Finding Warehouse Space in Unexpected Places

Three years ago during a tour of a local warehouse, our host pointed to a bay of pallet rack and complained, “You see all that wasted space up there, above the pallets? The slots are the wrong size.” To be honest, I had never thought of the space between the top of a pallet and the beam above it as waste, but sure enough he was right—there was quite a bit of air up there.

Slots in most unit-load warehouses are a uniform size, which creates wasted space above many pallets.

After touring warehouses for many years, I have come to believe that most unit load warehouses have a slots of a single size, presumably the size of the tallest pallet handled regularly, or perhaps two slots, with a smaller slot to handle smaller pallets with less waste. That there are some warehouses with a second slot size shows that the industry has long recognized, at some level at least, the problem of lost space above a stored pallet.

After thinking for a while, we wondered what size that second slot should be. How should it be determined? And should there be a third slot size, or a fourth? Or would having multiple slot sizes risk not being able to store an arriving pallet because it is too tall? How much space could be saved with a “best profile” of slots (assuming one exists)? Ten percent? Twenty percent? (Hint: it’s more than 20 percent.)

I am pleased to report that after more than a year of working on this problem, Luis Cardona and I have published How to Determine Slot Sizes in a Unit-Load Warehouse in IISE Transactions (for your viewing pleasure, we paid for open access on this article, so you can download the pdf at the link above for free). We have developed a method to determine the best profile of slots for a unit-load operation; meaning the best heights of the slots, and the number of slots for each height.

By creating the right profile of slot heights, wasted space above pallets is minimized.

The model requires a user to provide four pieces of data: (1) an inventory history for all skus (one year of daily data is best); (2) pallet heights for all skus, (3) the desired number of slot heights (between 1 and 10), and (4) a required “service level.” By service level we mean the probability that on a given day, all pallets in the warehouse can be stored (not to be confused with service level in inventory theory). The model then specifies the heights and the number of slots for each slot type that minimizes the sum of wasted space above pallets, while meeting the service level requirement.

The results from our experiments are impressive. It turns out that a typical warehouse should expect 20–40 percent space savings (you read that right), depending on the variability of pallet heights and some other things. But here’s the most amazing part, to me anyway: with the proper slot profile, a unit-load storage area occupies a much smaller footprint, contains more pallet positions (because they are smaller), has a higher service level, and costs less because there are fewer bays of rack. There are more cross beams because more slots, yes, but they occupy far fewer bays so the overall cost is less. A totally dominant solution.

The algorithm that solves this problem is complex; I refer you to Luis’ web site and video for more information. For the researchers, you can find all the details in the paper. For those interested in implementing the model, Luis has made it easy by posting an interactive web tool that produces the slot profiles and gives interesting ways to view the output. If you have a specialized problem or would like us to help with a project, feel free to email me.

Happy Slotting.

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