It’s a Matter of Time


When performing operations analysis on patrol, one necessary ingredient is an accurate workload assessment. The best work schedule depends on how closely your available patrol units align with the demand for service at any given time. This demand for service is most accurately measured by how much time is dedicated to handling calls. Since the number of calls handled is an easy metric to track, this number is sometimes used to assume a resulting amount of work. Fortunately there are now tools available that show the inadequacy of relying on the quantity of calls for service. The unique circumstances of every response causes significant variance in time required. Using the number of calls can be misleading and should not be the primary measurement.

Fortunately, Computer-aided Dispatch (CAD) Systems provide the capability to accurately track all phases of a response to a call: dispatch time, en-route time, arrive time, and clear time. Using those four time stamps, we are able to asses the two most important pieces of data for analysis- travel time and on-scene time. Knowing how much time elapsed in each of these categories allows us to apply an advanced mathematical relation called a queueing model. This mathematical model asserts that a given quantity of available resources can handle a certain amount of work. Therefore, with a known quantity of work, we can determine how many resources are needed to adequately staff for it.

A problem I have regularly seen when examining data from CAD systems is a lack of arrive and clear time stamps. In an emergency, the officer’s focus is primarily on responding to the scene as quickly as possible to render assistance. Enforcing the requirement that they press a key on their mobile computer or relay to dispatch their arrival is often thought of as a nuisance, and habits may form to avoid it completely. When an arrive or clear time stamp is missing from the record, it is unknown how much time was allocated to that call. Because of this, there are only two options for analysis: assume an amount of time or ignore the time completely.

To highlight this problem, I analyzed a sample of CAD data from 34 police and sheriffs departments. I have not shared the names of the agencies, but they cover agencies with a dozen officers to those with over a thousand. I gathered all events that were classified as citizen-generated and had a significant likelihood that time was actually spent on the event but was missing. This method excluded those where the unit was preempted or cancelled before arriving on scene.

The graph in Figure 1 shows the percentage of missing arrive or clear time stamps. Events may have had an arrival but no clear, or had no arrival but a clear at least 10 minutes later than the en-route time stamp.

Agency 6 shows nearly 25% of their unit responses did not log an arrive time. This means that up to one quarter of their on-scene time is unknown. We know when the unit cleared from the call, but we don’t know how long it took to arrive on the scene and therefore the amount of service time spent handling the event.

Agency 32 shows a different kind of problem. There was an arrival time logged, however there was no clear time. The only choice we have here is to assume a certain amount of time spent on-scene. We have two options here. We guess the amount of time spent on-scene – which could be wildly inaccurate; or, we choose to not include the call in analysis. In order to avoid including guessed data in mathematical analysis, 25% of their unit responses must be completely ignored. The result is a significant under-counting of demand for service. If this was a problem that was evenly distributed at all times, one could just inflate the workload by 25% (my inner-analyst cringes while typing this). However, this type of problem tends to be more prevalent when certain officers or groups of officers are on duty. This is not a technical problem, it is a policy problem.

I would encourage every agency to do a review of their own data to identify if a policy needs to be amended, enforced, or implemented. The accuracy of these time stamps may determine if an officer will have backup or not when in danger.

Figure 1

Written by Dan Harris, President and CTO of Corona Solutions

“You will never have enough officers, and no one else does either.”

Let us assume that a patrol force is authorized 100 patrol officers of 200 total sworn officers. Let us also assume that the agency has an annual turnover rate of ten percent, meaning 20 officers leave the department each year. Agencies should understand the Replacement Cycle concept. In American law enforcement it is typical to have one year pass from the time an officer leaves the department until he/she has been replaced by a trained, capable officer. That year covers the time required for the authorization to hire, the recruiting process, the background investigation, the hiring offer and acceptance, police academy training, and the field training program.

Given the above information, of the 200 authorized officer positions, only 90 percent (180) are filled at any one time. This vacancy rate usually produces another undesirable effect. Agencies usually fill their promoted or specialized positions from the pool of patrol officers. Thus, when a captain retires, they are down a patrol officer. When a detective resigns, they are down another patrol officer. If half of the sworn officer positions are for patrol, then the effective turnover rate is double that of the agency. In our example agency, they can expect to have only 80 patrol officers of the 100 authorized positions. For an agency this size to be “up to staff” is practically impossible. This agency should plan their operations around a staff of 80 officers, not 100. Or, they can begin the hiring process prior to having actual vacancies, preparing themselves for the probable turnover.

This being said, we can help you do more with less.

10-Hour Shifts: Expensive Luxury, or Effective Deployment?

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Long a favorite of shift workers, the 10-hour shift has also frequently been the subject of management complaints about the difficulty of matching on-duty staffing to workload over the 24-hour day and seven-day week. A recent report from the Police Foundation titled The Shift Length Experiment ( has added new empirical evidence to support the staff preferences, but the challenge remains to justify the schedule. We will answer that challenge here.

In order to cover the 24-hour day with 8-hour shifts there must be at least three shifts per day starting eight hours apart. Given that workload varies continuously during the day, and given that with this plan the on-duty staffing can change no more than three times per day, then there must be periods of time when the staffing level is either above or below the demand.

This is a simplified chart of a 24-hour period with three standard 8-hour shifts. Even though the staffing for each shift is optimized to match the demand, there are very few times when the staffing matches the demand. The day shift (0700-1500) is overstaffed at the beginning then significantly understaffed by the end. The evening shift (1500-2300) is seriously understaffed at the beginning, but then overstaffed later. The night shift (2300-0700), like the evening shift, is understaffed at the beginning, and then slightly overstaffed later on.

For this demand profile the obvious resolution would be to add an overlapping, or “cover” shift during the busy periods. However, doing so would not only place more staff than necessary on duty during several hours of that overlap, it would take staff away from other hours when they are needed more.

The 10-hour shift offers one resolution to this problem. Because there are at least 30 shift-hours scheduled per day (3 shifts * 10 hours) there are six hours per day that can be used for overlap(s) during busy times. The six hours of overlap do not have to be consecutive. For example, in the below chart the Day shift works from 0700-1700, the Evening shift 10-hour shift graphworks from 1400-2400, and the Night shift works from 2200-0800. This yields overlaps between 1400-1700 and 2200-2400 which are peak demand periods for this agency. On this chart, note how the total on-duty units closely follows the demand profile. This not only improves efficiency, it also improves officer safety.

A further benefit of the 10-hour plan is that one shift does not end just as the next one begins. Followed strictly on an 8-hour plan there is the strong possibility that no units would be on the street, in their beats, and available to respond to calls that come in at shift change. Most 10-hour plans have at least a one-hour overlap as one shift ends and the next begins. This gives the officers time to fuel their cars, return to the station and complete paperwork without incurring overtime and without leaving the beats unstaffed. For the oncoming shift, there is time for a briefing, preparing the vehicle, and driving to the beat,
available for calls.

The Hidden 7% Bonus
Officers on a 10-hour plan work four shifts per week; those on an 8-hour plan work five. Typically, a police shift begins with a briefing or roll call consuming about 30 minutes before the officer is on the street and ready for calls. There is one hour of breaks during the shift, then the last 30 minutes are consumed by paperwork and other end-of-shift activities. All together two hours out of each shift is lost to active patrol work. For a four-day week, that is eight hours; for a five-day week it is ten. The net gain in patrol time is nearly seven percent. That may not sound like much, but consider if you have 100 patrol officers
this is the equivalent of adding seven more at no cost.

Happier and Healthier Cops
According to the Shift Length Experiment* staff working four 10-hour shifts “averaged significantly more sleep and reported experiencing a better quality of work life than did their peers working 8-hour shifts. And officers working 12-hour shifts experienced greater levels of sleepiness (subjective measure of fatigue) and lower levels of alertness than
those assigned to 8-hour shifts. Importantly, those on 8-hour shifts averaged significantly less sleep per 24-hour period and worked significantly more overtime hours than those on 10- or 12-hour shifts” (abstract p. iv).

Having at least a portion of the weekend off is one of the chief interests we find when we work with agencies across North America. For most agencies, Friday and Saturday nights are busy times for police work, so there is a built-in conflict. 10-hour, 4-day schedules tend to make it more likely that each officer will regularly have at least part of the weekend off.

Most officers commute to work, and driving four times per week is naturally 20% less costly not only in travel expenses, but also in time.

Overall, it appears that 10-hour shifts are beneficial to the officers, management and the community. The essential step in implementing and managing a 10-hour plan is the analysis and optimization. Corona Solutions’ Ops Force Deploy provides schedule optimization to any agency that chooses to participate.

*The Shift Length Experiment, Amendola, Karen L, Police Foundation, 2011. (

About the author, Dale Harris:
Prior to co-founding Corona Solutions, Dale worked in law enforcement for 22 years as a sworn officer then as a crime analyst. For most of his career he was responsible for
operations analysis and scheduling for his department.

New Update for Deploy beta

Today, we introduce the latest update for our beta test version of Ops Force Deploy.  Many improvements to the interface have been made as well as many bugs fixed based on the feedback you have given us.

There are some changes to this version that we expect you will notice:

1. A Calculation Bug: 

In the previous beta release, there was a bug that could cause the “Fit” in Scheduler to change when the workflow was closed and re-opened.  We have addressed this issue and the fit number should now be consistent, but it will be different than the number you had seen in the last release.  This is explained also by #2 and #3 below.

2. An Improvement to the Mathematics

When we first started developing Deploy, we based our calculations on an established queuing model.  Over time, we have found ways to improve its accuracy based on our experience in applying this model to real police operations.  One of the limitations we found with the model is that it did not consider “Response Speed” when calculating “Probability of All Units Busy”.  “Response Time” has always correctly included the “Response Speed”.

When setting Operational Goals or allocating units based on “Probability All Units Busy”, the resulting probability was not influenced by this speed.  The reason this is important to consider is that when units are en-route to an event, they are unable to respond to other events (unless pre-empted by a dispatcher). In simple terms, if they are responding more slowly, it is more likely that all units will be busy.

I am happy to announce that we have enhanced the equations so that “Response Speed” will now directly affect this statistic.  Because of this change, you will likely see an increase in the number of units required to meet this Operational Goal.  Also, your “Fit” in Scheduler will change.  Please do not be alarmed by these changes.

3. “Lost Time” and Fit 

If you have any “lost time” set in your schedule profile for the beginning or ending of shift, the reduction of this time was not affecting your Fit.  We have addressed this issue so that the reduction of staff during their lost time will now be reflected in the Fit number.  The result of this is that your Fit is likely to go *down* vs before.  Since the lost time usually happens during shift overlaps where your schedule is overstaffed, reducing units based on this lost time now helps offset this over-staffing and results in a better fit to your workload.

We know there are still some pending feature requests from our customers and bugs that remain but we hope that you will log in and kindly let us know of any problems you may encounter so we can continue to work towards our next official release.

-Dan Harris, CTO