## PRODUCT FORECASTING

### AN OVERVIEW...

**General**: The first step in planning production and inventory management activities is forecasting future demand. The American Production and Inventory Control Society (APICS) consider a forecast to be an objective procedure, using data collected over time. A forecast involves an assumption that current trends will continue into the future. The term prediction is used to describe any activity that includes subjective evaluation. This section considers both objective and subjective procedures. However, the focus of the section is on objective procedures.

The foundation for any production activity is either an actual order or the forecast of future orders. In a make-to-stock environment, production activities arc based entirely on forecasts, because orders must be filled from existing stock. In a make-to-order environment, however, production activities are typically scheduled using Model-Option logic.

A discussion of forecasting usually focuses on quantitative techniques to manipulate data, neglecting how the data are obtained. We should recognize, however, that the maxim “garbage in, garbage out” applies to forecasting as well as to other computerized techniques. Therefore, we first discuss bow the data are obtained, verified, and recorded. No forecasting system can afford to neglect these critical activities.

It is also important to understand that whenever there is reason to suspect that the future will not be like the past, a prediction is preferable to a forecast, Electric utilities experienced average annual demand growth of 7 percent to 8 percent for a quarter century following the end of World War II. When the creation of OPEC sent oil prices skyrocketing, the companies continued to forecast based on the past, ignoring predictions that the rate of demand growth must fall in response to rising prices. The oversupply of power plants (particularly nuclear power plants) that resulted is well known. Before making a forecast, consider whether a prediction is more appropriate.

Production planning personnel are not responsible for forecasting for the long-range planning that is needed for planning facility construction and major equipment purchases. Rather, they perform shorter-range forecasts used in medium-term production planning and short-range master production scheduling. In this manual, we limit our discussion to shorter-range forecasts that are used to schedule production and to make short-term capacity plans.

Please notice that all of the complex detail of Forecasting is compressed in this section to give you a sense of what’s needed for your company, instead of dumping too much on you when it is not necessary!

### A SUMMARY OF THIS SECTION

Forecasting techniques are classified as qualitative, involving primarily judgment, and quantitative, involving primarily historical data and mathematical models. Quantitative techniques use both intrinsic data, data pertaining to the item to be forecast, and extrinsic data, All quantitative forecasting methods involve the implicit assumption that the near future will be similar to the recent past. To be reliable, all quantitative forecasting techniques require accurate data. Insuring accurate data requires that the data be monitored carefully to eliminate data input error and to adjust for one-time occurrences, such as special promotions.

The study of a set of data describing demand over time is called time series analysis. Three common techniques of time series analysis are moving averages, exponential smoothing, and time series decomposition. Time series decomposition is the most accurate of the three, but there is often too little data to permit decomposition, Winters' three-factor model, the most complex exponential smoothing application, is a good compromise whenever seasonal variation in demand exists but there is insufficient data to use time series decomposition.

All forecasts are subject to error, even when the model used for the forecast is properly defined. Production and inventory managers require an estimate of the average forecast error to determine appropriate levels of safety stock and other precautionary measures. The most frequently used measure of forecast error is the mean absolute deviation (MAD), the average of the absolute values of the forecasts minus the actual demands. And now for more detail...

### DATA

Forecasting systems *extrapolate* time series data. A time series is a historical record of the past activity. A fundamental assumption for extrapolation is that the future is related to the past in some way. This assumption does not require tomorrow to be just like today; it only requires stable relationships. Even in today's rapidly changing environment, fundamental relationships usually hold, at least in the short term. Some characteristics to note are the time intervals (weeks, months, years, etc.), the dimensions (units, dollars, kilograms, etc.), and the degree of data variability.

Time series data are of two types, *intrinsic* and *extrinsic*. Intrinsic time series data are data concerning past sales of the product to be forecast. Extrinsic time series data are data that are external but are related to sales of the product. For example, data describing sales of a related product are extrinsic. Before examining formal techniques to extrapolate time series data, let's first took at some sources of extrinsic data.

### Extrinsic Data Sources

Several sources for extrinsic data exist. One source is demographic data, data related to the characteristics of our customers. Suppose we wish to forecast sales for TRW automotive replacement parts by region. Data clearly of interest are data related to population trends in each region. Beyond total population data, we are interested in the driving age population, the driving age population by specific age group, and the population by income category. Another item of interest is the average time a car is kept. In the early 1980s the length of time people kept their cars began increasing, probably because of the increasing cost of new cars. Presumably, as the average automobile age increases, demand for replacement parts will also increase.

Demographic data are maintained in most large libraries, especially university libraries. Most such libraries employ research librarians whose job is to know where to find these data.

Data can also be collected within a company. Foremost among company data sources are various types of market intelligence, such as survey information, test panel data, and sales force feedback, Frequently, this type of data is considered of questionable value to production control, but the fault is often in its interpretation, not in the quality of the data itself. Market survey data are primarily obtained to aid in product promotion and new product introduction decisions. The specific procedures to conduct a market survey will not be covered in this text. We wish to point out that market survey data, because they are intended primarily for marketing purposes, must be viewed carefully in making production decisions, For example, a survey that establishes an intent to increase purchases may be useful in planning production capacity. Also the sample may shed light on the marketing mix (size, color, configuration) of the demand. These attributes are important in determining manufacturing mix.

Another source of data is sales force feedback. As salespeople contact customers or potential buyers, they accumulate information about what customers say they want and what competitors are offering or plan to offer (or withdraw from) the market. There are several difficulties in using these data for production decisions. Because the data are not obtainable in an orderly and regular manner, their comparability to other information is difficult to establish. Does the reported fact that Customer X intends to buy 15 percent more next month represent demand over that already scheduled? Since it is quite common to use already forecast sales to set sales force goals and hence compensation, the incentive exists to manipulate or withhold data to influence personal pay. The extent of deliberate bias is difficult to determine, and thus sales force feedback is questionable, but not altogether unusable.

### Modifying Intrinsic Data

At this point we will examine some sample time series data originating within a company and discuss the need for data modification. Activities that often bias data are sales promotion and new advertising campaigns. While it is obvious that production should be aware of any such activities, it nevertheless happens that such activities are not communicated adequately. Perhaps of greater concern is that the effects of such campaigns or promotions cannot be estimated accurately. Marketing and manufacturing personnel must share responsibility for both the forecast and the manufacturing schedule. Too often marketing estimates that X units will be sold; manufacturing, in the belief that marketing's estimates are optimistic, makes X less 10 percent. When the results are in, each blames the other for excess inventories or shortages. The only way to eliminate this problem is to have a master schedule on which both groups agree.

Two issues that relate to forecasting when special promotions occur are forecasting sales for the period after the promotion and adjusting the data to reflect the promotion. Consider the following sequence of sales data:

Month |
1 |
2 |
3 |
4 |
5 |

Sales |
100 |
100 |
100 |
200 |
? |

Given this sequence, what sales prediction would you make for Month 57 Write your answer before reading further. When this question was asked of a large audience of experienced forecasters at a 1983 APICS conference, a majority responded that they would forecast 0 for Month 5. Their reasoning was that in Month 4 there must have been a promotion, causing customers to overstock. This would, in turn, result in no orders until customers used their existing stocks.

No time series approach would reach this conclusion, logical though it is. Furthermore, a time series analysis package will derive distorted forecasts, given these data. Suppose a nonrecurring promotion did occur in Month 4 and sales for the first six months were:

Month |
1 |
2 |
3 |
4 |
5 |
6 |

Sales |
100 |
100 |
100 |
200 |
15 |
85 |

Clearly, a more useful set of sales data to give the forecasting system is simply six months of demand of 100 units each. This example demonstrates that modification of sales data is sometimes justified to improve forecast accuracy.

Data modification should be limited to correction of large anomalies having known causes. Furthermore, these causes should not recur on a regular basis. Data should not be modified because it appears to be peculiar and no cause for the irregularity is known. It is a mistake to alter data simply to reduce random variation. One arrives at too small an estimate of forecast error and, worse, too little effort to protect against forecast error.

### Data Quality and Accuracy

The validity and appropriateness of our data sources must be ascertained. We must also control for errors and make appropriate modifications for nonrecurring events.

An important source of errors is often found in data recording. These errors may be with regard to numeric quantity (recording 71 instead of 11) or identification (part 6A5Z instead of 6A52) or dimensionality (seven dozen in place of seven gross). The data processing system, whether manual or computerized, should be developed to find such errors, if possible, and to correct them or at least point them out for further investigation as to cause.

**Check Digits**: Check digits provide a way to catch most recording errors regarding part numbers. Errors in recording a part number are particularly insidious because they create errors in the data for two parts: the part that should have been entered and the part that was entered erroneously. Most check digits involve an algebraic manipulation of the first n - 1 digits of an n digit number to obtain the correct value for the nth digit. The example presented here uses a simpler scheme than is usually used, but serves to illustrate the general principle. Suppose a company has 500 end items that it has numbered 001 to 500. The company desires to add a check digit to the numbering system. A simple procedure is to use

X4 = (X1 + (2)X2 + (3)X3) mod 10

That is, the fourth digit is found by adding the first digit plus twice the second digit plus three times the third digit and extracting the unit position digit from the sum. Using this procedure, the check digit for part 134 is (1 + 2 x 3 + 3 x 4) mod 10 = (1 + 6 + 12) mod 10 19 mod 10 = 9. (The mod operator yields the remainder after long division is performed.) The revised part number becomes 1349. A common error in recording data is to transpose two digits. If part number 1349 is incorrectly recorded as 1439, the check digit procedure evaluates the check digit as (1 + 8 + 9) mod 10 =18 mod 10 = 8. The computer will refuse to accept this part number entry because the final digit must be 8 not 9. Well designed check digit systems will catch more than 99 percent of all errors in recording part numbers.

**Demand Filters**: A demand filter is created by recording a range of reasonable data for each part number. If in the past several months demand never has fallen below 100 or exceeded 200, 100 and 200 might be set as limits. The computer would automatically question any entry less than 100 or greater than 200. To avoid too much manual intervention, we must establish appropriate limits as a compromise between chasing down nonexistent errors and allowing erroneous data to enter the system. In choosing a value for a demand filter, one should use a fairly wide band for unimportant items and a narrow band for expensive and high volume items. The reason for a variable band width is that for low dollar volume items it is cheaper to carry safety stock to cover the effects of the error than it is to spend valuable management time correcting the error. For high dollar volume items, the reverse is true.

**Orders Versus Shipments**: Many forecasting errors have been made through failure to recognize the difference between orders and shipments. For example, orders and shipments differ in timing. Orders precede shipments by manufacturing lead time (make-to-order environments) or at least by order filling time (make-to-stock environments). Quantities shipped may be less than quantities ordered for a variety of reasons. Partial shipments may be made over a period of time to fill one order. Shipments may exceed orders because spare parts or allowances for defects may be included. Whatever the reason, the distinction between orders and shipments must be taken into account when using historical data to forecast.

**Price Changes**: Another factor to consider is that price changes may cause increased sales dollars but not increased unit sales. Historical variations in unit prices are frequently overlooked, and errors arise because a single conversion factor is used to translate past sales dollars into past unit sales. For example, a price increase from $2.50 to $2.75 last July means that the first six months' sales of $30,000 and the second half sales of $32,000 actually represent a decline in unit sales.

**Summary of Data Quality**: To summarize, one must examine the source and accuracy of the data on which forecasts will be built. No amount of ordinary photographic development technique can transform a fuzzy negative into a clear, sharp picture. Similarly, no forecasting technique can transform poor data into a good forecast. We must next present an overview of the forecasting process, including data considerations.

### FORECAST HORIZON AND SCOPE

The forecast horizon for a product must be at least as long as that product's total lead time. If the forecast horizon is shorter, then the earliest production activities, such as placing purchase orders for long lead time components, are performed with insufficient information. The forecast horizon should be as long as possible, i.e., as long as can be forecast accurately. The frequency of forecast updating depends on the value of the information obtained and on the volatility of product sales. Forecasts should be updated frequently for high dollar volume items less frequently for low dollar volume items. For high dollar volume items, the additional accuracy obtained by frequent updating is recovered by eliminating expensive safety stock. For items having volatile sales, i.e., sales subject to large changes in volume, frequent forecast updating helps to avoid expensive overproduction and underproduction. The value of the additional information must exceed the cost of obtaining it.

In general, forecasts are made for product groups rather than for individual items. Forecasts can then be divided by historical product mix to obtain individual item forecasts. Forecasts for individual items are rarely needed.

Consider the case of Wellco Carpet. To plan the weaving operation, one needs a forecast of carpet sales grouped by type of weave. We do not need to know how much of each weave will be dyed each color to plan weaving. Similarly, to plan the dyeing operation our principle concern is the quantity of carpet to be dyed each color, independent of weave type.

Information on both weave style and color can be obtained from the same forecast. Suppose our forecast calls for 100,000 square yards of carpet to be sold per day on the average. Suppose also that 23 percent of past sales was for Weave A and 13 percent was for Weave B. Then our plan for weaving calls for 23,000 square yards of Weave A and 18,000 square yards of Weave B. Using the same aggregate forecast of carpet sales, one can apply historical color mixes to plan the dyeing operation.

### BASIC FORECASTING TECHNIQUES

Forecasting techniques (using the term forecasting in its broadest sense) can be divided into two categories: qualitative and quantitative. The former, which may involve numbers, uses methodology that is not mathematical. Qualitative techniques rely on judgment, intuition, and subjective evaluation. Among the major techniques within this category are market research (surveys), Delphi (panel consensus), historical analogy, and management estimation (guess). In APICS terminology, all of these techniques represent predictions rather than forecasts (in the narrow sense). The other class of techniques, quantitative, can be divided into intrinsic and extrinsic types.

Intrinsic techniques often are called time series analysis techniques. They involve mathematical manipulation of the demand history for an item. These techniques are the most commonly used in forecasting for production and inventory control. The other group of quantitative techniques, extrinsic methods, creates a forecast by attempting to relate demand for an item .to data about another item, a group of items, or outside factors (such as general economic conditions).

### Qualitative Techniques

We mentioned some aspects of market research in discussing data sources. While these techniques are based on good theory and can yield valuable information for marketing decisions, they are not intended directly to support inventory decisions. Rather, they are intended to support product development and promotion strategies. Data gathered by these methods should be considered in some aggregate inventory or capacity planning decisions, but should not be the sole data source for such decisions.

The Delphi, or panel consensus, method may be useful in technological forecasting, that is, in predicting the general state of the market, economy, or technological advances five or more years from now, based on expert opinion, (The name for this method comes from the ancient Greek oracles of Delphi who forecast future events.) The process of creating a Delphi forecast is a variation of the following: A panel of futurists is asked a question, such as, In the next ten years which consumer products do you envision containing microprocessors as an integral part? Each specialist independently submits a list of such items to the panel coordinator. The combined lists then are sent back to each panel member for evaluation and rating of likelihood of occurrence. Panel members may see something that they hadn't thought of and rate it highly. Also members may have second thoughts about items they themselves previously submitted. After a sufficient number of cycles (generally two or three), the result is a list with high consensus. The Delphi technique is not a suitable technique for short-range forecasting, certainly not for individual products.

When attempting to forecast demand for a new item, one faces a shortage of historical data. A useful technique is to examine the demand history for an analogous product. If the related product is very similar, quantitative techniques may be used. But if the relationship is tenuous, it may be more appropriate to relate the products only qualitatively in order to get an impression of demand patterns or aggregate demand. For example, the seasonal demand pattern for an established product such as tennis balls may be used to estimate the expected demand pattern for tennis gloves. The actual level'. and trends for the latter cannot be determined in this manner with any precision, but the seasonal pattern may be expected to be similar.

Finally, we must not overlook management estimation (intuition) as prediction method. It is widely practiced with regard to new products or unexpected changes in demand for established product lines. Not everyone has estimation talent, however, Some studies have shown that a mathematical technique, consistently followed, will lead to better results than the "expert modification" of those forecasts. Nonetheless, many mathematical technique need significant quantities of historical data that may not be available. When substantial data are lacking, subjective management judgment may be the better alternative.

### Quantitative Techniques

Intrinsic techniques use the time-sequenced history of activity for a particular. item as source data to forecast future activity for that item. Such a history is commonly referred to as a time series. The characteristics of such series can be labeled in various' ways, and the algebraic representation of such graphs can be accomplished b' a variety of methods.

Generally, a time series can be thought of as consisting of four components or underlying factors: (1) cyclical, (2) trend, (3) seasonal, and (4) random (or irregular). The cyclical factor traditionally refers to the business cycle to long-range trends in the overall economy. The cyclical factor can be very important in forecasting for long-range planning. However, it is of little us in forecasting demand for individual products, which rarely have sufficient data to permit a distinction between the effect of the business cycle and the effect of the product life cycle. For that reason, the time series used for short term forecasting generally have only trend, seasonal, and random components. The trend component generally is modeled as a line, which is described by an intercept or base level, which we designate L, and a slope, which we designate T. The trend line may be modified by a seasonal phenomenon (S). All data are somewhat muddled by a random, irregular, or otherwise unpredictable variable(R).

Mathematically this process is based on a combination multiplicative and additive model of the following sort:

D = (L + T) x S + R

where D is demand. In this version F, trend, is expressed in the same units as £, level, and T may be positive or negative, R, random, is expressed in the same units, Its expected value is 0. S, seasonal, is a dimensionless number having an expected value of 1. For example, we may know that the demand for a certain Bruce Springsteen anthology is averaging 10,000 units per month, with a trend of minus 500 per month (the pattern is to sell 500 fewer units each month). However, the month currently being forecast is December; due to seasonal variation, December averages 40 percent higher than the typical month, Average forecast error using this model has been 800 units. In this example the demand forecast is

D= (10,000 - 500) x 1,4 + 0 = 13,300 units

Because the average forecast error has been 800 units, and because errors twice the average are not uncommon occurrences, we would not be surprised if December's actual sales were anywhere from 13,300 - 1,600 = 11,700 units to 13,300 + 1,600 = 14,900 units.

### TIME SERIES ANALYSIS

This section discusses some of the most common techniques for forecasting from intrinsic time series without explicitly looking for seasonal or trend factors. It also examines time series decomposition.

**Moving Averages**: Perhaps the simplest of all time series forecasting techniques is a moving average. To use this method, we calculate the average of, say, three periods of actual demand and use that to forecast the next period's demand. If this three-period average is to be used as a forecast, it would have to forecast demand in a future period, such as Period 8.

Because each average moves ahead one period each time, dropping the oldest value and adding the most recent, this procedure is called a moving average. The number of periods to use in computing the average may be anything from 2 to 12 or more, with 3 or 4 periods being common. If the time series is such that there is no upward or downward trend, then the moving average is a satisfactory technique. If, how-ever, there is any trend or any seasonal effect, then the moving average will not work very well. Moving averages lag behind any trends.