April 1996 € Volume 6 € Number 4

Forecasting Seasonal Demand

It is easy to assume that powerful and sophisticated forecasting algorithms, with their many formulas and control parameters, cannot be improved upon. But in most organizations there are many opportunities to strenghten current forecasting procedures using the power of information systems. It can be well worth the effort.

By Philip Rhodes, CFPIM

With the exception of forecasting the sales of a new product, no forecasting issue presents a greater challenge or is of greater importance than forecasting items with seasonal demand. Unfortunately, this function is weak in many forecasting packages, particularly those provided as part of a full suite of manufacturing system modules.

A product's seasonal sales pattern generally arises from one or more of the following causes:

The calendar (e.g., Thanksgiving and Christmas)
The weather (e.g., flu season or an early spring)
Dating, pricing promotions and "sales"

Calendar-based seasonal demand is the most predictable of seasonal sales patterns, but presents problems for slower-moving items. These items almost always have large random variations or "noise" in their demand. This noise to a large extent obscures the underlying seasonal sales pattern, which you would like to establish and use in forecasting.

Weather-based seasonals are unstable in their timing and present difficulties for even large-volume products. For example, white exterior house paint is a very high-volume product. But, because it is highly dependent on good weather, a wet spring can greatly delay its seasonal sales.

The height of a demand peak can also be highly variable. For example, the flu season is much worse in some years than in others, and may come in with a bang or build slowly to a lower peak. Fortunately, manufacturers will often use dating (e.g., if you buy now, you need not pay for 90 days) to encourage customers to stock up on these products well in advance of the peak season. In other cases, however, the retailer is stuck with the cash flow impact of the inventory they chose to build in anticipation of peak demand.

Reflecting the timing of promotions in forecasts should, in theory, not be an issue. Manufacturers usually plan their promotions well in advance and inform their distributors of these plans. Nevertheless, particularly with distributors, forecasts are often not updated to reflect known changes in the timing of promotions.

Predicting the full impact of a promotion in the three relevant intervals of time -- the periods before, during and after the promotion -- is always a challenge.

Forecasting seasonals
Forecasting software packages typically provide only one or two of the following approaches to developing forecasts for seasonal items.

Approach 1: Apply a growth factor (which can be calculated in numerous ways) to an item's prior 12 months' sales to forecast sales in each of the following 12 months.

Approach 2: Take a weighted average of the corresponding months (e.g. February with February) for two or more years of prior sales to develop the seasonal factors for each month.

Generally these 12 factors or "seasonal indices" for a year are "normalized" so as to sum to 12. With this approach a seasonal index of 1.23 for a month indicates that the item's sales are predicted to be 23 percent above the monthly average, called the "deseasonalized level of sales."

Approach 3: Under this approach a buyer or inventory manager will identify a group of items believed to have the same seasonal sales pattern (e.g., all exterior house paints). These seasonals are calculated for the group as a whole and then used in forecasting each of the individual items in the group.

Approach 4: At least one system on the market has an ability to take two or more years of history on a broad range of items and automatically make a determination as to which items have similar seasonals (in operations research this is called cluster analysis). Once these groups are established, the forecasting proceeds as above. The intent of this approach is to take the "burden" of grouping products off the shoulders of the personnel responsible for forecasting.

This last approach, particularly in the case of items with erratic movement, results in strange, largely meaningless groupings of items, leads to poor forecasts and is very difficult to review. It is discussed no further in this article.

The limitations of each approach
These approaches have limitations, and these limitations are compounded by the fact that forecasting packages typically provide no more than two of these approaches and provide little or no ability to compare the relative forecast accuracy of the alternatives.

Understanding the limitations inherent in each of these approaches to forecasting seasonals can help users make more informed choices and minimize the impact of these limitations. With some ingenuity and programming support, users can improve on the "canned" solutions supplied by their forecasting package.

Approach 1 -- applying a growth factor (it may be zero) to the prior year's sales-only has merit for high-volume items with stable seasonals. For low-volume items or items with unstable seasonals, this method yields poor results. This is because the "noise" (random variations) in a single year of historical data easily obscures the underlying seasonal behavior.

If you have only a single year of data for an item and cannot group the item with other products (Approach 3), you may achieve better results by going with a single average level of demand for the entire year or, in some cases, forecasting two levels of demand-one for the high season and a second for the slow season.

Approach 2 uses two or more years of relevant history for an item and averages them, applying a greater weight (perhaps using exponential smoothing) to the more recent year(s). While using two years of data is generally an improvement over a single year, the seasonals for slow-moving items or items with large but erratic sales may still be obscured by "noise" in the actual demand. For example, averaging two years of sales data for February in an effort to filter out the noise is usually ineffective for high noise levels (a mean absolute deviation of 50 percent or more).

An additional problem is that changes in the promotional period, distribution channels, major customers, etc., can easily cause use of the earlier year's demand in forecasting to result in less, rather than more accurate forecasts.

Approach 3, with some elaboration (to be discussed), is most likely to provide the best results. It "filters out" the random noise present in the demand of individual items by looking at a number of items together.

The idea here is to develop group (average) seasonals for items that are likely to have the same seasonal pattern. These, for example, could be a product group such as exterior house paints, all pharmaceuticals within a therapeutic class or items whose seasonal pattern is caused by a common annual promotion.

With careful planning, the number of these groups should be manageable. It then becomes practical to manually review the results and make adjustments based on information external to the time series). These adjustments most frequently include modifying the calculated seasonals to reflect new marketing plans, or removing some items from the group whose seasonal patterns clearly differ from those of the group (taken as a whole).

For example, large sizes of a pharmaceutical product may have different seasonals because it has a different market (hospitals rather than drug stores). Fortunately, there are statistical methods that can reliably identify these "non-conforming" items.

Identifying these non-conformers can also have an important marketing payback. It can reveal, for example, that red exterior house paint really has a different market or buying motivation from other exterior house paints-suggesting a possible promotional opportunity.

Forecasting promotions
Rather than throwing up their hands in frustration, companies can make a real effort to collect promotional data, analyze this information and use it in forecasting (and of course in evaluating promotional effectiveness for marketing purposes). To do this efficiently, however, requires a level of information systems support not available in many forecasting packages or properly supported by the order processing system.

Where the seasonal pattern is induced by promotions, these promotions should obviously be considered in establishing product groupings for forecasting purposes. The question is how to do this in a practical way.

Unless a product goes on promotion with all customers at the same time, its promotional sales and the specific promotion (code) should be identified at order entry time and a separate set of sales statistics maintained on these sales. That is, summary figures are maintained for promotional sales that supplement the usual statistics on total sales of the item.

Promotions have the obvious effect of shifting sales into the promotional period from later periods and, depending on the competitive situation or consumer behavior, may also increase total sales. An analysis of promotional sales, undistorted by sales of the same item to customers not included in the promotion, can lead to estimates of this shift, which can then be used in developing or revising seasonal indices.

A simplified exposition of this is provided below. Let's refer to the promotional period as period "p" and the subsequent periods as p+1, p+2 and p+3. Most typically these periods are months.

An analysis of a particular promotion or type of promotion (e.g., a 10 percent promotional discount in effect for one month) may reveal the following shifts in demand:

The "From" period	The percent of average sales shifted back to period P
p+1	x %
p+2	y %
p+3	z %

The seasonal indices, assuming there are no seasonal effects other than the promotion, would then be as follows:

For period	Shifted back to period P
p	1.0 + x% + y% + z%
p+1	1.0 - x %
p+2	1.0 - y %
p+3	1.0 - z %

If there are strong seasonal effects in addition to those induced by the promotion and promotional timing is being changed, then developing new seasonal indices becomes a two-step process. The first step is to "back out" the estimated promotional effect from the prior year's sales to estimate what the seasonal indices would have been without the promotion. The second step is to adjust these seasonal indices for the estimated effect of the new promotion.

Forecasting and controlling items with shifting (unstable) seasonals
When estimating the deseasonalized sales level for items with shifting seasonals, exponential smoothing does exactly the wrong thing.

Forecasting seasonal items requires estimating the current deseasonalized level of sales. It is this deseasonalized level of sales multiplied by the seasonal index for each month which provides forecasts for each month. (There may also be a trend or growth factor in the forecast.)

In most situations the use of exponential smoothing to update the deseasonalized level of sales each month is an excellent procedure -- far preferable to linear regression. Unfortunately, when the timing of seasonal peaks is unstable, exponential smoothing does exactly the wrong thing. Let's examine how exponential smoothing reacts to a seasonal peak for an item when that peak occurs one period earlier or later than indicated (anticipated) by the seasonal index.

A knowledgeable person observing that the season started one period earlier than usual (e.g. a dry, early spring encourages earlier house painting) would expect lower than usual sales in the subsequent period when the peak normally occurs. Seeing an earlier peak leads to an expectation of lower than usual sales in the next period. Exponential smoothing does the opposite of this.

This algorithm, observing that it underforecast in the earlier period, increases its forecast of the deseasonalized sales level and uses this higher level in forecasting the next period. The result is a forecast of an extra high peak rather than a lower one in the subsequent period.

Both the person and the exponential smoothing algorithm fail to anticipate the early peak. This cannot be helped. The knowledgeable person, however, can effectively readjust the forecast for the subsequent period. In contrast, exponential smoothing compounds the error.

Exponential smoothing exhibits a similar, but reverse problem when the peak season is delayed by one month.

Estimation of forecast errors
Forecasts, of course, are only one of four key inputs to the calculation of inventory control parameters, the others being a measure of forecast error, the replenishment lead time and the desired service level.

Many systems measure the forecast errors experienced each period and exponentially smooth those errors to arrive at a "forecast of forecast error." This estimate of forecast error then becomes an input in an automatic calculation by the system of statistical order points (and safety stock).

While this is reasonable for many items, in some situations it is an ineffective way of anticipating forecast errors and protecting against them with safety stock. Suppose, for example, an item has a period of peak demand that is three times average demand, and that this period of peak demand tends to shift from year to year. Again exterior house paint and flu remedies are excellent examples. The question becomes, "how do we protect ourselves should the peak hit a month earlier than usual?"

Using exponential smoothing to estimate the forecast error will give exactly the wrong result. Missing the forecast by a very wide margin when the peak occurred earlier than anticipated, the algorithm increases its forecast of forecast error for the subsequent period (and also increases the forecast as described above) -- just when the peak has passed and the need for safety stock has diminished.

This is not the only problem. Take the situation where sales are low for 11 months of the year and there is a single peak period with unstable timing.

As the forecasting algorithm rolls through the low months it will experience, on an absolute (not percentage) basis, a low level of forecast errors and subsequently adjust downward its forecast of forecast errors. The lowest estimate of forecast error is likely to occur just prior to peak season. Yet, this is just when the forecast is most uncertain (remember, we are discussing the situation where the peak season is unstable). Thus, we have the least protection (safety stock) when we are most in need of it.

To summarize the above, when the seasonal peak is unstable in its timing, the use of exponential smoothing to estimate (forecast) errors is likely to provide the most safety stock when it is unneeded and the least safety stock when it is most needed.

Companies need to recognize the above situation. Experienced buyers (or finished goods inventory managers in the manufacturing industry) try to make manual adjustments in the forecasts, order points or order quantities to compensate for this. There is great value, however, in having the system deal with these situations in a more "intelligent" manner.

Tracking signals
Tracking signals are very valuable in identifying out-of-control forecasts. But, by definition, they do this after the fact. And, of course, they also flag some forecasts that are not out of control and other forecasts that are no longer out of control. For example, when seasonals are unstable, a tracking signal can identify a problem that was only temporary and no longer exists.

In any case, tracking signals are no substitute for identifying systematic problems with forecasting procedures and working to eliminate them.

People vs. automated forecasting algorithms
It is easy to look at "sophisticated" forecasting algorithms, with their many formulas and control parameters, and assume that these "powerful" methods cannot be improved upon. It is also easy to fall into the trap of focusing on the various control parameters to the exclusion of more fundamental considerations.

In most organizations there are many opportunities, using the power of information systems, to strengthen current forecasting procedures. It can be well worth the effort.

Philip Rhodes, CFPIM, is president of Rhodes & Associates, Kendall Park, N.J.

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