Virtually all logistics processes are subject to some type of seasonality. Humanity and its social groups, since ancient times, have always had their activities controlled by some kind of periodic event: winter and summer, months of the year, weekly period and even throughout the hours of the day.
This rhythmic variation in activity has numerous implications, including a strong impact on logistics operations. The demand for products and services is generally influenced by seasonal components that must be taken into account for a more efficient use of available resources and opportunities. In this text, after discussing the technical concept of seasonality, we will present some simpler ways to measure it. The use of so-called seasonal indices goes beyond the simple process of forecasting demand, and is also used to monitor results, after discounting the seasonal effect. Forecasting software can help us with this task. However, we should always try to keep control of the forecasting process, preventing it from being seen as the result of a black box in which values are provided without the user knowing how they were obtained. Finally, it is worth evaluating in which situations a greater complexity in the process of determining seasonal indices would be justifiable, instead of using simpler methods that are also easier to understand.
CONCEPT OF SEASONALITY
When analyzing a series of sales data for a product or service, we almost always observe a periodic movement of this series over time. This periodic movement, often associated with the months of the year, characterizes what we call the effect or seasonal component. Practical examples of this type of situation abound: sale of beverages and food, consumption of fuel and electricity, sale of household appliances, hotel occupancy, air traffic, hospital medical care, and most notably, year-end sales.
In fact, in our retail sector, December is the strongest month of the year, with sales usually exceeding the average of the other months of the year by 50% or more. This fluctuation in demand at the end of the process (purchase by the final consumer) generates a wave that propagates throughout the entire logistics chain, with the necessary time lags. For example, for the product to be available for sale during the Christmas season, it must have been produced and delivered to the store well in advance; in turn, your order must have been prepared even earlier, as well as all the inputs of the production/logistics chain must have been properly foreseen.
From the point of view of production and logistics, the ideal world would be one in which the production and demand for a product or service were as stable as possible, thus requiring a minimum of intervention in the process. But, fortunately or unfortunately, the world is never as we would like it to be!
Thus, in our day-to-day activities, not only do we have to deal with the typical uncertainties of an economic environment of a random nature, but we also have to know how to take seasonality into account in our plans and actions. The first issue is how to measure seasonality, best illustrated through an example.
SEASONAL INDEX
The first step in analyzing a series of sales, even before identifying its possible seasonal pattern, is to identify its general behavior. Thus, let's consider the case of a product, whose series of past sales, in units/quarter, is shown in Table 1:
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Before using a quantitative technique in the study of a series of sales like this one, we must represent it in a graph so that we can identify its components. While other components are normally present in a sales series, such as the level and trend of sales, our current concern is with the seasonal component. In this case, it was already known that there was a strong seasonality in sales of the product, a fact confirmed by Graph 1:
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Observing this graph, we notice a regular oscillation movement in sales throughout the year, always with a peak in the first quarter and a low value in the third quarter. Now, this situation, typical of many products and services, necessarily leads to numerous logistical challenges, such as the supply of raw materials that can also have a seasonal supply, the definition of a storage/production policy suited to the costs involved and the characteristics of the situation, a distribution strategy involving logistic operators, distributors and customers and even a pricing policy. For all this preparation to be possible, a way of measuring seasonality is necessary, which is done through the so-called seasonal indices.
In principle, there are two ways to represent a seasonal effect:
- Through an additive component
- Through a multiplicative component
The additive component, as its name indicates, has as its principle the sum (addition) of installments associated with each seasonal period, quarter in this case. The multiplicative component is characterized by the use of a multiplicative factor for each period, usually in the form of a percentage. We will discuss, below, each of these representations, also presenting possible forms of calculation.
ADDITIVE COMPONENT
The additive component (related to the sum or addition operation) is represented by a fixed value for each quarter that is added (or subtracted) to the base value of sales for a given period. So, for example, first quarter sales of a year could be viewed as the year's average sales plus, say, 129 units, while the lower third quarter sales could be viewed as the year's average sales minus 150 units. In the same way, we would have a value to be applied to the other quarters of the year. Based on this formulation, we will consider as an approximation that the effect of the quarter is always the same for each of the quarters of each year. Thus, the first-quarter sales increase is, on average, 129 units, whatever the year considered, while the third-quarter sales are always 150 units below the quarterly average. Whether that's a good description of actual sales is another story, but we're off to a good start anyway!
How then could we calculate this additive seasonal effect?
There is no single way to do it, but a rule to be followed is that the sum of seasonal effects throughout the year is neutral, in this case equal to zero. Having this rule as a basis, a simple way to calculate the seasonal indices for each quarter (without worrying about the trend of the series) would be by calculating the average increase/decrease in sales for each quarter of the year, as exemplified in table 2 :
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In this table, defined by the differences between the sales values for each quarter and the average sales for the respective year, the sum of the values in each column, referring to the same year, is zero. Thus, for the first quarter of 1992, the value 125 indicates that the level of sales in this quarter was 125 units above the average for the year, while the value of –25 for the second quarter tells us that sales for this period were 25 units below the average for the same year. Now, by taking the average of the values for each of the quarters (average of the rows in the table), we will have a good estimate of the additive seasonal effect for each quarter.
Thus, based on the results obtained and assuming that the estimated sales for the next year would average 700 units per quarter, our seasonally adjusted forecast would be 829 (700+129) for the first quarter, 650 (700-50 ) for the second, 550 (700-150) for the third and finally 771 (700+71) for the fourth quarter.
Naturally, the numbers obtained are just forecasts, but duly adjusted to expectations of the expected level of sales and seasonal components. Continuing our analysis, let's now assume that actual sales for the first quarter of next year were 850 units. As this value surpassed our forecasts, we have two possible explanations for the fact: either the level of sales increased or the seasonality was stronger than expected. In any case, this finding was only possible after we had isolated the two sales components: level and seasonality.
But, the presented procedure is not the only way to calculate additive seasonal indices. The statistical theory of forecasts proposes other calculation options that, in general, are highly complex and add little to simpler methods such as the one we have seen here. In fact, although different methodologies provide different results when studying the same series of sales, the values obtained with more sophisticated methods, when applied to this same case, do not differ substantially from those obtained with this simple calculation of averages, which in addition to easier is also more intuitive.
In fact, the main criticism regarding the use of additive components does not reside in the procedure for calculating seasonal indices, but in their practical applicability. There are few real-world situations where a seasonal effect, such as a plot that adds or subtracts each period, is an adequate description of sales behavior. The most intuitive and usual way is to consider seasonality not as an absolute effect that is added or subtracted from sales, but as a multiplicative and relative effect, a percentage that is applied to each specific period, either to increase sales in that period. in relation to the average, or to reduce sales in the period due to a low seasonality. So rather than thinking of a period's sales as 150 more units, it would be better to think of it as, say, 40% above average. It is this idea of multiplicative components that we will discuss below.
MULTIPLICATION COMPONENT
An alternative to additive effects is the use of multiplicative components. In this case, a multiplicative neutral seasonal effect would correspond to a seasonal index equal to 1 (100%), an index greater than 1, say 1.50 (150%), would correspond to a period with seasonality 50% greater than an average month or day. The representation of seasonality as a multiplicative effect is a better way to translate the idea that the seasonality of sales would be an effect proportional to the level of sales, which is the common practice in most companies.
As with the additive component, there is no single way to calculate its values, but the basic rule is also valid that the sum of seasonal effects throughout the year is neutral; in this case, as they are effects that multiply the average level of sales, their average must be equal to 1 so that the seasonal effect over the course of a year is neutralized. Having this principle as a basis, we can calculate the multiplicative seasonal indices for the same data previously studied with the additive model.
In this case, we need a value that serves as a basis for calculating the seasonal effects of each quarter. A good option (there are even better ones!) is to take the ratio of sales for each quarter with the respective average for the year. Table 3 illustrates the application of this idea to our series:
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In this table, defined by dividing the sales values for each quarter by the respective average sales for the same year, the average of the values in each column, referring to the same year, is one (100%). Thus, for the first quarter of 1992, the value 133% indicates that the level of sales in this quarter was 33% above the average for the year, while the value of 93% for the second quarter tells us that sales in this period were 93% of the annual average, that is 7% below this average. Now, as we did in the previous case concerning additive effects, we take the average of the values for each of the quarters (average of the rows in the table). With this, we will have a good estimate of the multiplicative seasonal effect of each quarter.
So, based on the results obtained and assuming that the estimated sales for the next year would again average 700 units per quarter, our seasonally adjusted forecast would be 903 (700*129%) units for the first quarter, 623 ( 700*89%) for the second, 455 (700*65%) for the third and finally 819 (700*117%) for the fourth. Compared to the adjusted values in the additive case, we observe that our forecasts are now more loaded for both the strongest quarters (first quarter) and the weakest quarters (second and third); this is due to the fact that the calculations are made based on the estimated level of sales for the next year which, in this case, is a value above the past average as sales increase over time. Table 4 summarizes this comparison:
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Here again, we will be able to evaluate the result of future sales in relation to what we expected. So a sale of 850 units in the next quarter would be a good result or not? In this case, unlike the additive model, the answer would be no, as we expected a sale of 903 units! Naturally, as we live in a world of uncertainties, a result like this, despite being below expectations, would be absolutely normal due to the random elements present in the business environment.
The use of multiplicative components also has an additional advantage over additive components, as they allow a better comparison of seasonality between different products, different sectors of activity or even different establishments. This comparison would only be possible with the adoption of standardized seasonal indices (with a unit average) throughout the year, otherwise we would not have a common reference base.
Finally, we again have other options for calculating multiplicative seasonal indices such as methods known as classical decomposition or Holt Winters exponential smoothing. Although these methods are more sophisticated and therefore provide more accurate results, their application to our example leads to results very close to those obtained with a simple calculation of averages. And this is an empirical finding that authors of sales forecasting works have reached: in general, relatively simple methods provide results almost as good as more sophisticated methods, often not compensating for the price of greater mathematical complication and difficulty in understanding. .
CONCLUSION
As we have seen, seasonality can be easily quantified either to generate forecasts or to compare results from different periods or different products. With common sense and the correct use of basic statistical concepts such as calculating averages, we can obtain values almost as good as those provided by sophisticated and expensive forecasting software and, even better, we can do such calculations with a simple spreadsheet.
BOX 1
IS IT WORTH USING MORE SOPHISTICATED METHODS TO DETERMINE SEASONAL INDICES?
Although there are always gains in accuracy with the use of more sophisticated methods, practice shows that these gains are often not expressive in order to justify greater statistical complexity, requiring a more in-depth knowledge of forecasting techniques and also the use of more sophisticated software. expensive and difficult. It is clear that in general it is worth using more elaborate methods than those presented here, particularly in the case where forecast errors are costly. This high cost can be generated by the loss resulting from a pessimistic forecast below the actual, when we will often have to bear higher costs to meet sales or even by the loss of sales due to lack of production or service capacity. But we also have the loss resulting from an optimistic forecast above the real when we will have to bear a surplus of products in stock that, in order to be released, will need a substantial discount in prices or even become obsolete in the case of highly perishables or, in the case of services; such as transport, in which our operating capacity will be underutilized with consequent idleness.
BOX 2
FORECAST SOFTWARE
Although there is a recent trend towards integrating forecasting modules into logistics and ERP systems, there are several products on the market that address the forecasting problem. These products are classified into three categories: automatic, semi-automatic and manual. The automatic software, as the name implies, practically alone does the task of analyzing series and recommending the most appropriate forecasting method for the situation under study based on statistical criteria. Although they represent a good option, they tend to be used as black boxes in which the user has little or no possibility of intervening in the process, accepting or rejecting the results. One of the best-known products in this category is the Forecast Pro software (www.forecastpro.com) whose most complete version costs around US$1000,00. Forecast Pro incorporates an expert system for selecting the most appropriate forecasting method for each analyzed series.
Semi-automatic forecasting software are, in principle, statistical software such as SPSS, SAS or econometric software such as EVIEWS. In this case, the user makes a previous selection of the methods to be tested in his problem, leaving the computer to choose the optimal parameters that minimize the prediction error. The choice of the most suitable method is made by the user based on the results of the various tests. Finally, manual software are those in which the user defines the forecast method to be tested and its parameters; the software is used solely to evaluate the performance of the proposed method. In this case, there is a need for greater technical knowledge on the part of the user, but in compensation there is greater control of the forecasting process.
BIBLIOGRAPHY
For a more in-depth study of the determination of seasonal indices as well as forecasting techniques, we indicate three texts, all in English, but easy to read and acquire. A suggestion for acquiring these texts is through electronic bookstores on the Internet, such as Amazon (www.amazon.com)
DeLurgio, SA Forecasting Principles and Applications. New York, McGraw Hill, 1998.
Hanke, JE and Reitsch, A. G. Business Forecasting. 6th Ed., Prentice Hall, 1998
Makridakis, S., Wheelwright, S. and Hyndman, RJ Forecasting: Methods and Applications. 3rd Ed., New York: Wiley, 1998.
Mentzer, J. and Bienstock, C. Sales Forecasting Management. Sage, 1998.
