COMPARISON BETWEEN TOP-DOWN AND BOTTOM-UP APPROACHES FOR SALES FORECAST

Sales forecasting plays a very important role in the planning and coordination of information flows and physical products in a company, having relevant impacts on marketing management, production scheduling and control, logistical operations and capacity planning decisions. of the facilities.

The imperative for cost reduction and advances in information technology made companies seek to improve their methods and integration of sales forecasting processes, which, until then, was carried out by each area of ​​the company separately, which, almost always resulted in a loss of accuracy and increased inventory levels.

The increase in complexity in logistics systems, with the multiplication of points of sale, an increase in the number of production and storage sites and a reduction in the life cycle and proliferation of products, resulted in an increase in the difficulty of making sales forecasts. Retail companies, for example, need to perform forecasts for thousands of different items across hundreds of points of sale. These forecasts generally have low accuracy, which results in stockouts for some products and excessive inventory levels for others. There are two approaches for carrying out the sales forecast in these cases: Top-Down or Bottom-Up.

The Top-Down approach consists of making sales forecasts for consolidated series, that is, the forecast is made for aggregated sales of several products or several regions. In the Top-Down approach, also known as the analytical approach, the sales forecast is made for groups or families of products and then disaggregated for each item, according to the historical percentage of sales. It is also possible to make an aggregate forecast for a region and then decompose it into forecasts for the different locations that make up this region, according to their historical representativeness. Figure 1 shows a very common example of the Top-Down approach in the non-durable consumer goods industries: the company forecasts the sales of a certain product based on historical data of total sales and, subsequently, decides the volume to will be sent to each distribution center, according to their representativeness (in %).

Figure 1 – Example of Top-Down Approach

In the Bottom-Up approach, the forecast is performed directly for each item or for each location and, later, aggregated by family/group of products or by regions. Figure 2 presents an example of the Bottom-Up approach. In this case, the distribution centers have the autonomy to carry out the sales forecast for a given product, which is then sent to the factory and consolidated to generate production and shipping orders.

Figure 2 – Example of Bottom-Up Approach

The choice of one or another approach for realizing the sales forecast has operational and strategic impacts for the company. In general, companies opt for the strategy that minimizes the forecast error, but other factors are also taken into account, such as the implementation and operation costs of the method. The decision, therefore, which approach to choose is of great importance for a large number of companies, with emphasis on large retail, distribution and production companies of non-durable consumer goods. Some comparisons between the two approaches will be presented below, with regard to implementation and operation costs and accuracy.
IMPLEMENTATION AND OPERATION COST

With regard to costs, the main argument of advocates of the Top-Down approach is that storing information and making sales forecasts for thousands of items is very expensive. In this way, the Bottom-Up approach would be much more expensive in terms of: (a) data storage, (b) time required for calculation and (c) use of computational resources. However, some studies (Schwarzkopf, Tersine and Morris, 1988) show that there is no significant difference, in terms of cost, between the two approaches.

To compare costs between the Top-Down and Bottom-Up approaches, the quantitative method of simple exponential smoothing was used to carry out the forecasts, as this is a method widely used to calculate the forecast of future values ​​in relatively short series. stable, that is, series without seasonality and without trend. In this method, the sales forecast is calculated based on three parameters: prior period actual sales (Rt-1), prior period sales forecast (Pt-1) and the smoothing constant (a).

Equation 1 - Formula for calculating the Simple Exponential Damping

(a) Data Storage

The cost of data storage can be calculated by the cost of storage space and the effort required to keep the data up to date. In most information systems, the effort to update information is more important than the cost of storage space, as it involves both systems and people.

The cost of storage space is calculated based on the amount of information that is stored. In the Top-Down approach, to carry out the sales forecast, using the simple exponential smoothing method, for each item of a given product family, information on the total sales of this product family in the last period is required, the sales forecast totals for the last period and the representativeness of each item in relation to the total sales of the family. To obtain this historical representativeness, however, all information on the sales of each item in previous periods is necessary. In the Bottom-Up approach, to perform the same sales forecast, only the last period's sales information is needed. Thus, in general, the Bottom-Up approach requires less stored data to perform the forecast.

In addition to the amount of information that is stored so that sales forecasting can be carried out, another relevant dimension is the frequency with which this data is used. In the Bottom-Up approach, in all periods it is necessary to retrieve the sales and forecast information for the previous period of each item, that is, the information is updated in each period in order to obtain a new forecast. In the Top-Down approach, in general, there is no need to review the percentage of participation of each item in each period, since these percentages tend to remain relatively stable over time. The review of these percentages can, for example, be carried out annually. Thus, the only information to be updated periodically is the total sales and sales forecast for the product family. Thus, in general, the Top-Down approach requires less effort to update the parameters. However, when the representativeness series (in %) of each product are unstable, am
Both approaches require essentially the same maintenance effort.

Table 1 shows the differences between the approaches, in relation to the cost of data storage, indicating the one with the lowest cost. These differences are influenced by the characteristics of the sales series.

Table 1 - Comparison of data storage cost (lowest cost)

(b) Time Required for Calculation

Another cost measure for a sales forecasting system is the time required for the calculation, which can be measured by the number of mathematical operations performed to arrive at the sales forecast for each item.

In the Top-Down approach, the calculations for obtaining the sales forecast for each item would be:

(1) Calculate the product family sales forecast:

In this calculation we would have two multiplications and one addition, totaling three mathematical operations.(2) Multiply the sales forecast for the product family by the historical representativeness (in %) of each item:

In this calculation we would have a multiplication for each item that makes up the product family.

Thus, in the Top-Down approach, we have 3+N mathematical operations, where N is the number of items in the product family.

In the Bottom-Up approach, the calculations to obtain the sales forecast for each item would be:

(1) Calculate the sales forecast for each item:

In this calculation we would have two multiplications and one addition, totaling three mathematical operations for each item.

Thus, in the Bottom-Up approach, we have 3N mathematical operations, where N is the number of items in the product family.

Thus, when there is no need to constantly update the representativeness of each item, the Top-Down approach has a certain advantage. However, if it were necessary to periodically update the historical representativeness of each product, the number of mathematical operations to be carried out to obtain the sales forecast would be practically the same in both approaches. Note in Table 2 the comparison between the approaches.

Table 2 - Comparison of Required Time for Calculation (shorter time)

(c) Use of Computing Resources

The use of computational resources can be measured by accesses to the computer's hard disk. However, as it is difficult to assess the value of a hard disk access, the general rule follows that the difference between the two approaches lies in the fact that, as discussed earlier, in the Bottom-Up approach it is necessary to access a number information and, therefore, this approach requires a greater use of computational resources.

Despite the apparent differences between the Top-Down and Bottom-Up approaches, with regard to implementation and operation costs, Schwarzkopf, Tersine and Morris (1988) show through simulation that, in practice, these differences are not significant. They simulated forecasts for a set of 10.000 different items, including seasonal variations and trends in sales series, and found identical results for data storage costs and computer system usage in both approaches. The only difference found in the simulation was the time required for the calculation, which in the Top-Down approach was 4 seconds faster, which means that if the time for this operation cost R$1.000,00, the difference would be R$1,11 ,XNUMX.

The increased complexity of forecasts and the organizational structure of the company can influence the costs of each approach. However, as a general conclusion, it can be said that there are no significant cost differences between the Top-Down and Bottom-Up approaches for forecasting sales of individual items. The choice of methodology should be influenced by other factors, such as forecast accuracy.

ACCURACY OF SALES FORECAST

The measurement of accuracy is quite complex and must take into account, in addition to (a) the accuracy of the sales forecast, (b) the biases and (c) the robustness of the approach. In order to examine the performance of the Top-Down and Bottom-Up approaches on these factors, a specific method for performing the sales forecast will not be chosen. The choice and application of a forecasting method can make the analysis very complex and divert attention from the objective of comparing the accuracy of the approaches.

(the accuracy

The accuracy of the sales forecast is measured by the variability of the estimated values ​​in relation to the observed values. In other words, the accuracy of a sales forecasting approach is measured by the size of the error, that is, how different the observed values ​​are from the predicted values. The error is defined as the average of the squared difference between the estimates and the real values, being calculated by the variance (Var) of these values. Supporters of the Top-Down approach, based on the statistical principle that suggests that a series formed by the sum of several items is less variable than the series of individual items, claim that this would be inherently more accurate than the Bottom-Up approach.

The problem with this analysis lies in the fact that it does not consider a correlation between the series of sales of the two products. In most real cases, however, there is a positive or negative correlation between the sales of a family's products. For example, the increase in sales of a particular product can leverage sales of the entire product family of which it is a part. In this case, there is a positive correlation between the sales series. On the other hand, an increase in sales of a given product may decrease sales of a related product from the same family. The launch of a new package (new SKU – stock keeping unit) or the increase in advertising of an item can make consumers start to prefer this new item or the product in greater evidence to the detriment of another previously consumed product from the same family and , consequently, from the same company. This process is called “cannibalization” (or portfolio effect) and indicates a negative correlation between sales series.

For practical purposes, this means that the consolidated sales series of a product family with a strong positive correlation between its items will have a greater variance than the sum of the variances of the sales series for each item. Thus, the forecast error calculated by the Top-Down approach will be greater than the error of the Bottom-Up approach. In the case of a strong negative correlation, the inverse effect will be observed and the Top-Down approach will have advantages over the Bottom-Up approach. Table 3 shows the calculated variance for product sales series with positive and negative correlation.

Table 3 - Portfolio Effect

The effect of correlations between the series of sales of a company's products must be carefully studied, since, as seen in the example above, they have a great influence on the decision of which approach to adopt to carry out the sales forecast. Other studies (Gordon, Morris and Dangerfield, 1997) compared the two approaches, using different quantitative and qualitative methods and varying the characteristics of the sales series, and found similar results, that is, regardless of the method used to calculate the sales forecast, the Bottom-Up approach presents better results for positively correlated series and the Top-Down approach for negatively correlated series.

(b) biases

Evaluating only the accuracy of approach (a), other important factors of sales forecast accuracy are disregarded, such as the impact of biases (b) on product sales forecasts. Bias is a constant deviation (positive or negative) of the sales forecast from actual sales, caused by the inaccuracy of the sales forecasting method. The existence of biases is quite common in sales forecasts, since the methods are not exact and they are frequently influenced by optimistic or pessimistic judgments.

In the Bottom-Up approach, as the forecast is performed for each product, the bias in one of the series does not interfere with the accuracy, as the individual modeling process of each series eliminates the bias. In the Top-Down approach, the bias will have a negative impact on accuracy, as it will be incorrectly distributed among the forecasts for each item.

Thus, in addition to the error component related to accuracy, there is another error component that refers to the sales forecast model. In practice, it is necessary to assess whether this component plays a significant role that can change the decision of which approach to use for the accuracy criterion.

(c) Robustness

The robustness of an approach can be gauged by the influence of problematic or inadequate data on sales series. Statisticians believe that models based on aggregated data (Top-Down) are more robust, as models based on non-aggregated data (Bottom-Up) tend to be more sensitive to outliers in the sample.

In short, there are three dimensions of error that must be included in the process of choosing the approach to be used to perform sales forecasting: accuracy, biases and sensitivity to wrong data (influence of outliers). The Top-Down and Bottom-Up approaches behave differently in each of these dimensions, which makes the decision-making process of choosing the approach to be used quite complex.

The results suggest that the Top-Down approach reduces the effects of random error and the influence of outliers on the sales series, thus being more robust than the Bottom-Up approach. However, the latter behaves better against the effect of biases. Furthermore, the Top-Down approach introduces a complex interaction between the effects caused by biases and outliers in sales.

Regarding the accuracy of each approach, we can conclude that there are significant differences. The decision of which approach to use, however, depends a lot on the behavior of the sales series. Correlation between products, existence of biases and outliers and representativeness of each product will determine which approach should be used. In general, empirical studies indicate that the variable with the greatest impact on error and, therefore, the most important for the analysis, is precision. The existence of a positive or negative correlation (portfolio effect) between products, as shown in Table 3, has a strong impact on the decision of which approach should be used.

Positive correlations are found, for example, in products that follow the same seasonal variations. Negative correlations are often found in variations (size, packaging or model) of the same product. For example, sales of fans and air conditioners follow the same seasonal pattern, influenced by climatic factors, and show a strong positive correlation. The sales forecast must therefore be carried out separately (Bottom-Up). Among ventilators, there are several different models and, although sales follow seasonal effects, sales of each model are influenced by other factors, with “cannibalization” of sales between models. In this case, it will be more efficient to make an aggregate forecast for the entire family of fans and then disaggregate this forecast by the historical representativeness of each model (Top-Down).

CONCLUSION

As analyzed, there are positive and negative aspects in each of the approaches. The comparison between the Top-Down and Bottom-Up approaches shows that there is room for using both. While a Top-Down forecast can be more accurate, individual item forecasts can help identify demand patterns. Therefore, they are not mutually exclusive and can be used in combination, in a hybrid model.

If the company uses sales forecasting to develop strategic plans and decide budgets, the Top-Down approach may be preferred. On the other hand, if sales forecasting is used to organize production and distribution schedules, the Bottom-Up approach is likely to be chosen. In this way, the choice of approach depends, in addition to the behavior of the data, on the objectives of using the forecast by the company.

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