Some time ago, I got a call from the Chief of Police from a small city in the Mid-West. He had 6 officers and needed a minimum of 1-person coverage on a 24/7 basis. Their work schedule consisted of 8-hour fixed shifts. The officers were pretty happy with the schedule since they got every other weekend off. The problem was the high overtime expenses needed to cover vacations and other absences. The officers had an absence rate of almost 20%, which resulted in an overtime bill of around $80K a year. He was thinking about hiring another officer, but couldn't figure out how to use him to cover absences unless it was his full-time job.

I told him that he didn't need to hire more staff'; he needed a different schedule. 8-hour fixed shift schedules are not very efficient, especially in small groups like his. In his case, they would provide 1-person coverage 4 days a week and 2-person coverage 3 days a week. To ensure every other weekend was off, the double coverage was scheduled for weekdays only. Since most absences occurred on the weekends (when they only had 1-person coverage), they were forced to use overtime to avoid gaps in the coverage.

When choosing the best scheduling approach, he and his officers would have to make a tradeoff between shift length and format (fixed vs. rotating shifts) when selecting a new schedule. If having fixed shifts was most important schedule feature, they should adopt a 12-hour fixed shift schedule. If having 8-hour shifts was most important, they should adopt an 8-hour rotating shift schedule. Either approach would free up capacity to cover absences without excessive overtime. Flexible relief time could then be built right into the schedule.

With the12-hour fixed shifts, 3 officers would be assigned to each shift. Each shift would have a 3-week schedule in which one week was devoted to relief coverage and the other two weeks were devoted to the required coverage. They would have to work an average of 42 hours a week. Yes, overtime would be required, but a total of 12 hours per week for the entire group is all they would need. 

With the 8-hour rotating shifts, the 6 officers would work a 6-week schedule in which two weeks were devoted to relief coverage and 4 weeks were devoted to the required coverage. They would also average 42 hours a week.

The Chief said he'd have to think about it. He was hesitant to do this because the city was opposed to having employees work more than 40 hours a week and the officers were opposed to changing schedules. I never heard from him again. I suppose he's still incurring overtime every time someone is absent, having poor coverage, or maybe still searching for ideas on how to fix this. Or maybe he hired another officer. So he is either spending $60K a year for a 7th officer (wages + benefits) or $80K on overtime. What would you do?