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Let's say I have 2 different types of machines responsible for 2 different duties.

I have the PRODUCTION_MACHINES that EACH are able to produce a single unit of goods within 2 hours.

Then I have TRANSPORTER_MACHINES which are EACH able to collect and package away a single unit of goods from the production line at 95 seconds per TRANSPORTER_MACHINE.

QUESTION:

Assuming there are 5 PRODUCTION_MACHINES working, and they are operated at different starting times, how many TRANSPORTER_MACHINES do you need in order to MINIMIZE the IDLE_TIME incurred in the production process ?

(Whereby "IDLE_TIME" is defined as the time expended by EITHER the PRODUCTION_MACHINE or a TRANSPORTER_MACHINE waiting to have its good collected or produced.

HINT: Too many TRANSPORTER_MACHINES will add to the idle time as there are prone to be extra TRANSPORTER_MACHINES idly waiting for struggling PRODUCTION_UNITS to produce quickly enough to keep up with DEMAND.

... and vice-versa, too few TRANSPORTER_UNITS will also increase the idle time, this time for the PRODUCTION_MACHINES as some of them will have to wait for the struggling TRANSPORTER_MACHINES to keep up with their SUPPLY.)

Thank you very much !

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Observe that it takes a PM about 75 times as long to produce a widget as it takes a TM to clear that widget and let it start producing the next widget. And we have only 5 PMs.

Intuitively, it seems like we should have only one TM. It will be idle almost all the time, waiting for one of the PMs to finish. The PMs will be busy almost all the time, except right after they finish a widget and have to wait for the output to be cleared away.

Adding more TMs would simply add more idle time for them, while reducing the PM idle time by very little at best. Removing the sole TM would leave all of the PMs idle as soon as each of them finishes the first widget.

If the times were more similar, or the number of PMs were closer to 75, finding the answer would be more complex. This problem seems to be designed for a simple, intuitive answer.

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