William Dillard’s simple maxim1 succinctly captures the central—and perennial—inventory challenge facing retail managers. To make a sale, a retailer must have “on its wagon” the product the customer wants. Absence of an item often translates into a lost sale and reduced revenues and profits. The magnitude of such lost sales for retailers can be significant. For example, in 1994, roughly 25 percent of customers who entered a Macy’s store left without making a purchase because the product they were seeking was not available.2 On the other hand, the retail “wagon” should not be too full, since stocking retail shelves with unpopular items also results in excess costs—the cost of capital tied up in unwanted goods, the opportunity cost of the space that could be used for products that customers would buy if present, and, ultimately, lost margin when retailers must resort to price markdowns or product disposal to clear languishing items from their shelves. The main goal of retail inventory strategy is to maximize profitability by managing the inherent tension between stocking too much and stocking too little. Retail buyers of old grappled with this problem as they do today. But as product variety has increased and product life cycles have shortened, this tension has become increasingly acute, prompting inventory management practices to evolve in recent years to meet rapidly changing market demands. Although a seemingly mundane, tactical aspect of business, a firm’s inventory strategy reflects its approach to managing risk. Indeed, the inventory strategies chosen by firms in a supply channel—and the congruence of those policies across channel partners—have enormous implications for the channel’s speed, flexibility, and profitability. Conceptually, retail inventory management is straightforward enough: Forecast demand for a product; order the product in the appropriate quantity; stock it in the right retail locations; keep track of its sales and the resulting inventory levels; and replenish its store inventories if possible (either from the manufacturer if it offers replenishment services for that product or from the retailer’s central warehouse if the retailer had purchased a large quantity of the product in advance of the selling season). In practice, however, retail inventory management is fraught with challenges, such as long and uncertain order-fulfillment lead times, and errors in product identification and record keeping. Consider, for instance, how many store clerks still scan items incorrectly at the register. A customer may purchase three similar polo shirts in different colors or sizes, but because the price is the same for all, the clerk may simply scan one of them three times—-losing important information about consumer color and/or size preferences. Even without such obvious errors, forecasting demand at the SKU level has become difficult, as an ever wider array of products cycle through stores. Many lean retailing practices are rooted in retailers’ attempts to deal with growing demand uncertainty. In this environment, ordering large quantities of products far in advance of the selling season is simply too costly. Retailers now prefer to place relatively small orders before the season and then observe consumer response to the product offering before ordering more. As we described in Chapter 4, many have transformed their warehouses into modern distribution centers to facilitate the receipt and distribution of these smaller orders. The forecasting and inventory models presented in this chapter are not new; they have been recommended for years by statisticians and operations researchers.3 However, until the 1990s, retailers had neither the data collection and computing capabilities required to execute these models effectively nor the tremendous impetus to implement them that lean retailing has precipitated. Because the effects of lean retailing are sweeping across many industries, it is imperative that everyone involved understand how inventory policies have been affected. This chapter covers the key steps in retail inventory management: forecasting demand, choosing appropriate stocking strategies, and determining order quantities and frequencies. Although few retailers have embraced the complete set of forecasting and inventory models described in this chapter, lean retailers are moving in that direction. The Retail Forecasting Challenge We first turn to the problem of forecasting sales in retail stores. Imagine trying to predict how many women will walk into a particular downtown Boston store next week prepared to pay $48 (full price) for a size-8 pair of Levi blue jeans, with “long” pant length, “loose” fit, stonewashed finish, and a pleated waist—in other words, one particular SKU out of thousands. How will that compare to the number who would buy the same product but with a “short” pant length? How does a retail buyer even begin to approach the problem of making forecasts at such a minute level of detail? The buyer might start by trying to get historical data on the weekly sales of those Levi jeans in the store. But wait—should that be on the sales of those jeans throughout the Greater Boston area? Should the buyer base her prediction on sales of only this particular size and style or would it be more accurate to look at the sales of all jeans in this style and then multiply by the percent of all jean styles sold that were size-8 long? Maybe she should restrict herself to this year’s data to ensure that it is as current as possible. On the other hand, one would hate to lose the information that might be contained in past years’ selling patterns. The complexity of the problem, even for basic blue jeans, is staggering. Now consider the same exercise for a new dress style not previously available at retail—perhaps a style that gained attention when worn by a controversial film star at the most recent Academy Awards ceremony. How many of these dresses will sell this season? Specifically, how many will sell in a dark-peach tone in size 14? If the challenge of making such predictions for this season’s sales is not sufficiently daunting, try predicting how many of each item will sell during a given period next year.The impossibility of making -accurate predictions of demand long in advance of the selling season—especially at the SKU level—is clear. But because products are manufactured and ordered by SKU, some attempt must be made to forecast demand at that level. Most retailers have to make demand forecasts for products in two different categories: existing products for which historical sales data are available and new products with no selling history. The following section discusses the first category and provides general background on the elements of a demand forecast. It is followed by a short discussion of new product forecasting. Forecasting Demand for Products with a Selling History Creating a forecast for a product that the retailer has sold in the past starts with collecting and analyzing historical selling data. Those data provide insight into historical trends and suggest how the product’s sales are related to other factors like weather, holidays, special advertising campaigns, general economic indicators, or simply the passage of time. Air conditioners sell in greater quantities during summer months, for example, neckties just before Father’s Day, and consumer electronics when the economy is booming. Once these relationships are understood, predictions of future sales can be made, although a high level of uncertainty is always involved. Before discussing how one might analyze the trends in historical data, it is important to recognize three often overlooked aspects of demand forecasting. Three Caveats About Forecasting First of all, a product’s selling history is only representative of future sales if the product is sold in a stable environment. For the blue jeans discussed above, the selling environment will remain stable as long as competitors do not introduce competing products that draw from Levi’s demand; fashion preferences do not change; a new, more desirable type of denim is not introduced that customers prefer; and the economy does not dip into a recession. However, even for a basic product like blue jeans, it is unlikely that all these assumptions will hold. Given the volatile nature of demand in many industries, an assumption of stability is suspect, meaning that forecasts based on historical sales data may be less accurate than the historical data suggest. Consequently, lean retailers prefer to forecast demand, set target inventory levels, and place orders on a weekly basis, because the selling environment is much more likely to be stable into the next week than months into the future. Second, most firms gather sales data, not demand data. Customers rarely inform the sales clerk in a typical retail store if a desired product is out of stock; they either buy a different product or leave the store without making a purchase. Direct-mail firms, such as catalog companies and those that sell via television or the Internet, are important exceptions. Because the customer must write, call, or e-mail these retailers with a specific purchase request, these firms are able to capture actual consumer demand rather than sales numbers alone. Such retailers can also gather data about customer demographics, past purchases, and responses to potential substitute items, all of which add up to a gold mine of information about consumer preferences.4 In fact, the value of such data may induce traditional store retailers to offer incentives for customers to share their demand preferences, even when the product is not available in stock. In the mid-1990s, Nordstrom ran newspaper ads promising, for certain products, that if the size or color of an item the customer wished to purchase was not in stock at the store, Nordstrom would locate the desired item and mail it to the customer at no additional cost—both the item and its delivery were free. (Not surprisingly, Nordstrom limited this offer to a small number of basic styles and sizes and to one item per customer.) The only thing a customer had to do was tell a sales clerk what he or she wanted. This approach has benefits on three fronts: the retailer avoids a lost sale and its associated margin; a potentially dissatisfied customer is delighted by the store’s additional service and free product; and last, but certainly not least, for a very small fee—the wholesale cost of the product and shipping fees—Nordstrom gains critical information about consumer demand. Without such programs, retailers may find it difficult to judge how demand is faring after a product stocks out at the retail site and therefore may have trouble making sensible reordering decisions. The third caveat to bear in mind is that a “point forecast” (a single number) alone has relatively low value. If a buyer forecasts that customer demand for size-8 Levi jeans next week in one of its stores will be ten pairs, what does that mean? Will exactly ten pairs sell? Is ten the most likely number to sell—or will at least ten pairs sell? A forecast consisting only of a single number provides no indication of the degree of uncertainty. Indeed, the purpose of the forecasting process is to provide a basis for deciding how many units of a given product should be shipped to a store to minimize the costs—that is, risks—of over- and undersupply. But risk exists precisely because retailers are uncertain about what demand will be for their products. Therefore, to provide a useful basis for making decisions that minimize risk, a forecast should include an explicit assessment of the relative likelihood of different demand levels occurring. Our buyer might capture this information by saying that there is a 90 percent probability that weekly demand for size-8 jeans in the store will fall between two and seventeen units, with an “expected value” of ten units. She might add that there is a 50 percent probability that demand will fall between six and thirteen units. Figure 6.1 shows a demand distribution having these properties. (Note that there is a 95 percent chance that demand will be less than seventeen units next week—thus, if our buyer decides to stock seventeen units at the beginning of the week, the store should be able to offer a 95 percent order fulfillment rate on this SKU.) It is only with such probabilistic forecasts, which explicitly characterize uncertainty, that retailers can make inventory stocking decisions that minimize risk. Four Components of Historical Demand Data With these caveats in mind, let’s assume our store buyer has representative historical demand data for blue jeans for the last few years. She will first analyze the historical data by separating the causes of past changes in demand into the following categories: (1) trend, (2) seasonality, (3) cyclicality, and (4) random fluctuation.5 The trend in demand data describes a medium- to long-term growth or decline. Such trends occur in all industries and can be steadily increasing, steadily decreasing, or varying over time. Seasonality describes within-year trends that are associated with the season of the year and that occur year after year. For example, Figure 6.2 shows weekly demand for men’s dress shirts at a particular retailer: There are seasonal peaks in demand at Father’s Day and Christmas, when many shirts are bought as gifts. Cyclicality in demand describes longer-term, gradual rises and declines that are typically associated with aggregate business activity. For example, demand for new automobiles tends to increase during times of economic prosperity and decrease during recessionary periods. The final component of a demand distribution, random fluctuation, is perhaps the most critical; it is also the most difficult to assess and incorporate into inventory planning. Essentially, random fluctuation in demand cannot be explained by trends, seasonality, cyclicality, or other factors like advertising and new product introduction. Examine Figure 6.2. In addition to the seasonal trend associated with major holidays, random fluctuation in shirt sales occurred from week to week. For our purposes, note that high demand fluctuation decreases one’s ability to forecast demand accurately. Building a Demand Forecast After completing an analysis of how different factors relate to past demand fluctuations, our buyer can draw inferences about what future demand for women’s blue jeans might be in her store next week.6 In this case we assume a stable environment: specifically, that past relationships among variables are representative of future relationships among those variables. Although this may not be a realistic assumption for many situations, it makes it easier to understand the fundamentals of demand forecasting here. Let’s assume that the store’s demand for the size-8 Levi’s jeans last week can be described by the distribution in Figure 6.1. Let’s also assume that the average demand each week has been growing at a rate of about 1 percent, so that the average demand for the next week should be 10*(1.01) = 10.1 units, for the following week about 10*(1.01)2 = 10.2 units, and so on. Then the expected (average) demand is the solid black trend line shown in Figure 6.3. The buyer could incorporate demand uncertainty into the forecast by indicating different possible values of demand, and the likelihood of that actual demand will fall within those values. For example, in Figure 6.3, the lines directly above and below the solid trend line indicate a range of demand for which the likelihood of demand falling within that range is 50 percent. The lines further from the trend line indicate the range with a likelihood of 90 percent. Thus, for week 1, there is a 90 percent probability that demand will be between two units and -seventeen units, exactly as depicted in Figure 6.1. Predicting what -customers will do when they walk into the store will always be challenging, but the buyer can be confident that if she stocks seventeen units at the beginning of the next week, she has a 95 percent probability of meeting all consumer demand on this product. Forecasting Demand for New Products Of course, when a product has just been launched and no historical data exist on which to base a forecast, retailers confront additional challenges. In this case, most companies resort to informal forecasting methods. A common approach is to forecast “by analogy,”using data for similar products that have been on the market previously. One might assume, for example, that sales for this year’s new fashion will be similar to those for last year’s new fashion. This is clearly a subjective call; but once made, it gives retailers a basis for predicting demand patterns for a new product. Obviously, forecasting demand for new products accurately requires a broad understanding of consumer preferences and market trends. Fisher, Hammond, Obermeyer, and Raman have introduced a method that proved successful in predicting demand for new fashion skiwear as part of an “Accurate Response” forecasting and planning approach.7 This approach combined individual forecasts by members of the company’s Buying Committee, creating a probabilistic forecast whose uncertainty was determined by the level of agreement among forecasts made by individual managers. Statistical analysis showed that those garments for which the Buying Committee had the greatest disagreement were indeed those with the greatest demand uncertainty. The skiwear firm has credited the Accurate Response approach with increasing its profits by nearly two-thirds.8 The Impact of Product Variety on Forecast Uncertainty The forecasting challenges retailers confront have been amplified in recent years by product proliferation in almost every category. As a result, demand forecast uncertainty has grown substantially, thereby increasing the level of inventory that must be held to meet customer service requirements. High demand uncertainty, previously associated only with fashion products, is now pervasive, characterizing even those items once regarded as basics—such as power tools, industrial seals, men’s dress shirts, and blue jeans. A good rule of thumb for understanding how product proliferation affects demand uncertainty is that the demand uncertainty for a product category increases as the square root of the number of products in the category (assuming that the total demand for the product category remains unchanged and that the individual items in the category have demand distributions that are statistically independent and identically distributed). A common standardized measure of demand uncertainty, the coefficient of variation (Cv)—defined as the standard deviation of the demand distribution divided by the mean of the demand distribution—for a specific product is proportional to the square root of the number of products offered.9 For example, increasing the number of products offered in a category by a factor of four (say from fifty items to 200) without increasing total demand in the category would increase the coefficient of variation for each individual product by a factor of two. And, as we’ll see in the next section, doubling the demand uncertainty roughly doubles the amount of finished goods required to provide the same level of product availability in the store. Therefore, product variety is costly due to the increased demand uncertainty associated with each unit. Retailers thus must either limit product variety or change their way of doing business so as to minimize the impact of high variety. Lean retailing is the major such change that retailers are adopting to reduce significantly the costs associated with product variety. Setting Inventory Levels in the Store After completing the process of developing a demand forecast for each SKU, a retailer must determine how much of each item to stock on the shelves of its stores. Retailers have an incentive to stock high levels of inventory: They want both to provide sufficient display stock to attract customers—empty shelves are not inviting—and to have products available for those who wish to purchase them. Yet carrying inventory is expensive: Retailers pay capital costs for having their money tied up in inventory, for the physical floor space necessary to store goods, and for handling, managing, and monitoring the inventory.10 Most important, they pay a “risk premium” for carrying products that might become obsolete, either because they are damaged or fall out of fashion. A retailer’s decision about what to stock will depend on a variety of considerations, including the demand forecast for the product, the level of product availability it wishes to provide to customers, the frequency with which it will place replenishment orders, and the lead time to acquire replenishment units. We’ll describe later in this chapter how these factors affect retail inventory policy. A number of other straightforward costs are associated with any inventory stocking policy, such as the cost of ordering and transporting product; the cost of determining inventory levels; and the impact on purchase price of any quantity price discounts. In order to evaluate the performance of different inventory options, it is important to emphasize the less straightforward costs involved. Take the two primary types of inventory “errors” a firm can make: stocking too much of an item the customer does not want and stocking too little of something the customer does want. Although the categories for the costs of mismatched supply and demand are simple in concept, in reality they are difficult to measure accurately. Evaluating forced markdown costs is hard, for example, because one must separate markdowns made for promotional reasons from those made to liquidate stock that cannot be sold at full price. The difficulty of measuring these costs is further exacerbated by the fact that a given product may be attractive to different consumers at different prices, so determining the appropriate “full price” for a product is not an easy task. Stock-out costs are also complex. To determine the magnitude of a stock-out cost for a unit, one must understand consumer behavior. Will the customer buy a substitute item if a particular item is out of stock or return to the same store at a later date to purchase the item when it is again in stock? In these cases, stock-out costs are minimal. But the customer may leave the store because a desired item was not in stock, thereby not purchasing anything else; that means the stock-out cost would equal the margin on all the products the customer would have otherwise purchased. In the most extreme case, a stock-out might cause a customer to switch retailers, costing the lifetime value of that customer and others who might defect due to negative word-of-mouth. In addition, it is useful to divide the items retailers order into two groups: those for which additional units can be obtained from the supplier during the selling season for that product and those that cannot—that is, replenishable products versus nonreplenishables. This distinction matters, because inventory management differs for products in the two categories. All else being equal, a retailer would prefer to have replenishment opportunities for every product. Lean retailers’ rapid replenishment arrangements radically reduce the risk of undersupply—the retailer can essentially “correct” for those items that it ordered too little of prior to the start of the season—and of oversupply, since the retailer orders smaller initial quantities. In contrast, orders for nonreplenishable products must be placed in full prior to observing consumer demand for the product. The retailer “rolls the dice” and makes its entire order commitment based on preliminary demand forecasts, considerably increasing the risk of over- or undersupply. Inventory Models for Nonreplenishable Products When a retailer has no ability to replenish a product, the inventory decision is reduced to a single question: How many units of the item should a buyer order to maximize that product’s profitability? Retailer managers are relying less and less on their “gut” and past experience; lean retailers are increasingly using more sophisticated statistical models, even in the risky realm of nonreplenishables, to help guide stocking decisions. In this section we review briefly the well-known “news-vendor” problem to illustrate the basic trade-offs retailers must make when determining inventory stocking levels.11 To determine the optimal quantity for a SKU, the retailer finds the number of units to order so that the expected marginal cost of stocking an additional unit and not being able to sell it equals the expected marginal cost of not stocking that unit when it would have sold if available. Mathematically, this relationship translates as follows. Find the optimal inventory stocking quantity, Q*, that satisfies the relationship: [Probability the unit cannot be sold)](Co) = [Probability the unit could have been sold](Cu), that is [Prob(D