Question

The state government has decided to open a clinic in downtown Madras (India) for dispensing the Malaria vaccine to children from low-income households. The budget is tight and so the process must be as efficient as possible. The program administrator estimates that 45 children will arrive every hour to receive vaccinations during 10 hour day. (Assume, arrival takes place in a smooth / uniform way!)

A child, along with his or her guardian, enters the clinic and waits in the lobby until the receptionist can see them. There is only one receptionist and it takes him about 1 minute to fill out the required form for each child. The next step is to wait for one of the two nurses to become available for drug allergy consultation. Each nurse can handle about 25 patients per hour. After talking with a nurse, the child and his or her guardian go to the vaccination waiting area where three technicians are administering vaccinations. It takes approximately 5 minutes per child to administer the vaccination..

(i) How much waiting do you expect to find in front of the receptionist and the nurses, respectively? Why?

(ii) Do you expect waiting in the vaccination waiting area? Why?

Answer 1

As mentioned in the question the children are expected to come in a uniform manner and expected numbers are 45 an hour for 10 hours a day. So the total number is 450 and the time is 600 minutes. As the children are to come in uniformly, the time between each child enters the reception is 1.25 mins which is 75 seconds.

The nurses are to handle 25 children at their end per hour, which is a child in every 144 seconds. There are two nurses and so the time gets halved and becomes 72 seconds. So if each child comes in uniform at 75 seconds each, the nurses can handle them before any waiting will be required at the reception.

Now coming to the three technicians who administer the vaccine, each of them takes 5 minutes that is 300 seconds each but there are three of them so they can handle a child at every 100 seconds. which makes them handle 36 children every hour.

1. There will be no waiting in front of the reception or testing area as there are only 45 children coming in and reception can handle at around 60 an hour and the nurses can handle at around 50 an hour.

2. The waiting at the vaccination area totally depends on how many were rejected while testing for drug allergy. As nothing is mentioned about the rejection of those who have a drug allergy, let us assume no child was having an allergy and so will calculate the waiting time like that.

The fourth child to enter will have to wait for 75 that is 1.25 minutes and then it will go up for every child who enters by 75 seconds each till the end of the day.

Only 360 children will be able to complete in the given time, so either will have to stop the registrations after 360 or extend the time of the technicians by 2.5 hours.