I was standing in line at Sweetgreen, waiting to pick up an order, when I noticed the pickup shelves. At first glance, it felt arbitrary. But with a mathematical modeling mindset, I started noticing and began to ask questions. 

Fairly quickly, I realized that the shelves were labeled alphabetically and orders are placed there by first name, but the space was not divided equally. Some letters took up multiple shelves, but others were squeezed into a narrow section. And one letter didn't appear at all (I assume "T" fell off?). This system is doing something intentionally. But how does it work?

What We Can See, and What We Can’t

Some letters clearly show up more often (lots of shelf space). And others barely appear (just a little shelf space). Near the bottom, a few shelves are missing letters entirely. Probably because those shelves aren’t accessible from the kitchen, thanks to a wall blocking access. 

We can see that part of the system, but what about what we can’t see? That’s when I started wondering what questions were considered when this system was adopted:

• What data informed this design?
• Is it based on historical pickup frequency?
• How often is it updated?
• What assumptions are being made about customer behavior?
• What constraints shaped the final decision?

I’ve ordered from Sweetgreen in other locations before, and they don’t use this system. Usually, the shelves are grouped into alphabet ranges: A–F, G–L, and so on. That’s a simpler approach.

I've also encountered a similar system at stores like Starbucks, but anyone who has waited at a busy Starbucks knows that it can turn into a pileup pretty quickly. So, what’s different here? Is it order volume? Space? Pickup flow? How many orders do you need before a more specific system becomes necessary?

The questions started multiplying the longer I stood there (also, it was a busy time of day, so it was a pretty long wait).

Modeling Is Iterative 

But here's what struck me most, and what I would like to ask Sweetgreen's staff: I don’t know whether this pick-up system was designed all at once or adjusted gradually as patterns emerged. I don’t know what data, if any, sits behind it. What I do know is that it reflects choices. Someone decided how much space to give each letter, determining which shelves would need the most room. Someone had to work within the confines of the shelves and walls, and the steady flow of people coming in and out during lunch, to devise a system that would be intuitive and efficient.

This system doesn’t need to handle every possibility. It just needs to work well enough, most of the time. And whatever decisions were made here probably aren’t permanent. If patterns start to change, say if a number of Teresas, Tias, and Todds start placing orders, the shelves can change too. The layout can be adjusted. Most people would never notice. They’d just grab their food and leave.

Math Modeling Mindset in the Moment

I like moments like this because they remind me how often math modeling shows up. Sometimes it’s just sitting there on the wall while you’re waiting for lunch.

The next time you’re waiting for food, crossing a street, encountering a juice machine in Singapore, or watching a system behave in an unexpected way, pause and ask:

• What problem is being solved here?
• What assumptions might be in play?
• And what constraints shaped this solution?

That moment of noticing is where math modeling begins.