Whenever I am asked to help somebody figure out a solution to their scheduling problem, the first question I ask is, “How many officers do you have to work with?” I am particularly likely to ask the question when the original question posed to me is, “How can I come up with a 10 hour shift schedule for my department?” If the answer is that the agency has 10-15 full-time officers and wants 10 hour shifts, I have to break the bad news that there is no schedule that makes efficient use of that number of officers working four 10-hour shifts per week.
It is a mathematical fact that large agencies have more scheduling options than small agencies. There are lots of schedules out there (including every 4/10 schedule we’ve ever seen, heard of or dreamed up) that cannot be efficiently staffed with a small number of officers. Let’s look at an example.
The Happycop Police Department (HPD) wants its officers to work four 10 hour shifts per week. Since the taxpaying citizens 0f Happycop expect there to be at least one police officer on the street at all times, HPD has to run three shifts per day–two shifts would leave 4 hours per day uncovered. This means that they have to cover 21 shifts per week. Since each officer works 4 shifts per week, HPD has to hire six officers to cover all of the required shifts (5 officers would cover only 20 of the 21 shifts, leaving one uncovered).
If HPD chose 8 hour shifts, then they would still have to cover 21 shifts per week. However, since each officer work 5 shifts, the department would only have to hire 5 officers to cover all of the shifts. Hiring that 6th officer to accommodate 10 hour shifts represents a 20% increase in the cost of personnel needed to provide patrol coverage for the town.
One way to measure the efficiency (or inefficiency) of a schedule is to figure out how many hours of officer time is necessary to provide the minimum coverage required. In the case of HPD, the mandatory minimum coverage is one officer for the 168 hours of each week. In order to provide that coverage using a 4/10 schedule, the agency must hire 240 hours of officer time. This calculates out to 43% more hours of officer time than the required minimum.
Another way to calculate efficiency is to calculate the ratio of full-time officers to the minimum coverage provided. In the case of HPD, this ratio is 6:1 (six officers to provide minimum coverage of one).
So why doesn’t the same math apply to larger agencies? Larger agencies can run more shifts to mitigate the impact of the overlap inherent in a 4/10 schedule. Let’s consider the situation of BMPD (Big Metropolis Police Department). They run five 10-hour shifts per day. The shifts begin at 2400, 500, 1000, 1400 and 2000. This means that there are at least two shifts working the street at all times. If the coverage goal of BMPD is to have 10 officers on the street at all times, then they can put five officers on each shift, resulting in a need for 25 officer shifts per day (5 officers per shift x 5 shifts) or 175 officer shifts per week.
Since each officer covers 4 shifts per week, it takes 44 officers to provide the required coverage (44 officers x 4 shifts per week = 176 shifts). Now let’s look at how BMPD fares with respect to the efficiency measures we applied earlier to HPD.
BMPD must provide 1,680 hours of coverage per week (168 hours per week x 10 officers). To provide this coverage, they must hire 1,760 hours of officer time (44 officers at 40 hours per week). This represents approximately a 5% excess over the minimum hours needed to provide the coverage. Compare this to the 43% excess experienced by HPD.
Using the second efficiency measure, BMPD requires a 4.4:1 ratio of officers to minimum staffing level. This compares very favorably to the 6:1 ratio required by HPD.
This analysis is based on the assumption that there is a fair, reasonable schedule that will distribute the work days of the officers efficiently across the required shifts. The reality of the situation is that small agencies have less flexibility when it comes to distributing their officers work days across the work week. As a result, it is even more difficult for the small agency to operate a 4/10 efficiently.
There are a couple of important lessons to be learned from these examples.
1. Agency size is a major factor to be considered when designing a schedule.
2. It is hard for small agencies to schedule efficiently.
3. Small agencies should stick to schedules that do not require overlapping shifts. Eight or twelve hour shifts (or a combination of these two) are more efficient.
4. 4/10 schedules are extremely inefficient in small agencies.
5. Larger agencies can operate a 4/10 shift efficiently, but it is necessary to run more than 3 shifts per day. Five shifts per day is optimal, unless your coverage requirements vary substantially during the 24 hour period.