New Developments in Business Forecasting

Abstract

A SIMPLE VIEW OF TOP-DOWN VERSUS BOTTOM-UP FORECASTING (This is an ongoing column in The Journal which is intended to give a brief view on a potential topic of interest to practitioners of business forecasting. Suggestions on topics should be made via email to llapide@amrrsearch. Ed) Over time I have noted a few published papers that dealt with the topic of whether top-down or bottom-up forecasting was preferable and when. None of them seems to provide simple guidelines that forecast practitioners can understand and use on an everyday basis. When asked about which approach works best, my simple answer had always been to use a combination: start with bottom-up forecasting followed by top-down; with sometimes even middle-upand-down forecasting. This is especially the case in operational demand forecasting where having to forecast tens or hundreds of thousands of elements much of the forecasting has to be automated. One does not have the luxury to spend a lot of time worrying about or investigating whether and when each approach should be used. Also, since operational forecasts will invariably be adjusted by different participants during the forecasting process, the forecasts have a good chance of being adjusted top-tobottom and in-between anyway! WHAT ARE TOP-DOWN AND BOTTOM-UP FORECASTING? Figure 1 depicts the difference between bottom-up and top-down forecasting using an example where an item group is composed of three items. In top-down forecasting, a forecast is made for the group, which is then broken down into the lower-level item forecasts. In bottom-up forecasting, each of the lower-level items is separately forecast and the forecasts are then summed up to provide a forecast for the group. These forecast approaches are useful when forecasting based on hierarchical levels along specific dimensions; where higherlevel aggregated variables along a dimension are the sum of lower-level disaggregated variables, within the same dimension. Examples of these dimensions and levels are: Business unit dimension: company comprised of business divisions or units Product dimension: brand or product group comprised of items, products or stock-keeping-units Geographic dimension: country comprised of sales regions, districts or territories Operational dimension: plant/distribution center comprised of customer ship-to locations Time dimension: year comprised of quarters, months, weeks and days In top-down forecasting several methods can be used to break down the top-level forecast to allocate it to each of its components. These methods include: An equal share across all components Component shares based on historical demand represented by each of the components Component shares based on forecast demand represented by each of the components Obviously, for the last method, a forecast for each component is needed. Hence, it is really bottom-up forecasting since a lowerlevel forecast would have to precede the topdown allocation. WHY IS TOP-DOWN APPEALING? The top-down approach to demand forecasting is appealing because it is generally believed that the percentage variations for demand made up of components will be lower than those of the individual items. This is predicated on what is taught in statistics courses about the standard deviation of a mathematical sum of equally distributed independent variables. The standard deviation of the sum of independent variables is the square root of the sum of the variances. Thus, the relative standard deviation of the sum turns out to be less than the relative standard deviation of the variables. This can also be explained as being the result of compensating errors. The random variations of the individual components tend to cancel each other out when aggregated together -- resulting in a 'smoother' aggregate variable. BOTTOM-UP IS USUALLY PREFERABLE TO TOP-DOWN While it is generally true that the relative forecast error for a sum of demand components will be less than the relative forecast errors of the individual components, this does not lead to top-down being betterespecially in operational forecasting. …

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