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Forecasting
A forecast is a prediction of what will occur in the future. Meteorologists forecast the weather, sportscasters and gamblers predict the winners of football games, and companies attempt to predict how much of their product will be sold in the future. A forecast of product demand is the basis for most important planning decisions. Planning decisions regarding scheduling, inventory, production, facility layout and design, workforce, distribution, purchasing, and so on, are functions of customer demand. Long-range, strategic plans by top management are based on forecasts of the type of products consumers will demand in the future and the size and location of product markets.
Forecasting is an uncertain process. It is not possible to predict consistently what the future will be, even with the help of a crystal ball and a deck of tarot cards. Management generally hopes to forecast demand with as much accuracy as possible, which is becoming increasingly difficult to do. In the current international business environment, consumers have more product choices and more information on which to base choices. They also demand and receive greater product diversity, made possible by rapid technological advances. This makes forecasting products and product demand more difficult. Consumers and markets have never been stationary targets, but they are moving more rapidly now than they ever have before.
Management sometimes uses qualitative methods based on judgment, opinion, past experience, or best guesses, to make forecasts. A number of quantitative forecasting methods are also available to aid management in making planning decisions. In this chapter we discuss two of the traditional types of mathematical forecasting methods, time series analysis and regression, as well as several nonmathematical, qualitative approaches to forecasting. Although no technique will result in a totally accurate forecast, these methods can provide reliable guidelines in making decisions.
The Strategic Role of Forecasting in Supply Chain Management
and TQM
In today's global business environment, strategic planning and design tend to focus on supply chain management and total quality management (TQM).
Supply Chain Management
A company's supply chain encompasses all of the facilities, functions, and activities involved in producing a product or service from suppliers (and their suppliers) to customers (and their customers). Supply chain functions include purchasing, inventory, production, scheduling, facility location, transportation, and distribution. All these functions are affected in the short run by product demand and in the long run by new products and processes, technology advances, and changing markets.
Forecasts of product demand determine how much inventory is needed, how much product to make, and how much material to purchase from suppliers to meet forecasted customer needs. This in turn determines the kind of transportation that will be needed and where plants,
warehouses, and distribution centers will be located so that products and services can be delivered on time. Without accurate forecasts large stocks of costly inventory must be kept at each stage of the supply chain to compensate for the uncertainties of customer demand. If there are insufficient inventories, customer service suffers because of late deliveries and stockouts. This is especially hurtful in today's competitive global business environment where customer service and on-time delivery are critical factors.
Long-run forecasts of technology advances, new products, and changing markets are especially critical for the strategic design of a company's supply chain in the future. In today's global market if companies cannot effectively forecast what products will be demanded in the future and the products their competitors are likely to introduce, they will be unable to develop the production and service systems in time to compete. If companies do not forecast where newly emerging markets will be located and do not have the production and distribution system available to enter these markets, they will lose to competitors who have been able to forecast accurately.
A recent trend in supply chain design is continuous replenishment, wherein continuous updating of data is shared between suppliers and customers. In this system customers are continuously being replenished, daily or even more by their suppliers based on actual sales. Continuous replenishment, typically managed by the supplier, reduces inventory for the company and speeds customer delivery. Variations of continuous replenishment include quick response, JIT, VMI (vendor-managed inventory), and stockless inventory. Such systems rely heavily on extremely accurate short-term forecasts, usually on a weekly basis, of end-use sales to the ultimate customer. The supplier at one end of a company's supply chain must forecast the company's customer demand at the other end of the supply chain in order to maintain continuous replenishment. The forecast also has to be able to respond to sudden, quick changes in demand. Longer forecasts based on historical sales data for six to twelve months into the future are also generally required to help make weekly forecasts and suggest trend changes.
Levi Strauss employs a supply chain with regional clusters of suppliers, manufacturers, and distribution centers linked together, thereby reducing inventory and improving customer service. The goal of this supply chain design is to have inventory close to customers so that products can be delivered within seventy-two hours. Levi Strauss arranges weekly store orders based on actual sales patterns received electronically from stores through EDI (electronic data interchange). It uses weekly forecasts of demand that extend sixty weeks into the future. The forecast determines weekly inventory levels and weekly replenishment to customers. Suppliers also use this forecast and store sales patterns to manage and schedule their deliveries to customers.^3
Total Quality Management
Forecasting is crucial in a total quality management (TQM) environment. More and more, customers perceive good-quality service to mean having a product when they demand it. This holds true for manufacturing and service companies. When customers walk into a McDonald's to order a meal, they do not expect to wait long to place orders. They expect McDonald's to have the item they want, and they expect to receive their orders within a short period of time. An accurate forecast of customer traffic flow and product demand enables McDonald's to schedule enough servers, to stock enough food, and to schedule food production to provide high-quality service. An inaccurate forecast causes service to break down, resulting in poor
A long-range forecast is usually for a period longer than two years into the future. A long- range forecast is normally used for strategic planning--to establish long-term goals, plan new products for changing markets, enter new markets, develop new facilities, develop technology, design the supply chain, and implement strategic programs such as TQM. At Unisys long-range strategic forecasts project three years into the future; Hewlett-Packard's long-term forecasts are developed for years two through six; and at Fiat, the Italian automaker, strategic plans for new and continuing products go ten years into the future.
These classifications are generalizations. The line between short- and long-range forecasts is not always distinct. For some companies a short-range forecast can be several years, and for other firms a long-range forecast can be in terms of months. The length of a forecast depends a lot on how rapidly the product market changes and how susceptible the market is to technological changes.
Demand Behavior
Demand sometimes behaves in a random, irregular way. At other times it exhibits predictable behavior, with trends or repetitive patterns, which the forecast may reflect. The three types of demand behavior are trends, cycles, and seasonal patterns.
A trend is a gradual, long-term up or down movement of demand. For example, the demand for personal computers has followed an upward trend during the past few decades, without any sustained downward movement in the market. Trends are the easiest patterns of demand behavior to detect and are often the starting points for developing forecasts. Figure 10.1 (a) illustrates a demand trend in which there is a general upward movement, or increase. Notice that Figure 10.1(a) also includes several random movements up and down. Random variations are movements that are not predictable and follow no pattern (and thus are virtually unpredictable).
A cycle is an up-and-down movement in demand that repeats itself over a lengthy time span (i.e., more than a year). For example, new housing starts and, thus, construction-related products tend to follow cycles in the economy. Automobile sales also tend to follow cycles. The demand for winter sports equipment increases every four years before and after the Winter Olympics. Figure 10.1(b) shows the behavior of a demand cycle.
A seasonal pattern is an oscillating movement in demand that occurs periodically (in the short run) and is repetitive. Seasonality is often weather related. For example, every winter the demand for snowblowers and skis increases, and retail sales in general increase during the holiday season. However, a seasonal pattern can occur on a daily or weekly basis. For example, some restaurants are busier at lunch than at dinner, and shopping mall stores and theaters tend to have higher demand on weekends. Figure 10.1(c) illustrates a seasonal pattern in which the same demand behavior is repeated each year at the same time.
Demand behavior frequently displays several of these characteristics simultaneously. Although housing starts display cyclical behavior, there has been an upward trend in new house construction over the years. Demand for skis is seasonal; however, there has been an upward trend in the demand for winter sports equipment during the past two decades. Figure 10.1(d) displays the combination of two demand patterns, a trend with a seasonal pattern.
Instances when demand behavior exhibits no pattern are referred to as irregular movements, or variations. For example, a local flood might cause a momentary increase in carpet demand, or a competitor's promotional campaign might cause a company's product demand to drop for a period of time. Although this behavior has a cause and, thus, is not totally random, it still does not follow a pattern that can be reflected in a forecast.
Forecasting Methods
The factors discussed previously in this section determine to a certain extent the type of forecasting method that can or should be used. In this chapter we are going to discuss three basic types of forecasting: time series methods, regression methods, and qualitative methods.
Time series methods are statistical techniques that use historical demand data to predict future demand. Regression (or causal) forecasting methods attempt to develop a mathematical relationship (in the form of a regression model) between demand and factors that cause it to behave the way it does. Most of the remainder of this chapter will be about time series and regression forecasting methods. In this section we will focus our discussion on qualitative forecasting.
Qualitative methods use management judgment, expertise, and opinion to make forecasts. Often called "the jury of executive opinion," they are the most common type of forecasting method for the long-term strategic planning process. There are normally individuals or groups within an organization whose judgments and opinions regarding the future are as valid or more valid than those of outside experts or other structured approaches. Top managers are the key group involved in the development of forecasts for strategic plans. They are generally most familiar with their firms' own capabilities and resources and the markets for their products.
The sales force of a company represents a direct point of contact with the consumer. This contact provides an awareness of consumer expectations in the future that others may not
In the next few sections we present several different forecasting methods applicable for different patterns of demand behavior. Thus, one of the first steps in the forecasting process is to plot the available historical demand data and, by visually looking at them, attempt to determine the forecasting method that best seems to fit the patterns the data exhibit. Historical demand is usually past sales or orders data. There are several measures for comparing historical demand with the forecast to see how accurate the forecast is. Following our discussion of the forecasting methods, we present several measures of forecast accuracy. If the forecast does not seem to be accurate, another method can be tried until an accurate forecast method is identified. After the forecast is made over the desired planning horizon, it may be possible to use judgment, experience, knowledge of the market, or even intuition to adjust the forecast to enhance its accuracy. Finally, as demand actually occurs over the planning period, it must be monitored and compared with the forecast in order to assess the performance of the forecast method. If the forecast is accurate, then it is appropriate to continue using the forecast method. If it is not accurate, a new model or adjusting the existing one should be considered.
Time Series Methods
Time series methods are statistical techniques that make use of historical data accumulated over a period of time. Time series methods assume that what has occurred in the past will continue to occur in the future. As the name time series suggests, these methods relate the forecast to only one factor--time. They include the moving average, exponential smoothing, and linear trend line; and they are among the most popular methods for short-range forecasting among service and manufacturing companies. These methods assume that identifiable historical patterns or trends for demand over time will repeat themselves.
Moving Average
A time series forecast can be as simple as using demand in the current period to predict demand in the next period. This is sometimes called a naive or intuitive forecast.^4 For example, if demand is 100 units this week, the forecast for next week's demand is 100 units; if demand turns out to be 90 units instead, then the following week's demand is 90 units, and so on. This type of forecasting method does not take into account historical demand behavior; it relies only on demand in the current period. It reacts directly to the normal, random movements in demand.
The simple moving average method uses several demand values during the recent past to develop a forecast. This tends to dampen, or smooth out, the random increases and decreases of a forecast that uses only one period. The simple moving average is useful for forecasting demand that is stable and does not display any pronounced demand behavior, such as a trend or seasonal pattern.
Moving averages are computed for specific periods, such as three months or five months, depending on how much the forecaster desires to "smooth" the demand data. The longer the moving average period, the smoother it will be. The formula for computing the simple moving average is
EXAMPLE
Computing a Simple Moving Average
The Instant Paper Clip Office Supply Company sells and delivers office supplies to companies, schools, and agencies within a 50-mile radius of its warehouse. The office supply business is competitive, and the ability to deliver orders promptly is a factor in getting new customers and keeping old ones. (Offices typically order not when they run low on supplies, but when they completely run out. As a result, they
see how accurate the forecasting method is--that is, how well it does.
Three- and Five-Month Averages
Both moving average forecasts in the table above tend to smooth out the variability occurring in the actual data. This smoothing effect can be observed in the following figure in which the 3-month and 5-month averages have been superimposed on a graph of the original data:
The 5-month moving average in the previous figure smooths out fluctuations to a greater extent than the 3-month moving average. However, the 3-month average more closely reflects the most recent data available to the office supply manager. In general, forecasts using the longer-period moving average are slower to react to recent changes in demand than would those made using shorter-period moving averages. The extra periods of data dampen the speed with which the forecast responds. Establishing the appropriate number of periods to use in a moving average forecast often requires some amount of trial-and-error experimentation.
The disadvantage of the moving average method is that it does not react to variations that occur for a reason, such as cycles and seasonal effects. Factors that cause changes are generally ignored. It is basically a "mechanical" method, which reflects historical data in a consistent way. However, the moving average method does have the advantage of being easy to use, quick, and relatively inexpensive. In general, this method can provide a good forecast for the short run, but it should not be pushed too far into the future.
Weighted Moving Average
The moving average method can be adjusted to more closely reflect fluctuations in the data. In the weighted moving average method, weights are assigned to the most recent data according to the following formula:
EXAMPLE
Computing a Weighted Moving Average
The Instant Paper Clip Company in Example 10.1 wants to compute a 3-month weighted moving average with a weight of 50 percent for the October data, a weight of 33 percent for the September data, and a weight of 17 percent for the August data. These weights reflect the company's desire to have the most recent data influence the forecast most strongly.
SOLUTION:
The weighted moving average is computed as
Notice that the forecast includes a fractional part, 0.4. In general, the fractional parts need to be included in the computation to achieve mathematical accuracy, but when the final forecast is achieved, it must be rounded up or down.
This forecast is slightly lower than our previously computed 3-month average forecast of 110 orders, reflecting the lower number of orders in October (the most recent month in the sequence).
Determining the precise weights to use for each period of data usually requires some trial- and-error experimentation, as does determining the number of periods to include in the moving average. If the most recent periods are weighted too heavily, the forecast might overreact to a random fluctuation in demand. If they are weighted too lightly, the forecast might underreact to actual changes in demand behavior.
Exponential Smoothing
Exponential smoothing is also an averaging method that weights the most recent data more strongly. As such, the forecast will react more to recent changes in demand. This is useful if
usually judgmental and subjective and is often based on trial-and-error experimentation. An inaccurate estimate of α can limit the usefulness of this forecasting technique.
EXAMPLE
Computing an Exponentially Smoothed Forecast
PM Computer Services assembles customized personal computers from generic parts. Formed and operated by part-time State University students Paulette Tyler and Maureen Becker, the company has had steady growth since it started. The company assembles computers mostly at night, using part-time students. Paulette and Maureen purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal. Thus, they need a good forecast of demand for their computers so that they will know how many computer component parts to purchase and stock.
The company has accumulated the demand data shown in the accompanying table for its computers for the past twelve months, from which it wants to consider exponential smoothing forecasts using smoothing constants (α) equal to 0.30 and 0.50.
SOLUTION:
To develop the series of forecasts for the data in this table, we will start with period 1 (January) and compute the forecast for period 2 (February) using α = 0.30. The formula for exponential smoothing also requires a forecast for period 1, which we do not have, so we will use the demand for period 1 as both demand and forecast for period 1. Other ways to determine a starting forecast include averaging the first three or four periods or making a subjective estimate. Thus, the forecast for February is
The forecast for period 3 is computed similarly:
The remainder of the monthly forecasts are shown in the following table. The final forecast is for period 13, January, and is the forecast of interest to PM Computer Services:
Exponential Smoothing Forecasts, α = .30 and α =.
This table also includes the forecast values using α = 0.50. Both exponential smoothing forecasts are shown in Figure 10.3 together with the actual data.
In Figure 10.3, the forecast using the higher smoothing constant, α = 0.50, reacts more strongly to changes in demand than does the forecast with α = 0.30, although both smooth out the random fluctuations in the forecast. Notice that both forecasts lag behind the actual demand. For example, a pronounced downward change in demand in July is not reflected in the forecast until August. If these changes mark a change in trend (i.e., a long-term upward or downward movement) rather than just a random fluctuation, then the forecast will always lag behind this trend. We can see a general upward trend in delivered orders throughout the year. Both forecasts tend to be consistently lower than the actual demand; that is, the forecasts lag the trend.
The trend factor is computed much the same as the exponentially smoothed forecast. It is, in effect, a forecast model for trend:
β is a value between 0.0 and 1.0. It reflects the weight given to the most recent trend data. β is usually determined subjectively based on the judgment of the forecaster. A high β reflects trend changes more than a low β. It is not uncommon for β to equal α in this method.
Notice that this formula for the trend factor reflects a weighted measure of the increase (or decrease) between the current forecast, Ft+1, and the previous forecast, Ft.
EXAMPLE
Computing an Adjusted Exponentially Smoothed
Forecast
PM Computer Services now wants to develop an adjusted exponentially smoothed forecast using the same twelve months of demand shown in the table for Example 10.3. It will use the exponentially smoothed forecast with α = 0.5 computed in Example 10.3 with a smoothing constant for trend, β, of 0.30.
SOLUTION:
The formula for the adjusted exponential smoothing forecast requires an initial value for Tt to start the computational process. This initial trend factor is often an estimate determined subjectively or based on past data by the forecaster. In this case, since we have a long sequence of demand data (i.e., 12 months) we will start with the trend, Tt, equal to zero. By the time the forecast value of interest, F 13 , is computed, we should have a relatively good value for the trend factor.
The adjusted forecast for February, AF 2 , is the same as the exponentially smoothed forecast, since the trend computing factor will be zero (i.e., F 1 and F 2 are the same and T 2 = 0). Thus, we compute the adjusted forecast for March, AF 3 , as follows, starting with the determination of the trend factor, T 3 :
This adjusted forecast value for period 3 is shown in the accompanying table, with all other adjusted forecast values for the 12-month period plus the forecast for period 13, computed as follows:
exponential smoothing forecasts developed in Examples 10.3 and 10.4.
SOLUTION:
The values required for the least squares calculations are as follows:
Using these values, the parameters for the linear trend line are computed as follows:
Therefore, the linear trend line equation is
To calculate a forecast for period 13, let x = 13 in the linear trend line:
The following graph shows the linear trend line compared with the actual data. The trend line appears to reflect closely the actual data--that is, to be a "good fit"--and would thus be a good forecast model for this problem. However, a disadvantage of the linear trend line is that it will not adjust to a change in the trend, as the
exponential smoothing forecast methods will; that is, it is assumed that all future forecasts will follow a straight line. This limits the use of this method to a shorter time frame in which you can be relatively certain that the trend will not change.
Seasonal Adjustments
A seasonal pattern is a repetitive increase and decrease in demand. Many demand items exhibit seasonal behavior. Clothing sales follow annual seasonal patterns, with demand for warm clothes increasing in the fall and winter and declining in the spring and summer as the demand for cooler clothing increases. Demand for many retail items, including toys, sports equipment, clothing, electronic appliances, hams, turkeys, wine, and fruit, increase during the holiday season. Greeting card demand increases in conjunction with special days such as Valentine's Day and Mother's Day. Seasonal patterns can also occur on a monthly, weekly, or even daily basis. Some restaurants have higher demand in the evening than at lunch or on weekends as opposed to weekdays. Traffic--hence sales--at shopping malls picks up on Friday and Saturday.
