It's often difficult to communicate the results of a complex mathematic formula to operators. If the communication is unsuccessful, no action is taken. We had a clause in a contract with a construction firm concerning the maximum length of the line for meals. The line had to be less than a 20 minute wait at dinner.
I spent two days gathering data on mean service times and arrival rates. After running the calculations, I went to Earl our General Manager with the findings. He was a retired Army Sergeant with years of experience in mess halls. The site superintendent had a great rapport with Earl.
We engaged the chef in our conversation. He understood the line was too long and mentioned a spot on the wall which meant the wait would be unacceptable. I counted the number in line and his spot was one person off the number I calculated.
The chef insisted the waiting delay was temporary and only lasted for 15 minutes maximum. Earl would not allow for a concession. The workers were laying rail ties and were not a patient bunch. He decided to call in the top foreman from the largest crew to discuss alternatives. We got our solution in about 20 seconds.
The foreman decided the buses all left the camp at the same time in the morning and returned each night together. He ordered the buses to depart 5 minutes apart in the morning and evening to allow a more workable arrival rate. Problem solved!
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