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• Ger Koole PhD

# What is the best achievable forecast accuracy?

Updated: Feb 7, 2022 The WFM cycle starts with workload forecasting. A good forecast is the first step in good WFM: if the forecast is accurate, little real-time adaptations have to be done to the schedule. First, of course, we want an accurate daily forecast, but we need the forecast at the interval (often 15 minutes) level because the correct number of agents should be there at every moment of the day.

We define forecast (FC) accuracy as the relative (percentage-wise) difference between forecast and actual. Therefore, 5% FC accuracy is often used as a target. Of course, everybody understands that exceptions happen, but we would like to stick to the 5% accuracy as much as possible. Thus a target of achieving an accuracy of 5% or better in 90% of the intervals is quickly formulated. But how realistic is this target? To answer this, we have to dive into the nature of call arrival processes.

Call volume is determined by many factors, such as day of the week, holidays, the weather, campaigns, and so forth. But in the end, it is the customer who calls, and we cannot precisely predict every individual customer's behavior. Thus, no matter how good we are at forecasting, there will always be some remaining "noise." That noise is quantified by what we call the Poisson distribution, named after a famous French mathematician from around 1800. Without going into the mathematical details, it amounts to the following. When the FC is x, then the deviation from x will be in around 30% of the cases bigger than √x and in 0,3% of the cases even bigger than 3√x, just because of the Poisson noise.

An example: Suppose we have a quarter with a FC of 100. We follow the rule: in 30% of the cases, the error is more than √100 = 10, thus below 90 or above 110. 10 of 100 is 10%, therefore in 30% of the cases, the deviation is more than 10%, just because of the Poisson noise. Any FC error that is made will make the deviation bigger, it is the minimal error. A 5% FC accuracy in 90% of the intervals is unachievable in such a situation, it does not consider the unpredictable fluctuations.

The situation is very different when we look at daily totals. Suppose that the daily volume is 10000. Only in 0,3% of the cases, the deviation is bigger than 3√10000 = 300, only 3% of 10000. The probability of a deviation of 5% is even smaller than 0,3%. Here Poisson noise plays hardly a role, and a 5% accuracy seems like a fair objective. How ambitious this objective depends on the fluctuations in volume, but the effect of the Poisson noise is only in the tenths of percentages.

We see how Poisson noise can play a significant role in forecasting small volumes and that it is impossible in such a situation to obtain highly accurate forecasts. However, this plays less of a role when the volume is bigger, and we can expect a higher forecasting accuracy.

My book " Call center optimization " offers more information on call arrival processes, Poisson noise, and forecasting can be found in my book "Call center optimization."