Experienced supervisors, generally speaking, do a good job scheduling their staff to meet demand. They are good at predicting when they need more or fewer staff. Many, unfortunately, may be tempted to overstaff to meet all demand at all time.
In queueing theory, having no wait time for customers means having overcapacity (a.k.a. waste). In most non-life-threatening situations, it is OK to have wait times, as long as they’re not excessive. So how do you achieve that balance?
If you’re looking at staffing levels in a department (say ED), then you need to look at historical customer demand. In this case it is represented by the ED patient arrival pattern (i.e., average number of patients arriving for each hour) for each day of the week. This allows you to take into account the differences between days, including weekends and weekdays.
In this example, the patient arrival pattern is typical of that found in a mid-sized emergency department. As you can see, the staffing pattern does not match the demand pattern, so the staff schedules should be adjusted to match the demand (similar shape).
This graph would need to be recreated for each day of the week (or you can combine Mondays through Thursdays, and create a separate one for Fridays, Saturdays, and Sundays – the reason is that Mondays through Thursdays often have similar patterns).
This example is basic, but it can be refined in several ways, including by reducing the arrival calculation from hourly to 15-minute increments, and calculating the minimum and maximum number of patients arriving in each increment. The latter allows you to create a band surrounding the line which represents the range of arrivals. You can also refine it by breaking the annual data into quarterly chunks, to account for seasonality.
You can also calculate how many staff you need if you know how many patients one staff member can serve each hour. If doing that, you may want to consider using in your calculations the average number of patients arriving each hour plus 1 standard deviation. This gives you a small buffer to accommodate the times when more patients than average arrive. Basically, erring slightly on the side of overstaffing.
One thing to keep in mind is that there is always an element of guessing when doing staff schedules. Spreadsheets and historical data analysis are only tools that need to be supplemented with input from experienced supervisory staff. Never take the human input out of your analysis.