This weekend, my family and I went to a pumpkin patch. Everyone else had the same idea. The line stretched out of the pumpkin patch gates and through the parking lot. We waited in line for ten minutes and then balked. When we left, about 90% of those that were leaving did not have pumpkins. We arrived in the morning on Sunday. It was only going to get busier. I cannot imagine the amount of revenue that was lost. We found out later that it took nearly two hours to get through the line.
During our short wait and on our drive to another orchard, we discussed queuing and pumpkin patches.
First, the pumpkin patch could make money by moving the long line inside of the gates. Quite a few people left only because they could see how long the line was from their cars as they drove in. If they committed to at least getting out of their cars, they might have stayed long enough to buy pumpkins. Queuing in the parking lot was also a safety issue–nearly everyone in line had small children.
The long line was caused by the wait for the hayrides to the pumpkin fields. We couldn’t see the pumpkin fields from the front of the line. It is a long walk, which is hard with small children and large pumpkins. The only bottleneck was for the hayrides. The traffic outside of the pumpkin patch was not too congested and the parking lot was not nearly full. The pumpkin patch hired people to make sure there was no gridlock in the parking lot (there wasn’t), but overlooked the bottleneck for the hayrides.
There was plenty to do at the pumpkin patch aside from picking pumpkins. There was a store, haunted house, and a restaurant. If people had been given tickets for a scheduled FCFS hayride (with a time of when the hayride would be leaving), they could spend money while they waited for their turn. Waiting two hours for a pumpkin isn’t so bad if you are enjoying donuts and cider.
The queue leveled off and seemed to reach steady state. The rate out only equaled the rate in because so many balked at the long line. For those of you who study queues, is this typical?
Picking pumpkins should be modeled as an infinite server queue, and in practice, this assumption should be a good approximation. (An infinite server queue can model self-service). Maybe this could happen if pumpkins are planted closer to the entrance, so some people could bypass the hayrides and walk instead. This should be somewhat achievable: when we pick apples, many more people can pick at the same time.
There are real constraints that would ultimately limit the pumpkin patch throughput, even if they had a continuous stream of tractors to and from the pumpkin fields. This can be contrasted with, say, an amusement park or stadium, where a large number of people can be served in a short amount of time (even stadiums have their limits).
- The country road that leads up to the pumpkin patch is a two lane highway. It can only accommodate so many cars per unit of time. Having someone direct traffic on busy weekends could help if it gets bad (the apple orchard we went to does this).
- The parking lot was on grass. People drive slow and awkwardly on grass. The pumpkin patch isn’t profitable enough to warrant paving a huge lot to improve throughput. Amusement parks have many lanes so people can park in a short amount of time. That wouldn’t work in agricultural settings. Some congestion in the parking lot seems inevitable.
- Ultimately, there is a choke point at these types of orchards, where everyone goes through some central area to pay. Even with many makeshift registers set up outside the barn, paying for pumpkins would get pretty chaotic if it got too busy, even if the registers are well-staged. The places I have seen that efficiently coordinate a huge number of cash registers are well-designed and inside.
So now that I figured out how to efficiently run a pumpkin patch, should I open my own?