The Express Lane: How Much Can Be Sold Before It Stops Being Express

How to read this sheet

A priority lane creates no capacity. It moves waiting from the class that pays to the class that does not, and the last row of the table is the proof: at a hundred per cent express the wait is identical to the wait with no lane at all, to the second decimal. Everything else on the sheet is about how much of that redistribution can be sold before the buyers of it notice. Utilisation is what the answer really turns on. At seventy per cent a plant can sell a great deal of express and hurt nobody; at ninety it can sell almost none, because the queue it is dividing is already long. If the share this sheet returns looks impossibly small, the finding is not about the lane - it is that the plant is running too full to sell a promise on top of the work it already has, and the honest fixes are capacity, a longer standard lead time, or fewer promises. Three routes out and the sheet prices all of them. Cut the share to what can be delivered. Raise the promise to what is deliverable at the share being sold, which is the figure reported beside it and is usually the easiest conversation to have. Or accept the premium is at risk and price the risk - a customer paying for a day and a half and receiving one and seven tenths will notice, and the invoice is what is at stake. What is not modelled. Two classes only, when many houses run three or four; a third class sits between these two and can be interpolated but not read off this sheet. The queue is one server, so a plant with several machines that can each take any job will wait less than this says, while a plant where only one machine can take the urgent shade will wait more. Non-preemptive service is assumed - an express job waits for the machine to finish what it is on, which is right for a dye batch and wrong for anything that can be interrupted. And nothing here models the customer who pays for express every time out of habit, which is how a five per cent lane becomes a thirty-five per cent one without anybody deciding to sell it.