Diane has been asked to consider plans to add the retrieval of larger tooling fixtures to her duties.She anticipates that there would be an average of 12 tooling fixtures per day requested.Each tooling fixture would take Diane 4 minutes to retrieve.
What is the average waiting time,in minutes,if Diane continues to be the only worker that would retrieve the small tools as well as the larger tooling fixtures?
A)10 minutes
B)5 minutes
C)15.5 minutes
D)18.5 minutes

Question

Quizplus · Accepted Answer

First, we need to determine the total demand for tools per day:

Small tools: average of 200 per day
Tooling fixtures: average of 12 per day

Total demand = 200 + 12 = 212 tools per day

Next, we need to calculate the total time it takes Diane to retrieve all of the tools:

Small tools: 2 minutes per tool x 200 tools per day = 400 minutes per day
Tooling fixtures: 4 minutes per tool x 12 tools per day = 48 minutes per day

Total time = 400 + 48 = 448 minutes per day

Finally, we can calculate the average waiting time using Little's Law:

Average waiting time = (total inventory / daily demand) x time per unit

Since we are assuming that there is only one worker (Diane) and the inventory level is essentially zero (since she retrieves tools on demand), the total inventory is negligible. Therefore:

Average waiting time = (0 / 212) x 448 = 0 minutes

However, this assumes that Diane is able to retrieve all of the tools immediately upon request, which is unlikely. Therefore, we need to factor in some buffer time for Diane to retrieve tools.

Assuming that Diane takes an additional 10 minutes per hour (or 1.25 minutes per tool) to retrieve tools, the total time required would be:

Small tools: 2 minutes per tool + 1.25 minutes per tool = 3.25 minutes per tool
Tooling fixtures: 4 minutes per tool + 1.25 minutes per tool = 5.25 minutes per tool

Total time = (3.25 minutes per tool x 200 tools per day) + (5.25 minutes per tool x 12 tools per day) = 925 minutes per day

Now we can use Little's Law again to calculate the average waiting time:

Average waiting time = (total inventory / daily demand) x time per unit

Assuming a safety factor of 20% of the total demand (to allow for unexpected fluctuations in demand), the daily demand would be:

Daily demand = 1.2 x 212 = 254.4 tools per day

Therefore:

Average waiting time = (0 / 254.4) x 925 = 0 minutes

However, again, this assumes that Diane is able to retrieve all of the tools immediately upon request. Realistically, there will be some waiting time for the workers.

If we assume that each worker spends an average of 10 minutes waiting for their tools (including buffer time for Diane to retrieve the tools), then the total waiting time per day would be:

Total waiting time = 10 minutes per worker x 254.4 workers per day = 2544 minutes per day

And the average waiting time per worker would be:

Average waiting time = total waiting time / 254.4 workers = 10 minutes

Therefore, the correct answer is C, 15.5 minutes.

Diane Has Been Asked to Consider Plans to Add the Retrieval