Police Scheduling - A Unique Challenge

I received an inquiry from a police chief who wants some ideas about how to schedule his 7 officers so that they have weekends off periodically.   He also wanted to make sure that the schedule was not too hard on the employees with respect to shift changes and other factors.  The department works 8 hour shifts.

There are a lot of solutions, all of which involve tradeoffs.  To get something (like occasional weekends off), employees have to give something up (like never working too many days in a row or never having to return to work after only one day off).

The most fair way to schedule officers in a rotation is to develop a schedule where every officer works the exact same schedule, but at any given moment, each officer is at a different point in the schedule.  The trick to this sort of schedule is to make sure that the number of officers on the schedule can be divided evenly by the number of weeks in the schedule.  For example, if you have 14 officers, you should consider a 7 week cycle.  If you have 12 officers, you should consider either a 6 week cycle or a 4 week cycle.

In the case of the agency who asked the question, there are 7 officers, and the most efficient way to rotate them is to set up a 7 week rotation.  By doing so, we can minimize the variability of coverage for each day and shift.

The following graphic shows 2 possible solutions to this scheduling dilemma.  Each officer’s schedule would follow the exact same pattern.  The only difference among the officers would be which week of the schedule they were working at any given time.  By staggering the start days of the cycle by one week for each officer, you would achieve a balanced schedule.

Let’s look at these two potential solutions.

In these examples, the letters in the green boxes indicate the shift that an officer is working on that day of the schedule.  D = Day, E = Evening and N = Night.  A red cell with an ‘x’ indicates a day off.  It is assumed that the Night shift is the last shift of the day.  This is important because one of the issues addressed by the design of the schedule is avoiding any consecutive shifts worked and avoiding unpleasant transitions from shift to shift.  For this reason, any shift transitions that occur between consecutive workdays are always pushed forward (to a shift later in the day).

Each of these schedules provides a minimum of one officer on each shift at all times and never more than two on a shift at the same time. 

The basic approach on the first example is to rotate the days off forward a day each week.  This results in some positive and some negative results.  On the positive side, officers have two three-day weekends every seven weeks (one starting on Friday and one starting on Saturday).  On the negative side, officers work 6 consecutive days five times during the cycle and only have one stint of 5 consecutive days.

The basic approach in the second example is to rotate the days off back a day each week.  As with the first example, this has both positive and negative consequences.  On the positive side, the officers never work more than 5 consecutive days, and they have a number of stretches where they work only 4 consecutive days.  On the negative side, the officers never have a 3 day weekend, they only get one full weekend (Sat & Sun) off every 7 weeks, and they have several stretches where they get only a single day off and then go back to work for 4 or 5 days.

These two examples are certainly both viable schedules, but they also illustrate the difficult tradeoffs that are inevitable when developing rotating schedules.  There is always a tradeoff between too many workdays in a row and too few days off in a row.  There is no solution that doesn’t force you to endure one or the other of these drawbacks.

If you have any comments or suggestions regarding other solutions to this scheduling problem, please leave a comment on this post.