Question

The dispenser for a certain medication can hold up to 5 units, which are dispensed one unit at time upon demand. The demand for this particular medication, however, varies throughout the day, with some days more requests being made than others. Assume that the dispenser is restocked once a day, and any units of medication above the 5 will have to be special ordered.

A hospital worker counts the number of units of medication that were restocked each day over the past 100 days, yielding the following.

Units of Medication Restocked	Frequency (out of 100 days)
0	12
1	15
2	10
3	20
4	13
5	30

What is the average number of medication units that are restocked in this dispenser on a daily basis?

1. What percentage of time was the dispenser completely empty upon restocking (i.e. had to be restocked with 5 units)?
2. We do not have data on how many times medication was special ordered, but we know that it may be up to what percentage of time?
3. In a few sentences, considering all the above, do you think that that stocking only up to 5 units of the medication in the dispenser is adequate? (Note: Traditional management methods typically consider only the average, Management Engineering methods typically consider the probability distribution)

Answer 1

To find the average number of medication units that are restored:

(No.of units * restocked frequency): sum this across the dataset i.e 0*12 + 1*15 + 2*10 + 3*20 + 4*13 + 5*30 = 297

Average = 297/(sum of frequencies) = 297/100 = 2.97

a) restocked frequency corresponding to 5 units = 30

Total No.of days over which the data was obtained = 100

Therefore, the required percentage is: 30/100 = 30%

b) It may be upto 30% of the time. Since, owing to the demand, 30% of the time the dispenser had to be completely restocked. They might have expected additional demands, and might have ordered extra units to cope with it.

c) The average number of medication units that are restocked is approximately 3. And, only 30% of the time did they have to restock the dispenser completely. So, the current capacity of the dispenser is adequate based on the data obtained from the hundred days observation.