in order quantity. To understand EOQ, it is important to understand the
differences between the fixed and variable costs that are listed above. Also, it is important
to realize that the division between fixed and variable costs may change depending on the
context. If additional personnel must be hired, staffing costs may be considered variable.

Ordering cost and holding cost can be described with the analogy of two children sit-
ting on a seesaw. When one goes up, the other goes down, and vice versa. This trade-off
appears to present somewhat of a quandary: If an effort is made to decrease total annual
variable holding costs, total annual variable ordering costs will increase—and vice versa.
A solution to this dilemma is to combine the two costs as total annual variable costs and
minimize only that cost. As Figure 10.2 indicates, there is just one point at which total
costs are minimized. The order quantity associated with that point is called the economic
order quantity (EOQ).

Figure 10.2: Total annual variable costs

EOQ

Total costs

Order quantity

Variable
holding
costs

Variable
ordering

costs

A
n

n
u

a
l

va
ri

a
b

le
c

o
s

ts

von70154_10_c10_303-338.indd 312 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

Assumptions of the EOQ
Figure 10.2 indicates the economic order quantity point. A set of simplifying assumptions
can be made because the EOQ model is a simplification of real ordering processes. Those
assumptions are described here. Later, variations of the EOQ model will be considered
when some of these assumptions are not necessary.

1. Constant known demand: The first assumption is that demand is fairly stable, or
constant, and reasonably known.

2. Cost per unit is not dependent on order quantity: Most things can be purchased at a
lower cost per unit if they are purchased in larger quantities. For instance, large
sizes of laundry detergent usually cost less per ounce than smaller sizes. This
example, however, makes purchase cost a variable cost—something for which
the EOQ model does not account. Thus, the assumption is that purchase cost per
unit remains the same, regardless of whether the amount is one, 100, or 1,000
units each time.

3. Entire order delivered at once: This assumption relates to how inventory is replen-
ished. Gradually building up inventory, as would happen in a clothing factory,
is one possibility. As a particular model of jacket is produced, the inventory of
that jacket builds up gradually. Another possibility is for all units in an order
to arrive at one time, which is what happens when a retail store orders from a
factory. The factory ships an entire order of the jacket at one time and the store’s
inventory is replenished all at once. It is this latter, instantaneous replenishment
that is assumed by the EOQ. This assumption, combined with the assumption of
constant demand, results in the inventory pattern depicted in Figure 10.3.

4. Ordering and carrying costs known and independent: The final assumption is that the
variable costs of ordering and carrying inventory are known. In many cases, such
costs can be determined from company records or from the accounting depart-
ment; however, they are sometimes not readily available and must be estimated.
Also, the assumption is made that these two costs are not related in any way, and
that only variable costs are effected by the order quantity.

These assumptions may seem restrictive, and possibly unrealistic. Recall, however, that
the EOQ model is the basic starting point. This model may be altered to relax some of
these assumptions—and more closely match reality.

von70154_10_c10_303-338.indd 313 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

Figure 10.3: Basic EOQ inventory pattern

E
O

Q

Time

In
v
e

n
to

ry
l

e
v
e

l

Inventory replenished

Mathematics of EOQ
Stating the EOQ formula in mathematical terms requires the use of variables to represent
the parameters. The variables are:

D 5 demand rate (units/year)

Q 5 order quantity or lot size (units)

Co 5 variable ordering cost ($/order)

Ch 5 variable holding cost ($/unit/year)

Once again, please note that these are the variable costs and that the variable ordering
costs will represent additional costs incurred when another order is placed. Holding costs
also include only the variable costs associated with keeping one more unit in inventory.
These variables are stated as cost per unit per year because the model is illustrating annual
costs.

Another way of stating inventory holding costs is to divide Ch into two components. The
elements that make up variable holding costs depend on the number of units in inventory
and the value of each unit. In most instances, it is possible to state inventory holding cost,
Ch, as a percentage of unit cost per year ($/year). The greatest part of this percentage is

von70154_10_c10_303-338.indd 314 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

accounted for by capital tied up in the inventory. Because capital cost is usually stated as
a percentage, it is especially convenient to state holding cost in this form. To do so, the
following variables are used:

v 5 cost or value of item ($/unit)

r 5 holding-cost percentage of unit value ($/$/year)

Then Ch 5 vr.

Regardless of how many units are ordered at a time, the number of orders can be deter-
mined by dividing annual demand, D, by the order quantity, Q. Thus,

Orders placed per year 5
D
Q

Since the cost per order is Co, annual variable ordering costs can be easily calculated as
follows:

Annual variable ordering costs 5
D
Q

Co

Annual Variable Holding Costs

Notice in Figure 10.3 that if the order quantity is set equal to the EOQ, the theoretical
inventory pattern is a straight line between the EOQ and zero. Remember the assumption
is that demand is constant over time, which makes the drawdown of inventory a straight
line. Suppose, instead, that the variable Q represents the quantity ordered each time. In that
case, the maximum inventory level would be Q, assuming inventory is replenished just as
it reaches zero. Minimum inventory would still be zero. This fluctuation in the inventory
level makes the calculation of annual holding costs somewhat difficult because there will
be a different number of units in inventory at any one time. To make matters worse, each
unit will be in inventory for a different length of time—some for a very short period, oth-
ers longer. There is also an easier, but equivalent, way to determine annual holding costs.

The method used to determine annual holding costs is based on average inventory level.
Because inventory follows a uniform pattern, with a maximum of Q and a minimum of
zero, the average level will be halfway between the maximum and minimum values, or
Q/2. In terms of the number of units in inventory, and the time each unit spends there, the
fluctuating system shown in Figure 10.3 is actually equivalent to maintaining Q/2 units at
all times, as shown in Figure 10.4. This simplifies the calculation of annual variable hold-
ing costs to:

Annual variable holding costs 5
Q
2

Ch

von70154_10_c10_303-338.indd 315 2/22/13 3:48 PM

CHAPTER 10Section 10.3 Economic Order Quantity Model

Figure 10.4: Average inventory

Time

Q

0

Q

2

In
v
e

n
to

ry
l

e
v
e

l

Average
inventory

Economic Order Quantity Formula

Total annual variable costs will be the sum of holding costs and ordering costs. Using the
formulas noted above, this will be:

Total annual variable costs 5
Q
2

Ch +
D
Q

Co

The economic order quantity will be the point at which the total cost function is mini-
mized. …