How do you count a million milk crates?

We were losing hundreds of thousands of milk crates a year. At $4 a piece, it was half a million dollars. Conventional wisdom was that the majority of the loss was stores using them for storage, or people taking them home for furniture or their garage, but the volume we were seeing had nothing to do with people wanting cheap shelving.

A hidden supply chain

Milk crates are made out of high-density polyethylene, and HDPE is a commodity whose price tracks crude oil. A single crate weighs about three pounds, and a recycler will pay 14 to 28 cents a pound for ground plastic, depending on the market. Each crate brings 50 to 80 cents in scrap value, free money if you don’t pay for the crate itself.

The crews work at night, driving behind grocery stores and bakeries and loading empty crates off the dock. From there, the crates go to a rented warehouse with an industrial grinder inside. Whole crates go in one end. Plastic pellets come out the other. The pellets get bagged and shipped overseas, where they get melted down and turned into pipes and flower pots. Ironically sometimes new crates. A certain percentage of the crates we bought were made out of those stolen in the first place.

The dairy industry loses 20 to 25 million crates a year this way. $80 to $100 million. One dairy in Downey, lost 424,000 crates in a single year. $1.6 million in replacements, for one plant. The LA County Sheriff’s department had a dedicated unit for it, the Industrial Plastic Theft Task Force, and they recovered $6 million in stolen plastics in one year of raids.

The Dairy Institute eventually hired a private investigator who ran stings. He’d load up a truck with milk crates and drive around to recyclers offering to sell. Eleven of them bought without question. All eleven got arrested. From there he expanded across Orange, San Diego, and LA counties. Miami ran its own version of the sting and got two dozen arrests plus $1.5 million in stolen crates.

How do you count what’s missing?

We knew we were losing crates. We could see it in the replacement costs. But we didn’t know how many were actually being lost, because there were always confounding variables. Were stores holding onto crates in their backrooms, or was it truly missing? If the majority of the crates were still in the network, then it was an operational controls question. If they aren’t, then it’s still an operational controls question, just different levers.

But we didn’t even know how many were in circulation, which meant we couldn’t measure the loss rate, which meant we couldn’t tell whether anything we tried was working. Not knowing how much was out there was the worst part. Do we plan a large water run or will that cause us to run out of crates and short milk to the stores?

An email blast would increase the crate return, but was that 10% of the problem or 90%?

The crates are never all in one place. At any given moment they’re scattered across the creamery, trucks, store back rooms, distribution centers, and a nontrivial number of them are in a warehouse in Commerce getting fed into a grinder. You can’t pause the whole system and count. Ecologists have the same problem with animal populations.

Capture Recapture

You can’t count every fish in a lake. But you can estimate it. Capture-recapture. You catch a sample of animals, mark them, release them back into the population, and then wait for them to mix in. When you catch another sample and count how many marked ones show up, you can estimate how big the total population is. Say you marked 100 fish and your second catch of 50 has 5 marked fish in it. That’s 10 percent, so the total population is about 1,000. We did the same thing with milk crates. This solution would let us count crates that were lingering in backrooms and trucks, because the marked crates would mix into the population. Crates that were lost would not be counted.

We deployed a fixed number of gray crates into the distribution network. Then we waited. Once the system had time to mix, we started counting. Every time a batch of crates came back to the creamery, we recorded how many gray crates were in it.

The simple Petersen estimator assumes you do your sampling all at once, and our data didn’t work like that. Returns came in over weeks, so we used a beta-binomial model instead. In a beta-binomial setup the true share of colored crates floating around out there is a latent variable, and every returning batch updates it. At the start the estimates come out wide. Then the batches accumulate and the posterior tightens, and you get to watch the uncertainty shrink in real time. It approached an equlibrium.

For the first time we had a defensible number, the size of the project. How many crates were actually in circulation, how many were gone, and what that was worth in dollars. The annual replacement spend was about $500,000, and from the results we brought in, we estimated that $250,000 of that was organized theft. The retail side had a better staffed loss prevention unit with former detectives that picked up the case from us, once we could show them the scale of the problem.

What I think about milk crates

Milk crate and plastic reusable container loss is still significant, but decreasing. The last project I worked on at the company when I left was on a different type of theft. The tools for combatting it have gotten more sophisticated, but the underpinning needing to have numbers that square with reality hasn’t. A recurring theme on this blog is accurate measurement, and for me, the milk crates episode encapsulates that. Not knowing if on the other side of the wall you have 200,000 crates or 0 is a legitimately terrifying feeling. Vibes aren’t good enough.

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