Police Scheduling - A Unique Challenge

The following question was posed regarding rotating 12-hour shifts:

 I was wondering based on the sample schedule you posted how you handle the problem of rotating shift.  If we look at officer 12 night shift and he has to be moved to a dayshift (nature of rotating shifts), how do you stop him from going from a night shift directly into a 24hour work period.  If he rotates with another shift then he will go from one short week to another short week. The following schedule shows the solution:

There are a couple of items to note.  Groups One and Three transition between shifts during the three-day off duty period that runs from Saturday through Monday, while Groups Two and Four transition between shifts during the two-day off duty period between Monday and Thursday.

 When you schedule this out, you get the following results.


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The question was posed, “What would you recommend for twelve street officers wanting to work twelve hour shifts, when the city does not want overtime used?”

Fortunately, there is a very straightforward solution to this scheduling problem that highlights some basic principles of 12 hour schedules. The graphic below shows the recommended schedule to address this problem.  We’ll explore some of the key ideas behind it.

1.  Officers are paired off with opposing schedules, i.e., when one officer is
     working, the other is off and vice-versa.
2. Every officer has a designated “Short Day” when he/she works
     only 8 hours instead of 12.
3. Officers are allocated to the two shifts according to need. In this case,
     they are evenly split between the day shift and night shift.  Just be
     sure that when you move officers between shifts you move both officers in a
     pair (see item 1 above).
4. Officers’ short days are spread around the week so that no single day is
     too short during the 4 hours of the shift they are not covering.

The start and end times of the shifts are completely discretionary. Many agencies use 6:00 - 18:00 and 18:00 - 6:00 because this aligns with daily fluctuations in activity, but this varies from agency to agency.  Another thing to keep in mind is that you can schedule the 8 hour short shift for any time during the normal 12 hour shift (beginning, middle or end), depending on your needs.

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.

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.

How can I find or figure out a schedule that works for my agency? 

This is, of course, the $64,000 question when it comes to scheduling in a 24/7 environment, and, unfortunately, there is no “one-size-fits-all” answer.  Finding the right schedule for your agency is a matter of making a series of informed tradeoffs based on a large number of factors.

This posting and many future postings will examine the tradeoffs involved in finding a schedule that works for you.   Among the factors that you need to consider are: 

• Who are you most concerned about keeping happy, your employees or your city’s budget office?

Ideally, you would come up with a schedule that will make everyone happy.   That may be possible, but there is almost certainly going to have to be some sort of compromise between the budget and employee morale.   It is important to decide up front what the limits are on the budgetary side so that you can know how far you can go when considering other factors.

• What are your coverage goals?

It is always better to figure out what you are hoping to accomplish, rather than try a bunch of schedules and see what you get.  You can base your coverage goals on a wide variety of factors, both quantitative and qualitative.  For example, if you have calls-for-service data that shows when your officers are busiest responding to calls, you can decide to provide more coverage during busy times and less coverage during quiet times. If you think that you need high visibility on the street during certain hours or on certain days of the week, then you can consider this when establishing coverage goals.

• How “fair” do you want the schedule to be, and what is your definition of “fair”? 

Most agencies strive to be fair to their employees, but not everyone agrees on what it means to be fair.  For example, is it fair that employees with more seniority get better schedules than new hires?  Does being fair mean that everyone gets a chance to have weekends off from time to time?  Does being fair mean that everyone moves from shift to shift periodically?  Sometimes, being completely evenhanded and fair requires the agency to sacrifice its coverage goals or has a negative impact on the budget.  Sometimes, you can make your employees’ lives overly complicated by too frequent shift rotations or day-off rotations.

• How do you like to handle training?    

Training consumes valuable work hours that cannot be allocated to day-to-day duties of your employees. Every scheduling process should consider how training will impact staffing levels.  Conversely, every scheduling process should consider how maintaining minimum staffing levels will impact your ability to train, particularly when you are trying to train large groups of employees.

• How long a day can you tolerate?

There is constant debate about the merits and demerits of a 12 hour workday.  Each agency has to decide how long is too long when it comes to setting the length of your employees’ work day.   Some agencies believe that 12 hours is too long for an employee to function at peak levels. Others believe the same about 10 hour shifts.  On the other hand, some agencies routinely schedule all or some of their employees to work double 8-hour shifts.  In order to save yourself a lot of wasted time while developing a schedule, it is better to decide up front what your maximum hours per work day will be.

This is only the beginning. There are numerous other factors that will be identified in future
posts.  Once I’ve summarized the different factors, I will start exploring each one in detail.   I will also be posting analysis of various schedules that we have seen or developed, showing how the various factors are weighed against one another.

Please feel free to post comments if there is something you want me to cover or if you have reactions to what I’ve posted.

 Stay tuned…