Efficient Entrance

We were in line to buy tickets to enter a tourist attraction. The line was accumulating, even though the place had two cashier windows open.

I inclined my ear toward the windows and heard people at each station discussing memberships. Meanwhile we, and everyone behind us, were interested in simply buying tickets for the day.

I thought it was an inefficient process to have all available windows processing memberships. My plan would be to have one window dedicated to normal tickets – the quick transaction – and one window that would take membership applications as well as sell tickets.

That would have made my experience better. But would it be better overall?

Let’s assume it takes an average of 2 minutes to buy a set of tickets. And let’s assume an average of 10 minutes to buy an annual membership.

In order to replicate my situation, let’s assume the two memberships are at the beginning of the line. So for the first 10 minutes, the line does not move as both windows are busy with memberships. Then there are 20 minutes left to sell tickets. At 2 minutes each, times 2 windows, that equals 20 sets of tickets.

So in 30 minutes, 2 windows process 20 sets of tickets and 2 memberships. How does that compare with my proposed setup?

The first window is only tickets. In 30 minutes, it processes 15 sets of tickets.

The second window is memberships and tickets. This window takes 20 minutes for memberships and then has 10 minutes for tickets, so 5 sets of tickets.

The total is still 20 sets of tickets and 2 memberships.

That doesn’t show any difference. But the difference does show up in the average wait time.

Average wait time in the first case is 0 for the memberships and then 10 + ((0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18) / 10) = 10 + 90/10 = 19 minutes per set of tickets

Average wait time in the second case is (0 + 10) / 2 = 5 minutes for memberships and then (0 + 2 + 4 + … + 26 + 28) / 15 = 210/15 = 14 minutes for the first window and (20 + 22 + 24 + 26 + 28) / 5 = 120/5 = 24 minutes for the second window.

The average is not 14 + 24 / 2 (which equals 19 minutes), since more people had the lower wait time. The average is 210 + 120 / 20 = 16.5 minutes.

So dedicating a window to the slower process results in a lower wait time for 90% of the clients.

Not only is it faster, but it also feels faster to everyone, since the main line is always moving. With the original configuration, it felt very slow because the whole line did not move at all for 10 minutes.

See, I am going to wait at the fords of the wilderness until word comes from you to inform me.

2 Samuel 15:28

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This little article thingy was written by Some Guy sometime around 12:14 pm and has been carefully placed in the Ponder category.

3 Responses to “Efficient Entrance”

  1. js Says:

    I would agree to this even more if you tell me they could have gotten their memberships online before showing up.

    But if they couldn’t, the place might not want to discriminate against membership-getters, since that might discourage people from buying memberships. In other words, making day-pass buyers a tiny bit more irritated might be worth it if it encourages (or at least does not discourage) some people from getting memberships. If someone is on the fence about a membership, sees that the membership-free-line is moving, he may say, “I’ll just get the day pass.”

  2. Some Guy Says:

    I like this idea, which I’ve seen in a number of places (and no, that number is not zero): stop by the ticket office or membership services or gift shop before you leave that day, tell them you want a membership and show your receipt, and your day ticket price is applied toward your membership fee.

    Everyone wins – people get through the gate faster, people on the fence get to try the venue for the day without committing to a membership, and people who want memberships can get them.

  3. Ricky Anderson Says:

    We did problems like this all the time in my operations management class. We’d spend hours figuring out how to make bank queues faster, etc. Then I would never see it used in the real world and now I do everything online and am a hermit and can’t be exposed to the sun.

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