In many call centres there is a surprising degree of consistency across a week: most Sundays occupy the same proportion of the week’s volume as all the other Sundays, most Mondays occupy the same proportion of the week’s volume as all the other Mondays,… and so on.

If you find there isn’t a great amount of consistency, it’s usually because of a particular customer touch-point or some other anomaly such as public holidays. In that case, you ought to be able to extract these aberrations from the data to leave underlying day-of-week distributions generally consistent from one week to another. You would obviously need to re-introduce the variances back into the forecast later on.

For example, if you only bill your customers all on the same day once per month then it’s likely that your call distribution will be spiked by billing calls. Sending them out on, say, the 10^{th} of every month could mean a busy Tuesday this month or a busy Friday next month. Being so obvious, it ought to be possible to extract these spikes out of the data to leave the underlying, non-billing calls behind. At the end of the process, you’ll want to re-introduce the billing response into your shaped forecast. Similarly, if your call centre was to take bets on horse races then you would have volume heavily skewed towards the larger race meetings. Again, it should be possible to extract these deviations from the underlying volume ready to add back in later on.

We’ll now assume that your data has a pretty consistent distribution from Sunday to Saturday.

Suppose we take the same data as we had before, but now divide by the day-of-week distribution, effectively taking out the impact of days of the week from our historical data. We would then have the imaginary monthly call volume as if every day of the week were the same. Now we can line the data up by 1^{st}, 2^{nd}, 3^{rd} of the month rather than worry about the day of the week. This would highlight any genuine intra-month shape independent of the day of the week.

The same data as before now reveals an underlying monthly “shape” as follows, where the red line is the simple average of the other lines:

Using Excel, you can add a trendline (e.g. 6-order polynomial) to smooth out the irregularities and provide a mathematical formula describing the curve. If you get your old textbooks out on how to build polynomials you should find that you can derive the formulae in the spreadsheets making them dynamic as more data becomes available.

Now, with our improved underlying monthly shape, and re-applying the day-of-week distribution, we apply adjustments for weekends, public holidays and special events and end up with what is typically a very robust daily forecast (again, dependent on your initial monthly forecast).

There is just one last thing to consider. If your underlying drivers (e.g. customer numbers) are driving your monthly call volume up or down month on month, you might need to add some “slope” to your underlying monthly shape to make sure the weekly levels are consistently correct across the whole month.