Inventory that is "in the pipeline" moving from one link to another is

image1

Paul A. Souders/Corbis

Chapter

eleven

Chapter Outline

Introduction

11.1 The Role of Inventory

11.2 Periodic Review Systems

11.3 Continuous Review Systems

11.4 Single-Period Inventory Systems

11.5 Inventory in the Supply Chain Chapter Summary

Managing Inventory throughout the Supply Chain

Chapter ObjeCtives

By the end of this chapter, you will be able to:

· Describe the various roles of inventory, including the different types of inventory and inventory drivers, and distinguish between independent demand and dependent demand inventory.

· Calculate the restocking level for a periodic review system.

· Calculate the economic order quantity (EOQ) and reorder point (ROP) for a continuous review system, and determine the best order quantity when volume discounts are available.

· Calculate the target service level and target stocking point for a single-period inventory system.

· Describe how inventory decisions affect other areas of the supply chain. In particular, describe the bullwhip effect, inventory positioning issues, and the impacts of transportation, packaging, and material handling considerations.

326

image5.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  327

Inventory Management at Amazon.com

Baumgarten/VARIO IMAGES/SIPA/Newscom

Employees pick items off the shelves at an Amazon.com warehouse in Leipzig, Germany.

WHEN they first started appearing in the late 1990s, Web- based “e-tailers” such as Amazon.com hoped to replace the “bricks” of traditional retailing with the

“clicks” of online ordering. Rather than opening dozens or even hundreds of stores filled with expensive inventory, an e-tailer could run a single virtual store that served cus-tomers around the globe. Their business model suggested that inventory could be kept at a few key sites, chosen to ­minimize costs and facilitate quick delivery to custom-ers. In theory, e-tailers were highly “scalable” businesses that could add new customers with little or no additional ­investment in inventory or facilities. (Traditional retailers usually need to add stores to gain significant increases in their customer base.)

But how has this actually played out for Amazon over the years? Table 11.1 contains sales and inventory figures, pulled from the company’s annual reports, for Amazon for the years 1997 through 2012. The first column reports net sales for each calendar year, and the second column contains the amount of inventory on hand at the end of the year. The third column shows inventory turns, which is calculated as (net sales/ending inventory). Retailers generally want higher inventory turns, which indicate that they can support the same level of sales with less inventory. Inventory turns is of-ten thought of as a key measure of asset productivity.

Looking at Amazon’s performance over the years ­provides some interesting insights. Consider Figure 11.1. In late 1999, Amazon learned that managing inventory can be challenging even for e-tailers. That was the year the com-pany expanded into new product lines, such as electron-ics and housewares, with which it had little experience.

Table 11.1  Amazon.com Financial Results, 1997–2012

Inventory

Net Sales

($Millions)

Inventory

Year

($Millions)

(Dec. 31)

Turns

1997

$148

$9

16.4

1998

$610

$30

20.3

1999

$1,640

$221

7.4

2000

$2,762

$175

15.8

2001

$3,122

$143

21.8

2002

$3,933

$202

19.5

2003

$5,264

$294

17.9

2004

$6,921

$480

14.4

2005

$8,490

$566

15.0

2006

$10,711

$877

12.2

2007

$14,835

$1,200

12.4

2008

$19,166

$1,399

13.7

2009

$24,509

$2,171

11.3

2010

$34,204

$3,202

10.7

2011

$48,077

$4,992

9.6

2012

$61,093

$6,031

10.1

Amazon’s purchasing managers were faced with the ques-tion of how many of these items to hold in inventory. Too little, and they risked losing orders and alienating custom-ers; too much, and they could lock up the company’s re-sources in unsold products. Only later, when sales for the 1999 holiday season fell flat and Amazon’s inventory levels skyrocketed did the purchasing managers realize they had overstocked. In fact, as the figures show, by the end of 1999,

image6.jpg image7.jpg 328  PART IV • Planning and Controlling Operations and Supply Chains

image8.jpg

Inventory Turns at Amazon.com, 1997–2009

25.0

20.0

15.0

10.0

5.0

0.0

1999

2001

2003

2005

2007

2009

2011

2013

1997

Figure 11.1  Inventory Turns at Amazon.com, 1997–2009

Amazon’s inventory­ turnover ratio was 7.4—worse than that of the typical brick-and-mortar retailer at the time.

After 1999, Amazon seemed to learn its lesson. Inven-tory turns rose to nearly 22 in 2001, but have fallen steadily ever since, to 10.1 turns for 2012, even as Amazon’s sales have risen sharply. But why? The decline in inventory turns over the past decade is due in large part to a shift in Amazon’s­ business strategy. Instead of trying to build com-petitive advantage based on low-cost books (Amazon’s original business model), the company now seeks to provide

customers with convenient shopping and fast delivery for a wide range of products. Such a strategy requires more in-ventory to support the same level of sales.

So today, how does Amazon compare to its brick-and-mortar competitors? Amazon handily beats traditional book retailer Barnes & Noble, whose inventory turns for 2013 were just 4.6. Yet Best Buy, which sells computers, phones, video games, and appliances, generated 6.9 inventory turns in 2013—not bad, especially considering all the retail stores Best Buy must support.

image9.jpg

Introduction

Inventory

According to APICS, “those stocks or items used to sup-port production (raw materials and work-in-process items), supporting activities (mainte-nance, repair, and operating supplies) and customer service (finished goods and spare parts).”

APICS defines inventory as “those stocks or items used to support production (raw materials and work-in-process items), supporting activities (maintenance, repair, and operating supplies) and customer service (finished goods and spare parts) .”1 In this chapter, we discuss the critical role of inventory—why it is necessary, what purposes it serves, and how it is controlled.

As Amazon’s experience suggests, inventory management is still an important function, even in the Internet age. In fact, many managers seem to have a love–hate relationship with inventory. Michael Dell talks about inventory velocity—the speed at which components move through Dell Computer’s operations—as a key measure of his company’s performance.2 In his mind, the less inventory the company has sitting in the warehouse, the better. Victor Fung of the Hong Kong-based trading firm Li & Fung, goes so far as to say, “Inventory is the root of all evil.”3

Yet look what happened to the price of gasoline in the United States during the spring of 2007. It skyrocketed, primarily because refineries were shut down for maintenance and suppliers were caught with inadequate reserves. And if you have ever visited a store only to find that your favorite product is sold out, you might think the lack of inventory is the root of all evil. The fact is, inventory is both a valuable resource and a potential source of waste.

image10.jpg

1Definition of Inventory in J. H. Blackstone, ed., APICS Dictionary, 14th ed. (Chicago, IL: APICS, 2013). Reprinted by

permission.

2J. Magretta, “The Power of Virtual Integration: An Interview with Dell Computer’s Michael Dell,” Harvard Business

Review 76, no. 2 (March–April 1998): 72–84.

3J. Magretta, “Fast, Global, and Entrepreneurial: Supply Chain Management, Hong Kong Style,” Harvard Business Review

76, no. 5 (September–October 1998): 102–109.

image11.jpg image12.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  329

11.1 The Role of Inventory

image13.jpg

Consider WolfByte Computers, a fictional manufacturer of laptops, tablets and e-readers. Fig- HYPERLINK \l "page346" ure 11.2 shows the supply chain for WolfByte’s laptop computers. WolfByte assembles the laptops from components purchased from companies throughout the world, three of which are shown in the figure. Supplier 1 provides the displays, Supplier 2 manufactures the hard drives, and Sup-plier 3 produces the keyboards.

Looking downstream, WolfByte sells its products through independent retail stores and through its own Web site. At retail stores, customers can buy a laptop off the shelf, or they can order one to be customized and shipped directly to them. On average, WolfByte takes about two days to ship a computer from its assembly plant to a retail store or a customer. Both WolfByte and the retail stores keep spare parts on hand to handle customers’ warranty claims and other service requirements.

With this background, let’s discuss the basic types of inventory and see how they fit into WolfByte’s supply chain.

Cycle stock

Components or products that are received in bulk by a downstream partner, gradually used up, and then replenished again in bulk by the upstream partner.

Safety stock

Extra inventory that a company holds to protect itself against uncertainties in either demand or replenishment time.

Inventory Types

Two of the most common types of inventory are cycle stock and safety stock. Cycle stock refers to components or products that are received in bulk by a downstream partner, gradually used up, and then replenished again in bulk by the upstream partner. For example, suppose Supplier 3 ships 20,000 keyboards at a time to WolfByte. Of course, WolfByte can’t use all those devices at once. More likely, workers pull them out of inventory as needed. Eventually, the inventory runs down, and WolfByte places another order for keyboards. When the new order arrives, the inven-tory level rises and the cycle is repeated. Figure 11.3 shows the classic sawtooth pattern associ-ated with cycle stock inventories.

Cycle stock exists at other points in WolfByte’s supply chain. Almost certainly, Suppliers 1 through 3 have cycle stocks of raw materials that they use to make components. And retailers need to keep cycle stocks of both completed computers and spare parts in order to serve their customers.

Cycle stock is often thought of as active inventory because companies are constantly using it up, and their suppliers constantly replenishing it. Safety stock, on the other hand, is extra in-ventory that companies hold to protect themselves against uncertainties in either demand levels or replenishment time. Companies do not plan on using their safety stock any more than you plan on using the spare tire in the trunk of your car; it is there just in case.

Let’s return to the keyboard example in Figure 11.3. WolfByte has timed its orders so that a new batch of keyboards comes in just as the old batch is used up. But what if Supplier 3 is late in delivering the devices? What if demand is higher than expected? If either or both these condi-tions occur, WolfByte could run out of keyboards before the next order arrives.

Imagine the resulting chaos: Assembly lines would have to shut down, customers’ orders couldn’t be filled, and WolfByte would have to notify customers, retailers, and shippers about the delays.

Figure 11.2

WolfByte Computers

Supply Chain

Supplier 1

image14.jpg

WolfByte

Computers

Supplier 2

Supplier 3

image307.jpg image2Customer Retail store

image15.jpg image16.jpg

Customer

image17.jpg image18.jpg 330  PART IV • Planning and Controlling Operations and Supply Chains

Figure 11.3

Cycle Stock at WolfByte

Computers

Anticipation inventory

Inventory that is held in antici-pation of customer demand.

Hedge inventory

According to APICS, a “form of inventory buildup to buffer against some event that may not happen. Hedge inventory planning involves specula-tion related to potential labor strikes, price increases, unset-tled governments, and events that could severely impair the company’s strategic initiatives.”

Transportation inventory

Inventory that is moving from one link in the supply chain to another.

Smoothing inventory

Inventory that is used to smooth out differences between upstream produc-tion levels and downstream demand.

Figure 11.4

Safety Stock at WolfByte

Computers

Keyboard order

Another order

20,000

received ...

received ...

level

Inventory

10,000

Inventory

And the

drawn down

process

gradually ...

repeats itself

0

Time

image19.jpg

One solution is to hold some extra inventory, or safety stock, of keyboards to protect against fluctuations in demand or replenishment time. Figure 11.4 shows what WolfByte’s inventory­ levels would look like if the company decided to hold safety stock of 1,000 keyboards. As you can see, safety stock provides valuable protection, but at the cost of higher inventory lev-els. Later in the chapter, we discuss ways of calculating appropriate safety stock levels.

There are four other common types of inventory: anticipation, hedge, transportation, and smoothing. Anticipation inventory, as the name implies, is inventory that is held in anticipation of customer demand. Anticipation inventory allows instant availability of items when custom-ers want them. Hedge inventory, according to APICS, is “a form of inventory buildup to buffer against some event that may not happen. Hedge inventory planning involves speculation related to potential labor strikes, price increases, unsettled governments, and events that could severely impair the company’s strategic initiatives.”4 In this sense, hedge inventories can be thought of as a special form of safety stock. WolfByte has stockpiled a hedge inventory of two months’ worth of hard drives because managers have heard that Supplier 2 may experience a temporary shut-down over the next two months.

Transportation inventory represents inventory that is “in the pipeline,” moving from one link in the supply chain to another. When the physical distance between supply chain partners is long, transportation inventory can represent a considerable investment. Suppose, for example, that Supplier 2 is located in South Korea, and WolfByte is located in Texas. Hard drives may take several weeks to travel the entire distance between the two companies. As a result, multiple orders could be in the pipeline on any particular day. One shipment of hard drives might be sitting on the docks in Kimhae, South Korea; two others might be halfway across the Pacific; a fourth might be found on Route I-10, just outside Phoenix, Arizona. In fact, the transportation inventory of hard drives alone might dwarf the total cycle and safety stock inventories in the rest of the supply chain.

Finally, smoothing inventory is used to smooth out differences between upstream pro-duction levels and downstream demand. Suppose management has determined that WolfByte’s assembly plant is most productive when it produces 3,000 laptops a day. Unfortunately, demand from retailers and customers will almost certainly vary from day to day. As a result, WolfByte’s

Keyboard order

Another

21,000

received ...

order received ...

level

11,000

Inventory

Inventory

And the

drawn down

process

gradually...

repeats itself

1000

Safety stock of 1,000 keyboards

image20.jpg

Time

image21.jpg

4Definition of Hedge Inventory in J. H. Blackstone, ed., APICS Dictionary, 14th ed. (Chicago, IL: APICS, 2013). Reprinted­ by permission.

image22.jpg

Figure 11.5

Smoothing Inventories at

WolfByte Computers

CHAPTER 11 • Managing Inventory throughout the Supply Chain  331

image23.jpg

4,000

systems

3,000

Demand

Computer

2,000

Production

Inventory

1,000

0

1

2

3

4

5

6

7

8

9

Day

image24.jpg

managers may decide to produce a constant 3,000 laptops per day, building up finished goods inventory during periods of slow demand and drawing it down during periods of high demand. (Figure 11.5 illustrates this approach.) Smoothing inventories allow individual links in the sup-ply chain to stabilize their production at the most efficient level and to avoid the costs and head-aches associated with constantly changing workforce levels and/or production rates. If you think you may have heard of this idea before, you have: It’s part of the rationale for following a level production strategy in developing a sales and operations plan (see Chapter 10).

Inventory drivers

Business conditions that force companies to hold inventory.

Supply uncertainty

The risk of interruptions in the flow of components from upstream suppliers.

Inventory Drivers

From this discussion, we can see that inventory is a useful resource. However, companies don’t want to hold more inventory than necessary. Inventory ties up space and capital: A dollar ­invested in inventory is a dollar that cannot be used somewhere else. Likewise, the space used to store inventory can often be put to more productive use. Inventory also poses a significant risk of obsolescence, particularly in supply chains with short product life cycles. Consider what happens when Intel announces the next generation of processor chips. Would you want to be stuck hold-ing the old-generation chips when the new ones hit the market?

Finally, inventory is too often used to hide problems that management really should resolve. In this sense, inventory can serve as a kind of painkiller, treating the symptom without solving the underlying problem. Consider our discussion of safety stock. Suppose WolfByte’s managers decide to hold additional safety stock of hard drives because of quality problems they have been experi-encing with units received from Supplier 2. While the safety stock may buffer WolfByte from these quality problems, it does so at a cost. A better solution might be to improve the quality of incoming units, thereby reducing both quality-related costs and the need for additional safety stock.

With these concerns in mind, let’s turn our attention to inventory drivers—business condi-tions that force companies to hold inventory. Table 11.2 summarizes the ways in which various inventory drivers affect different types of inventory. To the extent that organizations can manage and control the drivers of inventories, they can reduce the supply chain’s need for inventory.

In managing inventory, organizations face uncertainty throughout the supply chain. On the upstream (supplier) end, they face supply uncertainty, or the risk of interruptions in the

Table 11.2 

Inventory Drivers and

Their Impact

Inventory Driver

Impact

Uncertainty in supply or demand

Safety stock, hedge inventory

Mismatch between a downstream partner’s demand and the most

efficient production or shipment volumes for an upstream partner

Cycle stock

Mismatch between downstream demand levels and upstream

production capacity

Smoothing inventory

Mismatch between timing of customer demand and supply

Anticipation inventory

chain lead times

Transportation inventory

image25.jpg

image26.jpg image27.jpg 332  PART IV • Planning and Controlling Operations and Supply Chains

Demand uncertainty

The risk of significant and unpredictable fluctuations in downstream demand.

flow of components they need for their internal operations. In assessing supply uncertainty, managers need to answer questions such as these:

· How consistent is the quality of the goods being purchased?

· How reliable are the supplier’s delivery estimates?

· Are the goods subject to unexpected price increases or shortages?

Problems in any of these areas can drive up supply uncertainty, forcing an organization to hold safety stock or hedging inventories.

On the downstream (customer) side, organizations face demand uncertainty, or the risk of significant and unpredictable fluctuations in the demand for their products. For example, many suppliers of automobile components complain that the big automobile manufacturers’ forecasts are unreliable and that order sizes are always changing, often at the last minute. Under such conditions, suppliers are forced to hold extra safety stock to meet unexpected jumps in de-mand or changes in order size.

In dealing with uncertainty in supply and demand, the trick is to determine what types of uncertainty can be reduced and then to focus on reducing them. For example, poor quality is a source of supply uncertainty that can be substantially reduced or even eliminated through business process or quality improvement programs, such as those we discussed in Chapters 4 and 5. On the other hand, forecasting may help to reduce demand uncertainty, but it can never completely eliminate it.

Another common inventory driver is the mismatch between demand and the most efficient production or shipment volumes. Let’s start with a simple example—facial tissue. When you blow your nose, how many tissues do you use? Most people would say 1, yet tissues typically come in boxes of 200 or more. Clearly, a mismatch exists between the number of tissues you need at any one time and the number you need to purchase. The reason, of course, is that packaging, shipping, and selling facial tissues one at a time would be highly inefficient, especially because the cost of holding a cycle stock of facial tissues is trivial. On an organizational scale, mismatches between demand and efficient production or shipment volumes are the main drivers of cycle stocks. As we will see later in this chapter, managers can often alter their business processes to reduce produc-tion or shipment volumes, thereby reducing the mismatch with demand and the resulting need for cycle stocks.

Likewise, mismatches between overall demand levels and production capacity can force companies to hold smoothing inventories (Figure 11.5). Of course, managers can reduce smooth-ing inventories by varying their capacity to better match demand or by smoothing demand to better match capacity. As we saw in Chapter 10, both strategies have pros and cons.

The last inventory driver we will discuss is a mismatch between the timing of the cus-tomer’s demand and the supply chain’s lead time. When you go to the grocery store, you expect to find fresh produce ready to buy; your expected waiting time is zero. But produce can come from almost anywhere in the world, depending on the season. To make sure that bananas and lettuce will be ready and waiting for you at your local store, someone has to initiate their move-ment through the supply chain days or even weeks ahead of time and determine how much anticipation inventory to hold. Whenever the customer’s maximum waiting time is shorter than the supply chain’s lead time, companies must have transportation and anticipation inventories to ensure that the product will be available when the customer wants it.

How can businesses reduce the need to hold anticipation inventory? Often they do so both by shrinking their own lead time and by persuading customers to wait longer. It’s hard to be-lieve now, but personal computers once took many weeks to work their way through the supply chain. As a result, manufacturers were forced to hold anticipation inventories to meet customer demand. Today, manufacturers assemble and ship a customized laptop or tablet directly to the customer’s front door in just a few days. Customers get fast and convenient delivery of a prod-uct that meets their exact needs. At the same time, the manufacturer can greatly reduce or even eliminate anticipation inventory.

In the remainder of this chapter, we examine the systems that are used in managing vari-ous types of inventory. Before beginning a detailed discussion of these tools and techniques of inventory management, however, we need to distinguish between two basic inventory catego-ries: independent demand and dependent demand inventory. The distinction between the two is crucial because the tools and techniques needed to manage each are very different.

image28.jpg

Independent demand inventory

Inventory items whose demand­ levels are beyond a company’s complete control.

Dependent demand inventory

Inventory items whose demand­ levels are tied directly­ to a company’s planned production­ of another item.

CHAPTER 11 • Managing Inventory throughout the Supply Chain  333

image29.jpg

Independent versus Dependent Demand Inventory

In general, independent demand inventory refers to inventory items whose demand levels are beyond a company’s complete control. Dependent demand inventory, on the other hand, refers to inventory items whose demand levels are tied directly to the company’s planned production of another item. Because the required quantities and timing of dependent demand inventory items can be predicted with great accuracy, they are under a company’s complete control.

A simple example of an independent demand inventory item is a kitchen table. While a furniture manufacturer may use forecasting models to predict the demand for kitchen tables and may try to use pricing and promotions to manipulate demand, the actual demand for kitchen tables is unpredictable. The fact is that customers determine the demand for these items, so fin-ished tables clearly fit the definition of independent demand inventory.

But what about the components that are used to make the tables, such as legs? Suppose that a manufacturer has decided to produce 500 tables five weeks from now. With this informa-tion, a manager can quickly calculate exactly how many legs will be needed:

500 * 4 legs per table = 2,000 legs

Furthermore, the manager can determine exactly when the legs will be needed, based on the company’s production schedule. Because the timing and quantity of the demand for table legs are completely predictable and under the manager’s total control, the legs fit the definition of dependent demand items. Dependent demand items require an entirely different approach to managing than do independent demand items. We discuss ways of managing dependent demand­ items in more depth in Chapter 12.

Three basic approaches are used to manage independent demand inventory items: periodic­ review systems, continuous review systems, and single-period inventory systems. We examine all three approaches in the following sections.

11.2 Periodic Review Systems

image30.jpg

Periodic review system

An inventory system that is used to manage indepen-dent demand inventory. The inventory level for an item is checked at regular intervals and restocked to some prede-termined level.

One of the simplest approaches to managing independent demand inventory is based on a periodic­ review of inventory levels. In a periodic review system, a company checks the inven-tory level of an item at regular intervals and restocks to some predetermined level, R. The actual order quantity, Q, is the amount required to bring the inventory level back up to R. Stated more formally:

Q = R - I

(11.1)

where:

Q = order quantity

R = restocking level

I = inventory level at the time of review

Figure 11.6 shows the fluctuations in the inventory levels of a single item under a two-week periodic review system. As the downward-sloping line shows, the inventory starts out full and then slowly drains down as units are pulled from it. (Note that the line will be straight only if demand is constant.) After two weeks, the inventory is replenished, and the process begins again.

Figure 11.6

Periodic Review System

R

Restocking level

level

Inventory

Q

Q

2

4

6

8

Weeks

image31.jpg

image32.jpg image33.jpg 334  PART IV • Planning and Controlling Operations and Supply Chains

A periodic review system nicely illustrates the use of both cycle stock and safety stock. By replenishing inventory every two weeks, rather than daily or even hourly, the organization spreads the cyclical cost of restocking across more units. And the need to hold safety stock helps to determine the restocking level. Increasing the restocking level effectively increases safety stock: The higher the level, the less likely the organization is to run out of inventory before the next replenishment period. On the flip side, because inventory is checked only at regular inter-vals, the company could run out of an item before the inventory is replenished. In fact, that is exactly what happens just before week 6 in Figure 11.6. If you have ever visited your favorite vending machine, only to find that the item you wanted has been sold out, you have been the victim of a periodic review system stockout.

As you might imagine, a periodic review system is best suited to items for which periodic restocking is economical and the cost of a high restocking level (and hence a large safety stock) is not prohibitive. A classic example is a snack food display at a grocery store. Constantly moni-toring inventory levels for low-value items such as pretzels or potato chips makes no economic sense. Rather, a vendor will stop by a store regularly and top off the supply of all the items, usu-ally with more than enough to meet demand until the next replenishment date.

Service level

A term used to indicate the amount of demand to be met under conditions of demand and supply uncertainty.

Restocking Levels

The key question in setting up a periodic review system is determining the restocking level, R.

In general, R should be high enough to meet all but the most extreme demand levels during the reorder period (RP) and the time it takes for the order to come in (L). Specifically:

R = mRP + L + zsRP + L

(11.2)

where:

mRP + L = average demand during the reorder period and the order lead time

sRP + L = standard deviation of demand during the reorder period and the order lead time

· number of standard deviations above the average demand (higher z values increase­ the restocking level, thereby lowering the probability of a stockout)

Equation (11.2) assumes that the demand during the reorder period and the order lead time is normally distributed. By setting R a certain number of standard deviations above the average, a firm can establish a service level, which indicates what percentage of the time inven-tory levels will be high enough to meet demand during the reorder period. For example, setting z = 1.28 would make R large enough to meet expected demand 90% of the time (i.e., provide a 90% service level), while setting z = 2.33 would provide a 99% service level. Different z values and the resulting service levels are listed in the following table. (More values can be derived from the normal curves area table in Appendix I.)

image34.jpg

z Value

Resulting Service Level

1.28

90%

1.65

95

2.33

99

3.08

99.9

image35.jpg

EXAMPLE 11.1

Establishing a Periodic

Review System for

McCreery’s Chips

McCreery’s Chips sells large tins of potato chips at a grocery superstore. Every 10 days, a McCreery’s deliveryperson stops by and checks the inventory level. He then places an order, which is delivered three days later. Average demand during the reorder period and order lead time (13 days total) is 240 tins. The standard deviation of demand during this same time period is 40 tins. The grocery superstore wants enough inventory on hand to meet demand 95% of the time. In other words, the store is willing to take a 5% chance that it will run out of tins before the next order arrives.

image36.jpg image37.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  335

image38.jpg

Using this information, McCreery’s establishes the following restocking level:

R = mRP + L + zsRP + L

= 240 tins + 1.65*40 tins = 306 tins

Suppose the next time the deliveryperson stops by, he counts 45 tins. Based on this information,­ he will order Q = 306 - 45 = 261 tins, which will be delivered in three days.

11.3 Continuous Review Systems

image39.jpg

Continuous review system

An inventory system used to manage independent demand inventory. The inventory

level for an item is constantly ­monitored, and when the ­reorder point is reached, an order is released.

While the periodic review system is straightforward, it is not well suited to managing critical and/or expensive inventory items. A more sophisticated approach is needed for these types of in-ventory. In a continuous review system, the inventory level for an item is constantly monitored, and when the reorder point is reached, an order is released.

A continuous review system has several key features:

1. Inventory levels are monitored constantly, and a replenishment order is issued only when a preestablished reorder point has been reached.

2. The size of a replenishment order is typically based on the trade-off between holding costs and ordering costs.

3. The reorder point is based on both demand and supply considerations, as well as on how much safety stock managers want to hold.

To simplify our discussion of continuous review systems, we will begin by assuming that the variables that underlie the system are constant. Specifically:

1. The inventory item we are interested in has a constant demand per period, d. That is, there is no variability in demand from one period to the next. Demand for the year is D.

2. L is the lead time, or number of periods that must pass before a replenishment order ar-rives. L is also constant.

3. H is the cost of holding a single unit in inventory for a year. It includes the cost of the space needed to store the unit, the cost of potential obsolescence, and the opportunity cost of tying up the organization’s funds in inventory. H is known and fixed.

4. S is the cost of placing an order, regardless of the order quantity. For example, the cost to place an order might be $100, whether the order is for 2 or 2,000 units. S is also known and fixed.

5. P, the price of each unit, is fixed.

Under these assumptions, the fluctuations in the inventory levels for an item will look like those in Figure 11.7. Inventory levels start out at Q, the order quantity, and decrease at a constant rate, d. Because this is a continuous review system, the next order is issued when the reorder point, labeled ROP, is reached. What should the reorder point be? In this simple model, in which the demand rate and lead time are constant, we should reorder when the inventory level reaches the point where there are just enough units left to meet requirements until the next order arrives:

ROP = dL

(11.3)

Figure 11.7

Continuous Review System

(with Constant Demand

Rate d)

For example, if the demand rate is 50 units a week and the lead time is 3 weeks, the manager should place an order when the inventory level drops to 150 units. If everything goes according

level

Q

Slope = –d

Inventory

ROP

L

L

Time

image40.jpg

image41.jpg image42.jpg 336  PART IV • Planning and Controlling Operations and Supply Chains

Figure 11.8

The Effect of Halving the

Order Quantity

Q

level

Inventory

Q'

ROP

Time

image43.jpg

Economic order quantity (EOQ)

The order quantity that minimizes­ annual holding and ordering costs for an item.

to plan, the firm will run out of units just as the next order arrives. Finally, because the inventory

Q level in this model goes from Q to 0 over and over again, the average inventory level is 2 .

image44.jpg

The Economic Order Quantity (EOQ)

How do managers of a continuous review system choose the order quantity (Q)? Is there a “best” order quantity, and if so, how do holding costs (H) and ordering costs (S) affect it? To understand the role of holding and ordering costs in a continuous review system, let’s see what happens if the order quantity is sliced in half, to Q as shown in Figure 11.8. The result: With quantity Q the manager ends up ordering twice as often, which doubles the company’s ordering costs. On the other hand, cutting the order quantity in half also halves the average inventory level, which low-ers holding costs.

The relationship between holding costs and ordering costs can be seen in the following equation:

Total holding and ordering cost for the year = total yearly holding cost

+ total yearly ordering cost

Q

D

= a

bH +

a

bS

(11.4)

2

Q

Yearly holding cost is calculated by taking the average inventory level (Q/2) and multiply-ing it by the per-unit holding cost. Yearly ordering cost is calculated by calculating the number of times we order per year (D/Q) and multiplying this by the fixed ordering cost.

As Equation (11.4) suggests, there is a trade-off between yearly holding costs and ordering costs. Reducing the order quantity, Q, will decrease holding costs, but force the organization to order more often. Conversely, increasing Q will reduce the number of times an order must be placed, but result in higher average inventory levels.

Figure 11.9 shows graphically how yearly holding and ordering costs react as the order quantity, Q, varies. In addition to showing the cost curves for yearly holding costs and yearly ordering­ costs, Figure 11.9 includes a total cost curve that combines these two. If you look closely, you can see that the lowest point on the total cost curve also happens to be where yearly holding costs equal yearly ordering costs.

Figure 11.9 illustrates the economic order quantity (EOQ) , the particular order quantity (Q) that minimizes holding costs and ordering costs for an item. This special order quantity is found by setting yearly holding costs equal to yearly ordering costs and solving for Q:

Q

D

a

bH =

a

bS

2

Q

Q2 =

2DS

H

Q =

2DS

= EOQ

(11.5)

H

where:

Q = order quantity

H = annual holding cost per unit D = annual demand

S = ordering cost

image45.jpg

Figure 11.9

The Relationships among Yearly Holding Costs, Yearly Ordering Costs, and the Order Quantity, Q

EXAMPLE 11.2

Calculating the EOQ at

Boyer’s Department

Store

CHAPTER 11 • Managing Inventory throughout the Supply Chain  337

image46.jpg image47.jpg

Total

Cost

(Q2

(H

(QD

(S

Order quantity (Q)

As Figure 11.9 shows, order quantities that are higher than the EOQ will result in annual holding costs that are higher than ordering costs. Conversely, order quantities that are lower than the EOQ will result in annual ordering costs that are higher than holding costs.

image48.jpg

You are in charge of ordering items for Boyer’s Department Store, located in Seattle. For one of the products Boyer’s carries, the Hudson Valley Model Y ceiling fan, you have the following information:

Annual demand (D) = 4,000 fans a year

Annual holding cost (H) = +15 per fan

Ordering cost (S) = +50 per order

Your predecessor ordered fans four times a year, in quantities (Q) of 1,000. The result-ing annual holding and ordering costs were:

Holding costs for the year + ordering costs for the year

· (1,000 2)+15 + (4,000 1,000)+50

· +7,500 + +200 = +7,700

Because holding costs are much higher than ordering costs, we know that the EOQ must be much lower than 1,000 fans. In fact:

EOQ =

2*4, 000*+50

, which rounds to 163 fans per order

+15

The number 163 seems strange, so let’s check to see if it results in lower annual costs:

Holding costs + ordering costs

· (163 2)+15 + (4,000 163)+50

· +1,222.50 + +1,226.99 = +2,449.49

Notice that holding costs and ordering costs are essentially equal, as we would expect. More important, simply by ordering the right quantity, you could reduce annual holding and ordering costs for this item by

+7,700 - +2,449 = +5,251

Now suppose Boyer’s carries 250 other products with cost and demand structures sim-ilar to that of the Hudson Valley Model Y ceiling fan. In that case, you might be able to save 250*+5,251 = +1,312,750 per year just by ordering the right quantities!

Of course, the EOQ has some limitations. Holding costs (H) and ordering costs (S) cannot always be estimated precisely, so managers may not always be able to calculate the true EOQ. However, as Figure 11.9 suggests, total holding and ordering costs are relatively flat over a wide range around the EOQ. So order quantities can be off a little and still yield total costs that are close to the minimum.

A more valid criticism of the EOQ is that it does not take into account volume discounts, which can be particularly important if suppliers offer steep discounts to encourage customers to order in large quantities. Later in the chapter, we examine how volume discounts affect the order quantity decision.

image49.jpg image50.jpg 338  PART IV • Planning and Controlling Operations and Supply Chains

Other factors that limit the application of the EOQ model include ordering costs that are not always fixed and demand rates that vary throughout the year. However, the EOQ is a good starting point for understanding the impact of order quantities on inventory-related costs.

Table 11.3 

Sample Variations in

Demand­ Rate and Lead Time

Reorder Points and Safety Stock

The EOQ tells managers how much to order but not when to order. We saw in Equation (11.3) that when the demand rate (d) and lead time (L) are constant, the reorder point is easily calculated as:

ROP = dL

But d and L are rarely fixed. Consider the data in Table 11.3, which lists 10 different com-binations of demand rates and lead times. The average demand rate, d, and average lead time, L, are 50 units and 3 weeks, respectively. Our first inclination in this case might be to set the reorder point at d L = 150 units. Yet 5 out of 10 times, dL exceeds 150 units (see Table 11.3). A better ­solution—one that takes into account the variability in demand rate and lead time—is needed.

When either lead time or demand—or both—varies, a better solution is to set the reorder point higher than ROP = dL. Specifically:

ROP =

+ SS

(11.6)

d

L

where:

SS = safety stock

Recall that WolfByte Computers carried a safety stock of 1,000 keyboards (Figure 11.4). Again, safety stock (SS) is an extra amount beyond that needed to meet average demand during lead time. This is added to the reorder point to protect against variability in both demand and lead time. Safety stock raises the reorder point, forcing a company to reorder earlier than usual. In doing so, it helps to ensure that future orders will arrive before the existing inventory runs out.

Figure 11.10 shows how safety stock works when both the demand rate and the lead time vary. We start with an inventory level of Q plus the safety stock (Q + SS). When we reach the new reorder point of d L + SS, an order is released. But look what happens during the first reorder pe-riod: Demand exceeds d L, forcing workers to dip into the safety stock. If the safety stock had not been there, the inventory would have run out. In the second reorder period, even though the lead time is longer than before, demand flattens out so much that workers do not need the safety stock.

image51.jpg image52.jpg image53.jpg

In general, the decision of how much safety stock to hold depends on five factors:

1. The variability of demand;

2. The variability of lead time;

3. The average length of lead time;

4. The desired service level; and

5. The average demand.

Demand Rate (D) in

Lead Time (L),

Demand During

Units Per Week

In Weeks

Lead Time (DL), in Units

60

3

180*

40

4

160*

55

2

110

45

3

135

50

3

150

65

3

195*

35

3

105

55

3

165*

45

4

180*

50

2

100

Average = 50 units

Average = 3 weeks

Average = 148 units

*Demand greater than d L

image54.jpg

image55.jpg

Figure 11.10

The Impact of Varying

Demand­ Rates and Lead

Times

CHAPTER 11 • Managing Inventory throughout the Supply Chain  339

image56.jpg image57.jpg

Q + SS

1st 2nd

reorder reorder

period period

ROP = dL + SS

image58.jpg image59.jpg

SS

Time

Let’s talk about each of these factors. First, the more the demand level and the lead time vary, the more likely it is that inventory will run out. Therefore, higher variability in demand and lead time will tend to force a company to hold more safety stock. Furthermore, a longer av-erage lead time exposes a firm to this variability for a longer period. When lead times are ex-tremely short, as they are in just-in-time (JIT) environments (see Chapter 13), safety stocks can be very small.

The service level is a managerial decision. Service levels are usually expressed in statisti-

cal terms, such as “During the reorder period, we should have stock available 90% of the time.”

While the idea that management might agree to accept even a small percentage of stockouts may

seem strange, in reality, whenever demand or lead time varies, the possibility exists that a firm

will run out of an item, no matter how large the safety stock. The higher the desired service level,

the less willing management is to tolerate a stockout, and the more safety stock is needed.

EXAMPLE 11.3

Let’s look at one approach to calculating the reorder point with safety stock. Like other

Calculating the Reorder

approaches, this one is based on simple statistics. To demonstrate the math, we’ll return

Point and Safety Stock

to Boyer’s Department Store and the Hudson Valley Model Y ceiling fan. Boyer’s sells, on

at Boyer’s Department

average, 16 Hudson Valley Model Y ceiling fans a day (d = 16), with a standard deviation

Store

in daily demand of 3 fans (sd

= 3). This demand information can be estimated easily from

past sales history.

If the store reorders fans directly from the manufacturer, the fans will take, on average,

9 days to arrive (L = 9), with a standard deviation in lead time of 2 days (sL

= 2). The

store manager has decided to maintain a 95% service level. In other words, the manager is

willing to run out of fans only 5% of the time before the next order arrives.

From these numbers, we can see that:

Average demand during the reoder period =

= 144 fans

d

L

Taking the analysis a step further, we can show using basic statistics that:

Standard deviation of demand per period

= sdL

=

sd2 +

2sL2

=

9 * 9 + 256 * 4

(11.7)

L

d

image60.jpg= 33.24

To ensure that Boyer’s meets its desired service level, we need to set the reorder point high enough to meet demand during the reorder period 95% of the time. Put another way, the reorder point (ROP) should be set at the ninety-fifth percentile of demand during the reorder period. Because demand during the reorder period is often normally distributed, basic statistics tells us that:

Reorder point (ROP) = ninety-fifth percentile of demand during the reorder period

· d L + zsdL

· 144 + 1.65*33.24

· 198.8, or 199

image61.jpg image62.jpg 340  PART IV • Planning and Controlling Operations and Supply Chains

image63.jpg

In this equation, 1.65 represents the number of standard deviations (z) above the mean that corresponds to the ninety-fifth percentile of a normally distributed variable. (Other z values and their respective service levels are shown in Table 11.4.) The more gen-eral formula for calculating the reorder point is, therefore:

ROP =

+ z

sd2 +

2sL2

(11.8)

d

L

L

d

where:

d = average demand per time period

L = average lead time

sd2

= variance of demand per time period

sL2

= variance of lead time

z = number of standard deviations above the average demand during lead time (higher z values lower the probability of a stockout)

Table 11.4  z Values Used in Calculating

Safety Stock

z Value

Associated Service Level

0.84

80%

1.28

90%

1.65

95%

2.33

99%

Notice that the first part of the equation, d L, covers only the average demand during the reorder period. The second part of the equation, z Ls2d + d2s2L, represents the safety stock. For Boyer’s, then, the amount of safety stock needed is:

z Ls2d + d2s2L = 1.65*33.24 = 54.88, or 55 fans

Of course, there are other methods for determining safety stock. Some managers consider variations in both the lead time and the demand rate; others use a definition of service level that includes the frequency of reordering. (Firms that reorder less often than others are less susceptible to stockouts.) In practice, many firms take an unscientific approach to safety stock, such as setting the reorder point equal to 150% of expected demand. Whatever the method used, however, these observations will still hold: The amount of safety stock needed will be affected by the variability of demand and lead time, the length of the average lead time, and the desired service level.

Quantity Discounts

In describing the economic order quantity, one of our assumptions was that the price per unit, P, was fixed. This was a convenient assumption because it allowed us to focus on minimizing just the total holding and ordering costs for the year (Equation [11.3]). But what if a supplier offers a price discount for ordering larger quantities? How will this affect the EOQ?

When quantity discounts are in effect, we must modify our analysis to look at total order-ing, holding, and item costs for the year:

Total holding, ordering, and item costs for the year =

a

Q

D

bH +

a Q bS + DP

(11.9)

2

where:

Q = order quantity

H = holding cost per unit

D = annual demand

P = price per unit (which can now vary)

S = ordering cost

image64.jpg

eXaMPle 11.4

volume discounts at hal’s Magic Shop

Chapter 11 • Managing inventory throughout the Supply Chain 341

image65.jpg

Because the EOQ formula (Equation [11.5]) considers only holding and ordering costs, the EOQ may not result in lowest total costs when quantity discounts are in effect. To illustrate, sup-pose we have the following information:

D = 1,200 units per year H = +10 per unit per year S = +30 per order

P = +35 per unit for orders less than 90; $32.50 for orders of 90 or more

If we ignore the price discounts and calculate the EOQ, we get the following:

EOQ =

2*1,200*+30

, which rounds to 85 units

+10

Total annual holding, ordering, and item costs for an order quantity of 85 are: a 852 b+10 + a 1,20085 b +30 + +35x1200

image66.jpg image67.jpg

· +425 + +423.53 + +42,000

· +42,848.53

But note that if we increase the order size by just 5 units, to 90, we can get a discount of

+35 - +32.50 = +2.50 per unit. Selecting an order quantity of 90 would give us the following annual holding, ordering, and item costs:

a 902 b +10 + a 1,20090 b +30 + +32.50x1200

image68.jpg image69.jpg

· +450 + +400 + +39,000

· +39,850.00

When volume price discounts are in effect, we must follow a two-step process:

1. Calculate the EOQ. If the EOQ number represents a quantity that can be purchased for the lowest price, stop—we have found the lowest cost order quantity. Otherwise, we go to step 2.

2. Compare total holding, ordering, and item costs at the EOQ quantity with total costs at each price break above the EOQ. There is no reason to look at quantities below the EOQ, as these would result in higher holding and ordering costs, as well as higher item costs.

image70.jpg

image3Robert Landau/Alamy

image71.jpg image72.jpg 342  PART IV • Planning and Controlling Operations and Supply Chains

image73.jpg

Hal’s Magic Shop purchases masks from a Taiwanese manufacturer. The manufacturer has quoted the following price breaks to Hal:

Order Quantity

Price Per Mask

1–100

$15

101–200

$12.50

201 or more

$10

Hal sells 1,000 masks a year. The cost to place an order is $20, and the holding cost per mask is about $3 per year. How many masks should Hal order at a time?

Solving for the EOQ, Hal gets the following:

EOQ =

2*1,000*+20

= 115 masks

+3

Unfortunately, Hal cannot order 115 masks and get the lowest price of $10 per mask. Therefore, he compares total holding, ordering, and item costs at Q = 115 masks to those at the next price break, which occurs at 201 masks:

Total annual holding, ordering, and item costs for an order quantity of 115 masks =

a 1152 b +3 + a 1,000115 b +20 + +12.50x1000

· +172.50 + +173.91 + +12,500

· +12,846.41

Total annual holding, ordering, and item costs for an order quantity of 201 masks = a 2012 b +3 + a 1,000201 b +20 + +10.00x1000

· +301.50 + +99.50 + +10,000

· +10,401.00

So even though an order quantity of 115 would minimize holding and ordering costs, the price discount associated with ordering 201 masks more than offsets this. Hal should use an order quantity of 201 masks.

11.4 Single-Period Inventory Systems

image74.jpg

So far, our discussions have assumed that any excess inventory we order can be held for future use. But this is not always true. In some situations, excess inventory has a very limited life and must be discarded, sold at a loss, or even hauled away at additional cost if not sold in the period intended. Examples include fresh fish, magazines and newspapers, and Christmas trees. In other cases, inventory might have such a specialized purpose (such as spare parts for a specialized ma-chine) that any unused units cannot be used elsewhere. When such conditions apply, a company must weigh the cost of being short against the cost of having excess units, where:

Shortage cost = CShortage = value of the item if demanded - item cost

(11.10)

Excess cost = CExcess = item cost + disposal cost - salvage value

(11.11)

For example, say that an item that costs $50 sells for $200, but must be disposed of at a cost of $5 if not sold. This item has the following shortage and excess costs:

CShortage = +200 - +50 = +150

CExcess = +50 + +5 = +55

image75.jpg

Single-period inventory system

A system used when demand occurs in only a single point in time.

Target service level

For a single-period inventory system, the service level at which the expected cost of a shortage equals the expected cost of having excess units.

Target stocking point

For a single-period inventory system, the stocking point at which the expected cost of a shortage equals the expected cost of having excess units.

CHAPTER 11 • Managing Inventory throughout the Supply Chain  343

image76.jpg

The goal of a single-period inventory system is to establish a stocking level that strikes the best balance between expected shortage costs and expected excess costs. Developing a single-period system for an item is a two-step process:

1. Determine a target service level (SLT) that strikes the best balance between shortage costs and excess costs.

2. Use the target service level to determine the target stocking point (TS) for the item.

We describe each of these steps in more detail in the following sections.

Target Service Level

For the single-period inventory system, service level is simply the probability that there are enough units to meet demand. Unlike a periodic and continuous review system, there is no re-order period to consider here—either there is enough inventory or there isn’t. The target service level, then, is the service level at which the expected cost of a shortage equals the expected cost of having excess units:

Expected shortage cost = expected excess cost

or:

(1 - p)CShortage = pCExcess

(11.12)

where:

p = probability that there are enough units to meet demand

(1 - p) = probability that there is a shortage

CShortage = shortage cost

CExcess = excess cost

The target service level (SLT) is the p value at which Equation (11.12) holds true:

(1 - SLT)CShortage = SLTCExcess

SLT =

CShortage

(11.13)

CShortage + CExcess

where:

CShortage = shortage cost CExcess = excess cost

Let’s use Equation (11.13) to test our intuition. Suppose the shortage cost and the excess cost for an item are both $10. In this case, we would be indifferent to either outcome, and we would set the inventory level so that each outcome would be equally likely. Equation (11.13) confirms our logic:

SLT =

CShortage

+10

= 0.50, or 50%

=

CShortage + CExcess

+10 + +10

But what if the cost associated with a shortage is much higher—say, $90? In this case, we

would want a much higher target service level because shortage costs are so much more severe

than excess costs. Again, Equation (11.13) supports our reasoning:

CShortage

+90

= 0.9, or 90%

=

CShortage + CExcess

+90 + +10

image77.jpg

EXAMPLE 11.5

Don Washing is trying to determine how many gallons of lemonade to make each day. Don

Determining the Target

needs to consider a single-period system because whatever lemonade is left over at the end

Service Level at Don’s

of the day must be thrown away due to health concerns. Every gallon he mixes costs him

Lemonade Stands

$2.50 but will generate $10 in revenue if sold.

image78.jpg image79.jpg 344  PART IV • Planning and Controlling Operations and Supply Chains

image80.jpg

In terms of the single-period inventory problem, Dan’s shortage and excess costs are defined as follows:

CShortage = revenue per gallon - cost per gallon = +10.00 - +2.50 = +7.50

CExcess = cost per gallon = +2.50

From this information, Don can calculate his target service level:

SLT =

CShortage

=

+7.50

= 0.75, or 75%

CShortage + CExcess

+7.50 + +2.50

Interpreting the results, Don should make enough lemonade to meet all demand ap-proximately 75% of the time.

image81.jpg

EXAMPLE 11.6

Every day, Fran Chapman of Fran’s Flowers makes floral arrangements for sale at the local

Determining the Target

hospital. The arrangements cost her approximately $12 to make, but they sell for $25. Any

Service Level at Fran’s

leftover arrangements can be sold at a heavily discounted price of $5 the following day.

Flowers

Fran wants to know what her target service level should be.

Fran’s shortage and excess costs are as follows:

CShortage

= revenue per arrangement - cost per arrangement = +25 - +12 = +13

CExcess

= cost per arrangement - salvage value = +12 - +5 = +7

Fran’s target service level is, therefore:

SLT =

CShortage

+13

= 0.65, or 65%

=

CShortage + CExcess

+13 + +7

Fran should make enough arrangements to meet all demand approximately 65% of

the time.

Target Stocking Point

To complete the development of a single-period inventory system, we next have to translate the target service level (a probability) into a target stocking point. To do so, we have to know some-thing about how demand is distributed. Depending on the situation, we can approximate the demand distribution from historical records, or we can use a theoretical distribution, such as the normal distribution or Poisson distribution. Furthermore, the distribution may be continuous

(i.e., demand can take on fractional values) or discrete (i.e., demand can take on only integer values). Example 11.7 shows how the process works when we can model demand by using the normal distribution, while Example 11.8 demonstrates the process for a historically based dis-crete distribution.

image82.jpg

EXAMPLE 11.7

In Example 11.5, Don Washing determined that the target service level for lemonade was:

Determining the Target

CShortage

+7.50

Stocking Point for

=

= 0.75, or 75%

Normally Distributed

CShortage + CExcess

+7.50 + +2.50

Demand

Don knows from past experience that the daily demand follows a normal distribution.

Therefore, Don wants to set a target stocking point (TS) that is higher than approximately

75% of the area under the normal curve. Figure 11.11 illustrates the idea.

image83.jpg image84.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  345

image85.jpg

75%

TS

Figure 11.11  Target Stocking Point for Don’s Lemonade Stands

The general formula for calculating the target stocking point when demand is nor-mally distributed is:

Target stocking point (normally distributed demand) = m + zSLT*s (11.14)

where:

m = mean demand per time period

SLT = number of standard deviations above the mean required to meet the target service level

s = standard deviation of demand per period

To further complicate things, Don also knows that the mean values and standard de-viations for demand differ by day of the week (Table 11.5) . Therefore, he will have to cal-culate different target stocking points for Monday through Friday, Saturday, and Sunday.

Table 11.5  Demand Values for Don’s Lemonade Stands

Day of the Week

Mean Demand, M

Standard Deviation of Demand, S

Monday–Friday

422 gallons

67 gallons

Saturday

719 gallons

113 gallons

Sunday

528 gallons

85 gallons

Using Equation (11.14) and the cumulative normal table (Table I.2 in Appendix I), Don quickly determines that a service level of 75% would require the target stocking point to be approximately 0.68 standard deviations above the mean. Therefore, the target stock-ing points are as follows:

m + zSLT*s

Monday–Friday: 422 + 0.68*67 = 467.56 gallons

Saturday: 719 + 0.68*113 = 795.84 gallons

Sunday: 528 + 0.68*85 = 585.8 gallons

image86.jpg

EXAMPLE 11.8

Determining the Target

Stocking Point for Non-

Normally Distributed

Demand

In Example 11.6, Fran Chapman calculated her target service level for floral arrangements:

CShortage

=

+13

= 0.65, or 65%

CShortage + CExcess

+13 + +7

Fran has kept track of arrangement sales for the past 34 days and has recorded the de-mand numbers shown in Table 11.6.

image87.jpg image88.jpg 346  PART IV • Planning and Controlling Operations and Supply Chains

image89.jpg

Table 11.6  Demand History for Fran’s Flowers

No. of Days With

Percentage of Days

This Demand Level

Experiencing This

Cumulative

Daily Demand

During the Past 34 Days

Demand Level

Percentage

10 or fewer

0

0 34 = 0%

0%

11

2

2

34

= 5.9%

5.9%

12

5

5

34

= 14.7%

20.6%

13

5

5

34

= 14.7%

35.3%

14

6

6

34

= 17.6%

52.9%

15

7

7

34

= 20.6%

73.5%

16

5

5

34

= 14.7%

88.2%

17

3

3

34

= 8.8%

97.0%

18

1

1

34

= 2.9%

100%

19 or more

0

0%

100%

Looking at Table 11.6, Fran realizes that if she wants to meet her target service level of 65%, she will need to stock 15 arrangements each day. This is because 15 arrangements is the first stocking point at which the probability of meeting expected demand (73.5%) is greater than the target service level of 65%. Conversely, if Fran stocked just 14 arrange-ments, according to Table 11.6, she would meet demand only 52.9% of the time.

11.5 Inventory in the Supply Chain

image90.jpg

So far, we have discussed the functions and drivers of inventory, and we have identified some basic techniques for managing independent demand inventory items. In this section, we broaden our scope to consider the ramifications of inventory decisions for the rest of the supply chain.

Bullwhip effect

According to APICS, “an extreme­ change in the supply position upstream in a supply chain generated by a small change in demand down-stream in the supply chain.”

The Bullwhip Effect

A major limitation of the EOQ model is that it considers the impact on costs for only a single firm. No consideration is given to how order quantity decisions for one firm affect other mem-bers of the supply chain. Therefore, even though the EOQ minimizes costs for a particular firm, it can cause problems for other partners and may actually increase overall supply chain costs. An example of this is the bullwhip effect.5 APICS defines the bullwhip effect as “an extreme change in the supply position upstream in a supply chain generated by a small change in demand down-stream in the supply chain.”6

To illustrate, suppose the ABC plant makes pool cleaners that are sold through six dis-tributors. The distributors have similar demand patterns and identical EOQ and ROP quantities:

Average weekly demand for each distributor = 500 pool cleaners (standard deviation = 100) Reorder quantity for each distributor = 1,500

Reorder point for each distributor = 750

Figure 11.12 shows the results of a simulation covering 50 weeks of simulated demand across the six distributors. Even though total weekly demand across the six distributors ranged from 2,331 to 3,641, the quantities ordered by the distributors to be shipped from the plant ranged from 0 to 7,500 in any one week.

image91.jpg

5Hau L. Lee, V. Padmanabhan, and S. Whang, “The Bullwhip Effect in Supply Chain,” Sloan Management Review 38, no. 3 (Spring 1997): 70–77.

6Definition of Bullwhip Effect in J. H. Blackstone, ed., APICS Dictionary, 14th ed. (Chicago, IL: APICS, 2013). Reprinted by permission.

image92.jpg

Figure 11.12

Total Demand across the Six Distributors

Resulting Total Quantities

(Q =  1,500 for Each

­Distributor) Ordered from

the ABC Plant

CHAPTER 11 • Managing Inventory throughout the Supply Chain 

347

4,000

3,500

3,000

Demand

2,500

2,000

1,500

1,000

500

0

1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Week

quantity

8,000

6,000

order

4,000

Total

2,000

0

1

4

7

10

13

16

19

22

25

28

31

34

37

40

43

46

49

Week

image93.jpg image94.jpg image95.jpg

Figure 11.13

Resulting Total Quantities

(Q =  750 for Each

­Distributor) Ordered from

the ABC Plant

What causes this? Quite simply, if a distributor reaches its reorder point, it places a large order. Otherwise, it does nothing. Therefore, a single-unit change in demand may de-termine whether a distributor places an order. So even though the distributors may be fol-lowing good inventory practice by ordering in quantities of 1,500, the impact on the supply chain is to increase demand variability at the plant. Ultimately, this demand variability will drive up costs at the plant, which will then be forced to pass on at least some of these costs to the distributors.

In order to reduce the bullwhip effect, many supply chain partners are working together to reduce order quantities by removing volume discount incentives and reducing ordering costs. Figure 11.13 shows, for example, what the quantities ordered from the plant would look like if order quantities were cut in half, to 750. Now the orders range from 750 to 4,500; this is not per-fect, but it’s a big improvement over what the range was before.

Inventory Positioning

Managers must decide where in the supply chain to hold inventory. In general, the decision about where to position inventory is based on two general truths:

1. The cost and value of inventory increase as materials move down the supply chain.

2. The flexibility of inventory decreases as materials move down the supply chain.

That is, as materials work their way through the supply chain, they are transformed, pack-aged, and moved closer to their final destination. All these activities add both cost and value.

quantity

5,000

4,000

3,000

order

2,000

Total

1,000

0

1

4

7

10

13

16

19

22

25

28

31

34

37

40

43

46

49

Week

image96.jpg

image97.jpg image98.jpg 348  PART IV • Planning and Controlling Operations and Supply Chains

Take breakfast cereal, for example. By the time it reaches the stores, cereal has gone through such a significant transformation and repackaging that it appears to have little in common with the basic materials that went into it. But the value added goes beyond transformation and pack-aging; it includes location as well. A product that is in stock and available immediately is always worth more to the customer than the same product available later.

What keeps organizations from pushing inventory as far down the supply chain as pos-sible? Cost, for one thing. By delaying the transformation and movement of materials, orga-nizations can postpone the related costs. Another reason for holding inventory back in the supply chain is flexibility. Once materials have been transformed, packaged, and transported down the chain, reversing the process becomes very difficult, if not impossible. Wheat that has been used to make a breakfast cereal cannot be changed into flour that is suitable for making a cake. Likewise, repackaging shampoo into a different-sized container is impractical once it has been bottled. The same goes for transportation: Repositioning goods from one location to an-other can be quite expensive, especially compared to the cost of delaying their movement until ­demand has become more certain. This loss of flexibility is a major reason materials are often held back in the supply chain. In short, supply chain managers are constantly trying to strike a balance between costs on the one hand and flexibility on the other in deciding where to posi-tion inventory.

image99.jpg

EXAMPLE 11.9

An especially good case for holding back inventory can be made if an organization can

Pooling Safety Stock at

hold all of its safety stock in a single central location while still providing reasonably fast

Boyer’s Department Store

service to customers. This is one example of inventory pooling, in which several locations

Inventory pooling

share safety stock inventories in order to lower overall holding costs. Suppose, for instance,

that Boyer’s has eight stores in the Chicago area. Each store sells, on average, 10 ceiling

Holding safety stock in a single

fans a day. Suppose that the standard deviation of daily demand at each store is 3 (sd = 3)

location instead of multiple lo-

and the average lead time from the fan manufacturer is 9 days, with a standard deviation

cations. Several locations then

share safety stock inventories

of 2 days. We showed in Example 11.3 that to maintain a 95% service level (z = 1.65), a

to lower overall holding costs

store would need to maintain a safety stock of 55 fans. The total safety stock across all eight

by reducing overall safety stock

stores would therefore be 8*55 = 440 fans.

levels.

But what if Boyer’s could pool the safety stock for all eight stores at a single store,

which could provide same-day service to the other seven stores? Because a single location

would have a demand variance equal to n times that of n individual stores:

Standard deviation of demand during lead time, across n locations = n*sdL

For Boyer’s, this calculates out to:

=

8*

*sd2 +

2*sL2

L

d

=

8*33.24

= 94 fans

And the pooled safety stock would be:

z*94 = 1.65*94 = 155.1, or 155 fans

By pooling its safety stock, Boyer’s could reduce the safety stock level by (440 - 155) = 285 fans, or 65%. Considering the thousands of items stocked in Boyer’s eight stores, centralizing Boyer’s safety stock could produce significant savings.

Transportation, Packaging, and Material Handling Considerations

We will wrap up our discussion of inventory in the supply chain by considering how inventory decisions—most notably, order quantities—are intertwined with transportation, packaging, and material handling issues. The point of this discussion is to recognize that, in the real world, there is more to determining order quantities than just holding, ordering, and item costs.

image100.jpg image101.jpg Chapter 11 • Managing inventory throughout the Supply Chain 349

image102.jpg

SupplY Chain ConneCtIons

inventOrY ManageMent anD pOOling grOupS at autOMOtive DealerShipS

Evans/AlamyBalfour

Greg

Automobile dealerships face a classic dilemma in deciding how to manage their inventories of service parts. On the one hand, customers expect their cars to be fixed promptly. On the other hand, dealerships

typically do not have the space or financial resources to stock all the possible items a customer’s car may need. If this wasn’t difficult enough, most dealerships do not have the inventory expertise on site to deal with these issues.

To address these concerns, many automotive manufacturers have developed information systems in which the manufacturer makes inventory decisions for dealerships, based on calculated reorder points. Of course, the dealerships may override these recommen-dations if they like. And if a part placed in the dealer-ship under the recommendation of the system sits at the dealership too long, the manufacturer will typically buy it back.

In addition, dealerships in the same geographic region typically establish “pooling groups.” These deal-erships agree to share safety stocks for expensive or slow- moving items. If one dealership runs out of the part, it can instantly check on the part’s availability within the pooling group (via an information system) and arrange to have the item picked up. The result is lower overall inventories and better parts availability for customers.

Consider an example. Borfax Industries buys specialized chemicals from a key supplier. These chemicals can be purchased in one of two forms:

DiMenSiOnalitY

fOrM

QuantitY

Weight

(WiDth/Depth/height)

priCe per Bag

Carton

144 bags

218 lb.

2 * 2 * 1

$25

pallet

12 cartons (1,728 bags)

2,626 lb.

4 * 4 * 3.5

$18

First, notice that the chemicals can be purchased in multiples of 144 bags per carton or 1,728 bags per pallet. It is highly unlikely that any EOQ value calculated by Borfax will fit per-fectly into either of these packaging alternatives.

If Borfax purchases a full pallet, it can get a substantial price discount. The supplier will also make a direct truck shipment if Borfax purchases five or more pallets at a time. This will reduce the lead time from 15 days to 5. However, pallets require material handling equipment capable of carrying nearly 3,000 pounds, as well as suitable storage space. On the other hand, the cartons are less bulky but will still require some specialized handling due to their weight. In choosing the best order quantity, Borfax must not only look at the per-bag price but also con-sider its material handling capabilities, transportation costs, and inventory holding costs.

chaPter SuMMary

image103.jpg

Inventory is an important resource in supply chains, serving many functions and taking many forms. But like any other resource, it must be managed well if an organization is to remain competi-tive. We started this chapter by examining the various types of inventory in a simple supply chain. We also discussed what drives inventory. To the extent that organizations can leverage inventory drivers, they can bring down the amount of inventory they need to hold in order to run their supply chains smoothly.

In the second part of this chapter, we introduced some basic tools for managing independent demand inventory. These tools provide managers with simple models for determin-ing how much to order and when to order. We then examined the relationship between inventory decisions and the bullwhip effect, the decision about where to position inventory in the supply chain, and how transportation, packaging, and material handling considerations might impact inventory decisions.

image104.jpg image105.jpg 350  PART IV • Planning and Controlling Operations and Supply Chains

Key Formulas

image106.jpg

Restocking level under a periodic review system (page 334):

R = mRP + L + zsRP + L

(11.2)

where:

= average demand during the reorder period and the order lead time

mRP + L

sRP + L

= standard deviation of demand during the reorder period and the order lead time

z = number of standard deviations above the average demand (higher z values increase the restocking level, thereby lowering the probability of a stockout)

Total holding and ordering costs for the year (page 336):

aQ2 bH + aDQ bS

image107.jpg

where:

Q = order quantity

H = annual holding cost per unit D = annual demand

S = ordering cost

Economic order quantity (EOQ) (page 336):

(11.4)

Q =

where:

Q = order quantity

H = annual holding cost per unit D = annual demand

S = ordering cost

2DS = EOQ

image108.jpg H

(11.5)

Reorder point under a continuous review system (page 340):

ROP =

+ z

sd2 +

2sL2

(11.8)

d

L

L

d

where:

d = average demand per time period

L = average lead time

sd2

= variance of demand per time period

sL2

= variance of lead time

z = number of standard deviations above the average demand during lead time (higher z values lower the probability of a stockout)

Total holding, ordering, and item costs for the year (page 340):

a Q2 bH + aDQ bS + DP

image109.jpg

where:

Q = order quantity

H = holding cost per unit D = annual demand

P = price per unit S = ordering cost

Target service level under a single-period inventory system (page 343):

CShortage

SLT = CShortage + CExcess

image110.jpg

where:

CShortage = shortage cost CExcess = excess cost

(11.9)

(11.13)

image111.jpg image112.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  351

Key Terms

image113.jpg

Anticipation inventory  330

Hedge inventory 

330

Service level  334

Bullwhip effect  346

Independent demand inventory  333

Single-period inventory system  343

Continuous review system  335

Inventory  328

Smoothing inventory 

330

Cycle stock  329

Inventory drivers 

331

Supply uncertainty 

331

Demand uncertainty  332

Inventory pooling 

348

Target service level 

343

Dependent demand inventory  333

Periodic review system  333

Target stocking point 

343

Economic order quantity (EOQ) 336

Safety stock  329

Transportation inventory  330

Using Excel in Inventory Management

image114.jpg

Several of the models described in this chapter depend on estimates of average demand and average lead time and on associated measures of variance (s2) or standard deviation (s). The spreadsheet model in Figure 11.14 shows how such values can be quickly estimated from historical data, using Microsoft Excel’s built-in functions. The spreadsheet contains historical

demand data for 20 weeks, as well as lead time information for 15 prior orders. From this information, the spreadsheet calcu-lates average values and variances and then uses these values to calculate average demand during lead time, safety stock, and the reorder point. The highlighted cells represent the input values. The calculated cells are as follows:

image115.jpg

Cell C32 (average weekly demand):

= AVERAGE(C12:C31)

Cell C33 (variance of weekly demand):

= VAR(C12:C31)

Cell G27 (average order lead time):

= AVERAGE(G12:G26)

Cell G28 (variance of lead time):

= VAR(G12:G26)

Cell F5 (average demand during lead time):

= C32*G27

Cell F6 (safety stock):

= F3*SQrt(g27*C33 +C32^2*g28)

Cell F7 (reorder point):

= F5+F6

A

B

C

D

E

F

G

H

I

1

Calculating the Reorder Point from Demand and Order History

2

3

z value (for desired service level:)

1.65

4

5

280.72

units

Average demand during lead time:

6

+ Safety stock:

125.47

units

7

Reorder point:

406.19

units

(Equation 10

-6)

8

9

***

Demand History

***

*** Order History

***

10

Lead time

11

Week

Demand

Order

(days)

12

1

33

1

10

13

2

14

2

6

14

3

18

3

12

15

4

37

4

9

16

5

34

5

10

17

6

53

6

8

18

7

31

7

8

19

8

21

8

8

20

9

19

9

7

21

10

44

10

3

22

11

43

11

8

23

12

37

12

9

24

13

45

13

7

25

14

43

14

8

26

15

36

15

8

27

16

40

Average:

8.07

28

17

28

Variance:

4.07

29

18

41

30

19

36

31

20

43

32

Average:

34.80

33

Variance:

106.27

image116.jpg

Figure 11.14 Excel Solution to the Reorder Point Problem

image117.jpg image118.jpg 352  PART IV • Planning and Controlling Operations and Supply Chains

Solved Problems

image119.jpg

P r o b l e m 1

P r o b l e m 2

Jake Fleming sells graphic card update kits for computers. Jake purchases these kits for $20 and sells about 250 kits a year. Each time Jake places an order, it costs him $25 to cover shipping and paperwork. Jake figures that the cost of holding an update kit in inventory is about $3.50 per kit per year. What is the economic order quantity? How many times per year will Jake place an order? How much will it cost Jake to order and hold these kits each year?

Solution

The economic order quantity for the kits is:

2*250*+25 = 59.76, or 60 kits +3.50

The number of orders placed per year is:

25060 = 4.17 orders per year

The total holding and ordering costs for the year (not counting any safety stock Jake might hold) are:

602+3.50 + 25060+25 = +105 + +104.17 = +209.17

The manufacturer of the graphic card update kits has agreed to charge Jake just $15 per kit if Jake orders 250 kits at a time. Should Jake accept the manufacturer’s offer?

Solution

For the EOQ, the total holding, ordering, and item costs for the year are:

60

+3.50 +

250

+25 =

250*+20 =

+105 + +104.17 + +5,000 = +5,209.17

2

60

If Jake takes the volume discount, he will order 250 kits at a time (after all, ordering more than 250 would only move him farther away from the EOQ, which minimizes holding and or-dering costs):

2502+3.50 + 250250+25 + 250*+15 = +437.50 + +25 + +3,750 = +4,212.50 Therefore, Jake should take the volume discount and order just once a year.

Discussion Questions

image120.jpg

1. You hear someone comment that any inventory is a sign of waste. Do you agree or disagree? Can managers simulta-neously justify holding inventories and still seek out ways to lower inventory levels?

2. In your own words, what is an inventory driver? What is the difference between a controllable inventory driver and an uncontrollable inventory driver? Give examples.

3. Which of the following are independent demand inven-tory items? Dependent demand inventory items?

a. Bicycles in a toy store

b. Bicycle wheels in a bicycle factory

c. Blood at a blood bank

d. Hamburgers at a fast-food restaurant

e. Hamburger buns at a plant that produces frozen dinners

4. In a supply chain, what are the pros and cons of pushing inventory downstream, closer to the final customer? How might modular product designs (Chapter 15) make it

more profitable for companies to postpone the movement of inventory down the supply chain?

5. (Use the EOQ and ROP formulas to answer this question.) Which variables could you change if you wanted to reduce inventory costs in your organization? Which ones would you prefer to change? Why?

6. The JIT/lean production movement has long argued that firms should:

a. Maximize their process flexibility so that ordering costs are minimized;

b. Stabilize demand levels;

c. Shrink lead times as much as possible; and

d. Assign much higher holding costs to inventory than has traditionally been the case.

Using the EOQ and ROP formulas, explain how such efforts would be consistent with JIT’s push for lower inventory levels.

image121.jpg image122.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  353

Problems

image123.jpg

(* = easy; ** = moderate; *** = advanced)

Problems for Section 11.2: Periodic Review Systems

1. Jimmy’s Delicatessen sells large tins of Tom Tucker’s Tof-fee. The deli uses a periodic review system, checking in-ventory levels every 10 days, at which time an order is placed for more tins. Order lead time is 3 days. Average daily demand is 7 tins, so average demand during the re-order period and order lead time (13 days) is 91 tins. The standard deviation of demand during this same 13-day ­period is 17 tins.

a. (*) Calculate the restocking level. Assume that the de-sired service level is 90%.

b. (**) Suppose that the standard deviation of demand during the 13-day period drops to 4 tins. What hap-pens to the restocking level? Explain why.

c. (***) Draw a sawtooth diagram similar to the one in Figure 11.3. Assume that the beginning inven-tory level is equal to the restocking level and that the demand rate is a constant 7 tins per day. What is the safety stock level? (Hint: Look at the formula for cal-culating restocking level.) What is the average inven-tory level?

2. Mountain Mouse makes freeze-dried meals for hikers. One of Mountain Mouse’s biggest customers is a sport-ing goods superstore. Every 5 days, Mountain Mouse checks the inventory level at the superstore and places an order to restock the meals. These meals are delivered by UPS in 2 days. Average demand during the reorder period and order lead time is 100 meals, and the stan-dard deviation of demand during this same time period is about 20 meals.

a. (**) Calculate the restocking level for Mountain Mouse. Assume that the superstore wants a 90% service level. What happens to the restocking level if the superstore wants a higher level of service—say, 95%?

b. (*) Suppose there are 20 meals in the superstore when Mountain Mouse checks inventory levels. How many meals should be ordered, assuming a 90% service level?

Problems for Section 11.3: Continuous Review Systems

3. Pam runs a mail-order business for gym equipment. An-nual demand for TricoFlexers is 16,000. The annual hold-ing cost per unit is $2.50, and the cost to place an order is $50.

a. (*) What is the economic order quantity?

b. (**) Suppose demand for TricoFlexers doubles, to 32,000. Does the EOQ also double? Explain what happens.

c. (**) The manufacturer of TricoFlexers has agreed to of-fer Pam a price discount of $5 per unit ($45 rather than $50) if she buys 1,500. Assuming that annual demand is still 16,000, how many units should Pam order at a time?

4. KraftyCity is a large retailer that sells power tools and other hardware supplies. One of its products is the

KraftyMan workbench. Information on the workbench is as follows:

Annual demand = 1,200

Holding cost = +15 per year

Ordering cost = +200 per order

a. (*) What is the economic order quantity for the workbench?

b. (**) Suppose that KraftyCity has to pay $50 per work-bench for orders under 200 but only $42 per workbench for orders of 201 or more. Using the information pro-vided above, what order quantity should KraftyCity use?

c. (*) The lead time for KraftyCity workbenches is 3 weeks, with a standard deviation of 1.2 weeks, and the average weekly demand is 24, with a standard devi-ation of 8 workbenches. What should the reorder point be if KraftyCity wants to provide a 95% service level?

d. (**) Now suppose the supplier of workbenches guar-antees KraftyCity that the lead time will be a constant 3 weeks, with no variability (i.e., standard deviation of lead time = 0). Recalculate the reorder point, using the demand and service level information in problem c. Is the reorder point higher or lower? Explain why.

5. Ollah’s Organic Pet Shop sells about 4,000 bags of free-range dog biscuits every year. The fixed ordering cost is $15, and the cost of holding a bag in inventory for a year is $2.

a. (*) What is the economic order quantity for the biscuits?

b. (**) Suppose Ollah decides to order 200 bags at a time. What would the total ordering and holding costs for the year be? (For this problem, don’t consider safety stock when calculating holding costs.)

c. (**) Average weekly demand for free-range dog biscuits is 80 bags per week, with a standard deviation of 16 bags. Ollah uses a continuous inventory review system to manage inventory of the biscuits. Ollah wants to set the reorder point high enough that there is only a 5% chance of running out before the next order comes in. Assuming that the lead time is a constant 2 weeks, what should the reorder point be?

d. (**) Suppose Ollah decides to use a periodic review system to manage the free-range dog biscuits, with the vendor checking inventory levels every week. Under this scenario, what would the restocking level be, assuming the same demand and lead time characteristics listed in problem 13 and the same 95% service level? (Note that because the standard deviation of weekly demand is 16,

basic statistics tells us the standard deviation of demand over 3 weeks will be 3 * 16 ≈ 28.)

6. Ollah’s Organic Pet Shop sells bags of cedar chips for pet bedding or snacking (buyer’s choice). The supplier has of-fered Ollah the following terms:

Order 1–100 bags, and the price is $6.00 a bag. Order 101 or more bags, and the price is $4.50 a bag.

Annual demand is 630, fixed ordering costs are $9 per order, and the per-bag holding cost is estimated to be around $2 per year.

image124.jpg image125.jpg 354  PART IV • Planning and Controlling Operations and Supply Chains

a. (*) What is the economic order quantity for the bags?

b. (**) What order quantity should Ollah order, based on the volume discount? Is this different from the EOQ? If so, how could this be?

c. (**) Suppose the lead time for bags is a constant 2 weeks, and average weekly demand is 12.6 bags, with a standard deviation of 3.2 bags. If Ollah wants to maintain a 98% service level, what should her reorder point be?

Problems for Section 11.4: Single-Period Inventory Systems

7. (**) David Polston prints up T-shirts to be sold at local con-certs. The T-shirts sell for $20 each but cost David only $6.50 each. However, because the T-shirts have concert-specific in-formation on them, David can sell a leftover shirt for only $3. Suppose the demand for shirts can be approximated with a normal distribution and the mean demand is 120 shirts, with a standard deviation of 35. What is the target service level? How many shirts should David print up for a concert?

8. Sherry Clower is trying to figure out how many custom books to order for her class of 25 students. In the past, the number of students buying books has shown the following demand pattern:

image126.jpg

Number of Students

Percentage of

Who Bought a Book

Observations

16 or fewer

0%

17

4%

18

15%

19

17%

20

18%

21

26%

22

10%

23

6%

24

4%

25

0%

a. (**) Suppose each custom book costs Sherry $12 to print, and she sells the books to the students for $50 each. Excess books must be scrapped. What is the tar-get service level? What is the target stocking point?

b. (**) Suppose printing costs increase to $22. Recalculate the new target service level and target stocking point. What happens?

9. One of the products sold by OfficeMax is a Hewlett-Pack-ard LaserJet Z99 printer. As purchasing manager, you have the following information for the printer:

image127.jpg

Average weekly demand

60 printers

(52 weeks per year)

Standard deviation of weekly

12 printers

demand

Order lead time

3 weeks

Standard deviation of order

0 (lead times are constant)

lead time

Item cost

$120 per printer

Cost to place an order

$2

Yearly holding cost per printer

$48

Desired service level during

99% (z = 2.33)

reordering period

a. (*) What is the economic order quantity for the printer?

b. (**) Calculate annual ordering costs and holding costs (ignoring safety stock) for the EOQ. What do you no-tice about the two?

c. (**) Suppose OfficeMax currently orders 120 printers at a time. How much more or less would OfficeMax pay in holding and ordering costs per year if it ordered just 12 printers at a time? Show your work.

d. (**) What is the reorder point for the printer? How much of the reorder point consists of safety stock?

For parts e and f, use the following formula to consider the impact of safety stock (SS) on average inventory levels and annual holding costs:

aQ2 + SSbH

e. (***) What is the annual cost of holding inventory, in-cluding the safety stock? How much of this cost is due to the safety stock?

f. (***) Suppose OfficeMax is able to cut the lead time to a constant 1 week. What would the new safety stock level be? How much would this reduce annual holding costs?

10. (***) OfficeMax is considering using the Internet to order printers from Hewlett-Packard. The change is expected to make the cost of placing orders drop to almost nothing, although the lead time will remain the same. What effect will this have on the order quantity? On the holding and ordering costs for the year? Explain using any formulas and examples you find helpful.

11. Through its online accessory store, Gateway sells its own products, as well as products made by other companies. One of these products is the WB150 WolfByte laptop computer:

Estimated annual demand

15,376 laptops

(50 weeks per year)

Cost

$640 per laptop

Lead time

2 weeks

Standard deviation of weekly

16 laptops

demand

Standard deviation of lead time

0.3 weeks

Holding cost per unit per

40% of item cost

year

Ordering cost

$25 per order

Desired service level

95% (z = 1.65)

a. (*) What is the economic order quantity for the lap-tops? Calculate annual ordering costs and holding costs (ignoring safety stock) for the EOQ.

b. (**) What is the reorder point for the laptops? How much of the reorder point consists of safety stock?

c. (**) Suppose Gateway decides to order 64 laptops at a time. What would its yearly ordering and holding costs (ignoring safety stock) for the monitor be?

d. (**) Because computer technologies become obsolete so quickly, Gateway is thinking about raising holding costs from 40% of item cost to some higher percentage. What will be the impact on the economic order quan-tity for laptops? Explain why.

image128.jpg image129.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  355

For parts e and f, use the following formula to consider the impact of safety stock (SS) on average inventory levels and annual holding costs:

aQ2 + SSbH

image130.jpg

e. (***) What is the annual cost of holding inventory, in-cluding the safety stock? How much of this cost is due to the safety stock?

f. (***) Suppose Gateway is able to cut the lead time to a constant 1 week. What would the new safety stock level be? How much would this reduce annual holding costs?

12. One of the products stocked by a Sam’s Club store is Sams Cola, which is sold in cases. The demand level for Sams Cola is highly seasonal:

· During the slow season, the demand rate is approxi-mately 650 cases a month, which is the same as a yearly demand rate of 650*12 = 7,800 cases.

· During the busy season, the demand rate is approxi-mately 1,300 cases a month, or 15,600 cases a year.

· The cost to place an order is $5, and the yearly holding cost for a case of Sams Cola is $12.

a. (**) According to the EOQ formula, how many cases of Sams Cola should be ordered at a time during the slow season? How many cases of Sams Cola should be ordered during the busy season?

b. (**) Suppose Sam’s Club decides to use the same or-der quantity, Q = 150, throughout the year. Calculate total holding and ordering costs for the year. Do not consider safety stock in your calculations. (Annual de-mand can be calculated as an average of the slow and busy rates given above.)

13. (**) During the busy season, the store manager has de-cided that 98% of the time, she does not want to run out of Sams Cola before the next order arrives. Use the following data to calculate the reorder point for Sams Cola:

image131.jpg

Weekly demand during the

325 cases per week

busy season

Lead time

0.5 weeks

Standard deviation of

5.25

weekly demand

Standard deviation of lead

0 (lead time is constant)

time

Number of standard

2.05

deviations above the mean

needed to provide a 98%

service level (z)

14. (**) Dave’s Sporting Goods sells Mountain Mouse freeze-dried meals. Dave’s uses a continuous review system to manage meal inventories. Suppose Mountain Mouse offers the following volume discounts to its customers:

1–500 meals: $7 per meal

501 or more meals: $6.50 per meal

Annual demand is 2,000 meals, and the cost to place an order is $15. Suppose the holding cost is $2 per meal per year. How many meals should Dave’s order at a time? What are the total holding, ordering, and item costs asso-ciated with this quantity?

15. (***) (Microsoft Excel problem) The following figure shows an Excel spreadsheet that compares total ordering and holding costs for some current order quantity to the same costs for the EOQ and calculates how much could be saved by switching to the EOQ. Re-create this spreadsheet in Excel. You should develop the spreadsheet so that the re-sults will be recalculated if any of the values in the high-lighted cells are changed. Your formatting does not have to be exactly the same, but the numbers should be. (As a test, see what happens if you just change the annual demand and cost per order to 5,000 and $25, respectively. Your new EOQ should be 91.29, and the total savings under the EOQ should be $5,011.39.)

image132.jpg

A

B

C

D

E

F

1

Calculating Savings under EOQ

2

3

Annual demand:

4,000

4

Annual holding cost, per unit:

$30.00

5

Cost per order:

$30.00

6

7

Current order quantity:

500

8

Current annual holding cost:

$7,500.00

9

Current annual ordering cost:

$240.00

10

Total cost:

$7,740.00

11

12

Economic order quantity:

89.44

13

EOQ annual holding cost:

$1,341.64

14

EOQ annual ordering cost:

$1,341.64

15

Total cost:

$2,683.28

16

17

Total savings under EOQ:

$5,056.72

18

Problems for Section 11.5: Inventory in the Supply Chain

16. (***) (Microsoft Excel problem) The following figure shows an Excel spreadsheet that calculates the benefit of pool-ing safety stock. Specifically, the sheet calculates how much could be saved in annual holding costs if the safety stocks for three locations were held in a single location.

Re-create this spreadsheet in Excel. You should develop the spreadsheet so that the results will be recalculated if any of the values in the highlighted cells are changed. Your formatting does not have to be exactly the same, but the numbers should be. (As a test, see what happens if you change Location 1’s average daily demand and variance of daily demand to 100 and 15, respectively. Your new pooled safety stock should be 30.34, and the total savings due to pooling safety stock should be $108.21.)

image133.jpg image134.jpg 356 part iv • planning and Controlling operationS and Supply ChainS

A

B

C

D

E

F

G

1

Calculating Savings Due to Pooling Safety Stock

2

3

Annual holding cost per unit:

$5.00

4

Lead time ( xed):

8

days

5

z value (for desired service level):

2.33

6

7

Average demand

8

Average

Variance of

Reorder

during

9

daily demand

daily demand

point

lead time

Safety stock

10

Location 1

50

4.5

413.98

400.00

13.98

11

Location 2

40

6.2

336.41

320.00

16.41

12

Location 3

30

5

254.74

240.00

14.74

13

Total units:

45.13

14

Total annual

holding cost:

$225.63

15

16

Average demand

17

Average

Variance of

Reorder

during

18

daily demand

daily demand

point

lead time

Safety stock

19

Pooled SS

120

15.7

986.11

960.00

26.11

20

Total annual holding cost:

$130.56

21

22

Savings due to pooling safety stock:

$95.07

Case stuDy

image135.jpg

northcutt Bikes: the Service Department

image136.jpg

Ievgen Sosnytskyi/Shutterstock

Introduction

Several years ago, Jan Northcutt, owner of Northcutt Bikes, recognized the need to organize a separate department to deal with service parts for the bikes her company makes. Because the competitive strength of her company was developed around customer responsiveness and flexibility, she felt that creating a separate department focused exclusively on aftermarket service was critical in meeting that mission.

When she established the department, she named Ann Hill, one of her best clerical workers at the time, to establish and man-age the department. At first, the department occupied only a cor-ner of the production warehouse, but now it has grown to occupy its own 100,000-square-foot warehouse. The service business has also grown significantly, and it now represents over 15% of the total revenue of Northcutt Bikes. The exclusive mission of the service department is to provide parts (tires, seats, chains, etc.) to the many retail businesses that sell and service Northcutt Bikes.

While Ann has turned out to be a very effective manager (and now holds the title of Director of Aftermarket Service), she still lacks a basic understanding of materials management. To help her develop a more effective materials management program, she hired Mike Alexander, a recent graduate of an outstanding business management program at North Carolina State University, to fill the newly created position of Materials Manager of Aftermarket Service.

The Current Situation

During the interview process, Mike got the impression that there was a lot of opportunity for improvement at Northcutt Bikes. It was only after he selected his starting date and re-quested some information that he started to see the full extent of the challenges that lay ahead. His first day on the job really opened his eyes. One of the first items he had requested was a status report on inventory history and shipped orders. In re-sponse, the following note was on his desk the first day from the warehouse supervisor, Art Demming:

We could not compile the history you requested, as we keep no such records. There’s just too much stuff in here to keep a close eye on it all. Rest assured, however, that we think the inventory positions on file are accurate, as we just completed our physi-cal count of inventory last week. I was able to track down a demand history for a couple of our items, and that is attached to this memo. Welcome to the job!

image137.jpg image138.jpg CHAPTER 11 • Managing Inventory throughout the Supply Chain  357

Mike decided to investigate further. Although the records were indeed difficult to track down and compile, by the end of his second week, he had obtained a fairly good picture of the situation, based on an investigation of 100 parts selected at ran-dom. He learned, for example, that although there was an aver-age of over 70 days’ worth of inventory (annual sales/average inventory), the fill rate for customer orders was less than 80%, meaning that only 80% of the items requested were in inven-tory; the remaining orders were backordered. Unfortunately, the majority of customers viewed service parts as generic and would take their business elsewhere when parts were not avail-able from Northcutt Bikes.

What really hurt was when those businesses sometimes canceled their entire order for parts and placed it with another parts supplier. The obvious conclusion was that while there was plenty of inventory overall, the timing and quantities were misplaced. Increasing the inventory did not appear to be the answer, not only because a large amount was already being held but also because the space in the warehouse (built less than two years ago) had increased from being 45% utilized just after they moved in to its present utilization of over 95%.

Mike decided to start his analysis and development of so-lutions on the two items for which Art had already provided demand history. He felt that if he could analyze and correct any problems with those two parts, he could expand the analysis to most of the others. The two items on which he had history and concentrated his initial analysis were the FB378 Fender Bracket and the GS131 Gear Sprocket. Northcutt Bikes purchases the FB378 from a Brazilian source. The lead time has remained constant, at three weeks, and the estimated cost of a purchase order for these parts is given at $35 per order. Currently North-cutt Bikes uses an order lot size of 120 for the FB378 and buys the items for $5 apiece.

The GS131 part, on the other hand, is a newer prod-uct only recently being offered. A machine shop in Nashville, Tennessee, produces the part for Northcutt Bikes, and it gives Northcutt Bikes a fairly reliable six -week lead time. The cost of placing an order with the machine shop is only about $15, and currently Northcutt Bikes orders 850 parts at a time. Northcutt Bikes buys the item for $10.75.

Following is the demand information that Art gave to Mike on his first day for the FB378 and the GS131: