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Operational Research

You can always be more efficient

Operational Research is all about using analysis to improve decision making. Dr Angela Moore uses mathematical modeling, statistical analysis, optimisation, sequencing and scheduling techniques to create simple heuristics you can employ to run your operation more efficiently.

Cover Shifts

 Most absence arrangements use cover shifts, in one form or another. Cover shifts are shifts which are there to cover for absence. They are a way of using Banked Hours in an orderly manner or for ensuring that overtime payments for cover work is fairly distributed. If you do not use a cover arrangement then the result is invariably chaos at times.

Cover shifts can either cover a specific shift or numerous shifts. They can be of a set length, or variable. They can have a requirement that the person comes into work for a nominal time and if not needed leaves, or they are at home unless called in. The circumstances will dictate the cover shifts used.

How many cover shift do you need?Absence table v2

We are often asked how many cover shifts should be scheduled each day. Well that depends on four factors, absence rate, number on shift, number of shifts and ability to run short.

Here is an example, your absence rate is 3%, and you work 12-hour shifts, with three shifts per day and have 12 on shift. Each cover shift can cover all three shifts. (The shifts do overlap) E.g. if there is an absence on the early shift the cover shift, can work it. If there is an absence on the late shift, the cover shift can work it, or if there is an absence on the night shift, the cover shift can work it. But the cover shift can only work one of the shifts.

Therefore the expectation is that on each day 1.08 (12x3x0.03) people will be absent. So most managers would schedule two cover shifts per day. Is this correct?

Let’s look at the probabilities of absence. You need either a brilliant mathematician or our e-book, Understanding Your Absence Rate. Here is an extract of the book on the right.


This shows that given three shifts per day, with an absence rate of 3% and 12 on shift you would look at the table for 365 days and 36 on each day. (The cover shifts can cover all three shifts so you look at what the cover shifts can cover not each individual shift). Therefore on 126 days, no one is absent, on 136 days one person is absent, on 72 days two people are absent, on 24 days three people are absent, on six days four people are absent and on one day per year five people will be absent.

Now knowing this, how many would you schedule to be on cover?

Well this will depend on your operation and the cost of running short. If the cost of running one person short for one shift either meant putting lives at risk or a high penalty then you would opt for five on cover each day. Most operations would look at the cost of bringing an extra person in against the potential benefits.

Let’s say that it’s a holidays included operation (just so that I can ignore the holiday complication) and there are 90 people on the shift pattern. Now we can use these probabilities to calculate the number of cover shifts each would have to work, the number of cover shifts they would be scheduled to cover and the probabilities of being called in.


Average number of cover shifts

Probability of working cover shift

Probability of running short

Number of missing people

1 cover shift





2 cover shifts





3 cover shifts





4 cover shifts





5 cover shifts





The table shows that if there was one cover shift scheduled per day, then on average each person would be scheduled to be on cover four times per year. On each cover shift they would have a 65% probability of being called in. This would mean that on 28% of the shifts you would be running short. During the course of the year you would expect to be running short by 142 people or 1,704 man-hours per year. That is on 72 days you would be short by one person, on 24 days you would be short by two people, on six days you would be short by three people and on one day per year, you would be short by four people.

Knowing these values how many would you have on cover?

Let’s put in some costs. If each person earns £10 per hour, but on cover they earn £15 per cover shift (time and a half), but the unions also don’t want their members waiting around at home so they are on cover but not called in it costs £5 per shift as a good will gesture. Now let’s assume that we can estimate the cost of one person missing per shift, and we set it at a cost of £500 to the company per shift. (Yes I know complete fabrication, but this is to make it simple.)

So using the table above, having no one on cover would cost, £500x1.08x365=£197,100, one person on cover will cost £15x12x239+£5x126+£500x142=£114,650. So one person on cover has saved the operation £82,450 per year. If two people are on cover per day it will cost £15x12x280+£5x388+£500x39=£71,840. If three people are on cover per day, it will cost, £15x12x352+£5x722+£500x8=£70,970. If four people are on cover per day it will cost, £15x12x376+£5x1084+£500x1=£73,600.

The costs are starting to rise now, so the optimal number would be three on cover per day. So having no cover arrangement would have cost £197,100 per year. Having three people per day on cover would cost £70,970 per year. That is a saving of £126,130 per year.

If you would like to know how many you should have cover per day, please contact us at This e-mail address is being protected from spambots. You need JavaScript enabled to view it and find out.