Improving the Quality of Foreign Military Sales Forecasting Using Benford's Law

Article excerpt


One approach to forecasting future sales might be called the "bottom-up" approach. In general, one tries to forecast the values of all major customers' orders for the upcoming year. Then, these are summed to obtain a forecast for the upcoming year's total sales. This approach can be used in conjunction with other methods, such as examining current sales trends, as part of the overall forecasting process. When using any forecasting method, one needs to understand the quality of the data being used. This paper shows how to use an intriguing mathematical phenomenon called Benford's Law to measure the quality of the data being used for bottom-up forecasting when large numbers of customer orders are expected.

The Bottom-Up Approach to Forecasting

Good forecasts of future sales often can be built by combining the results of several forecasting approaches. One that can be used might be called the "bottom-up" approach. Business-Dictionary. corn (2009) defines a bottom-up sales forecast as a "Method where ... the sales revenue estimates of each product or product line are combined to compute [the] revenue estimate for the entire firm." Suppose an organization has regular customers with whom it has done business over the years and those customers provide a large number of sales contracts having a wide range of dollar values. Historically, on any given year, a few new customers might have entered the market; a few customers might have left the market; but, as a general rule, the organization has a regular clientele. When the organization starts its forecasting process for next year's sales, it might individually meet with its customers to learn what they may desire to buy during that time frame. For example, suppose an interview with Customer A indicates that he or she intends to buy goods and services totaling $1,249,432 on one sales contract, $45,814 on a second sales contract, and $928 on a third sales contract. After the organization meets with each customer and obtains the dollar values for expected sales contracts for the forecast year, the forecaster can then list these sales contracts and their dollar values, add their dollar values, and thereby obtain a forecast for the upcoming year's sales. The dollar value of each sales contract can be considered a data point.

There are many good further discussions regarding bottom-up forecasting. For example, Kahn discusses key advantages and disadvantages of the approach in his 1998 article "Revisiting Top-Down Versus Bottom-Up Forecasting" [Kahn 1998].

There is a possible disadvantage of bottom-up forecasting in this situation. Some customers will perform due diligence and provide very reasonable sales contract dollar values. However, others might dismiss the request from the organization and provide data points of little or no value. The adage "garbage-in-garbage-out" certainly applies here, and the forecaster needs a way to measure the quality of these data points received to ensure that the resulting sales forecast for the upcoming year is of the best quality possible.

One forecasting data point quality measurement system to use is simple--albeit initially a very unusual approach. First, look again at the list of all sales contracts. Examine just the leading (first) digit of each sales contract. Using the example above, we expand the list by adding a third column as shown below; and we would continue the list for all sales contracts.

When the list is complete, determine the percentage of times each leading digit occurs in the list. For example, what percentage of the time does the leading digit "1" occur? If the percentage of occurrence does not coincide with Benford's Law for a certain leading digit, then this is an indicator of defective input quality; the forecaster should look again at all of the data inputs having that leading digit and perhaps re-contact certain associated customers. The question is, what would you expect each percentage to be? …