How leave days affect the number of workers employed
The Sunday Nation
Nairobi,
01 December 2013
Gilbert Mwangi is having a headache trying to
figure out the number of staff to employ. He writes: “I operate a medium
size supermarket. To run effectively 39 workers must be present. However
every worker has to take a three day break every month. Help me figure
out how many workers I should employ so as 39 workers will be present at
all times.”
Well, Gilbert, some problems are easier done
from “first principles” like this. You know you need 39 workers; what
would happen if you took in just one additional employee? To see the
working clearly, let's name the employees W1, W2 , W3.....W40.
On the first, second and third day of the
month, workers W2 to W40 will be on duty while W1 will take his
three-day leave. Then from day-4 to day-6, W1 would return and W2 would
take a break. After that, it will be W3's turn to go off-duty from day-7
to day-9. This interchanging process continues until the 30th day of the
month by which time it will be worker W10 on leave...to return on the
31st day, if the month has 31.
Clearly, only 10 workers have been able to
take their 3-day break during the month. We can extrapolate this easily
and find that if there are two extra workers, then 20 will be able to
take their leave. Further, 3 extras will release 30 and 4 will release
40.
Therefore Gilbert, you will need 4 extra
workers bringing the total to 43. That's easy to work out, but what
would happen if your business grows and now you need, say 60 workers on
duty at all times? Will you repeat the first principles calculation
again? And what if the labour laws are changed and workers are given
five leave days per month?
Well, you may not need to. You can generate a
general formula that can be used for all situations. What you need is a
simple factor that tells you the number of additional employees and you
can get it this way:
If there are M days in a month and workers
need L leave days per month, then the proportion of additional employees
required is L divided by M; that is L/M. In the current situation, the
workers are getting 3 days leave in a 30-day month, therefore you need
3/30 = 0.1 = 10% more workers. That is 10% of 39 = 3.9 = 4 extras – just
like we found from first principles.
But what do you do when the month has 31 days?
Well, a quick way to deal with that is to add one more worker in the
payroll bringing the total to 44.
What if one of the workers falls sick and is
hospitalised for several days? Now that’s difficult to estimate but
medical insurance professionals can help. They must have data on average
number of days that a worker falls sick – if they don’t have it, then
they are practically “flying blind”!
Nonetheless, this problem illustrates how the number of leave days affects the national economy. Gilbert must employ four people who will permanently stay at home! Their salary will come from the customers through an additional mark-up in the price of goods.
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