Smoothing inventory is commonly used when

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 =

2 DS

= 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

( Q 2

(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