What Is Cube-per-Order Index?

The short answer

Cube-per-order index, or COI, is a rule for deciding which products get the best storage locations. It ranks each item by the amount of space it takes up divided by how often it is picked. Items with a low COI, meaning small and frequently picked, earn the locations closest to where orders are packed and shipped. Items with a high COI, meaning bulky and rarely picked, get pushed to the back. It is one of the oldest ideas in warehousing, it dates to the 1960s, and it is still a sound place to start.

It is also, on its own, not the whole answer, and this article is honest about exactly where it stops. The short version: COI ranks each item as if it lived alone, and no item in a real warehouse does.

What COI actually measures

Start with the thing a front location really is. A slot near the packing area is scarce and valuable, because every pick from it is a short walk, and there are only so many of them. So the question slotting has to answer is which items deserve that scarce real estate. COI answers it with a single ratio. In the words of Bartholdi and Hackman’s textbook, the cube-per-order index of an item is:

the volume of space allocated to storing that sku divided by the number of picks, or the inverse of pick density

Read that second half, because it is the clearer way to hold it. Pick density is how many picks you get out of a unit of space. COI is the inverse, the amount of space you spend per pick. A location near shipping should go to whatever gives you the most picks for the least space, which is to say the lowest COI. Sort every item by COI from low to high, hand out the closest locations from the top of that list, and you have the classic method, introduced by J. L. Heskett in a 1960s paper titled "Cube-per-order index, a key to warehouse stock location."

The reason it has lasted sixty years is that it captures a real trade-off in one number. A small carton picked forty times a day and a pallet picked once a month might occupy the same shelf, and COI says the small fast carton has a far stronger claim to a front slot, because the space it costs you buys vastly more picks. That is correct, and it is not obvious to the eye, which is why placement done by intuition tends to get it wrong.

Why it divides by space, and not just picks

The tempting shortcut is to skip the space term and rank items by popularity alone. Put the most-picked things at the front. It sounds right and it is wrong, for a reason the textbook makes concrete.

Bartholdi and Hackman plot twenty-five thousand items by how often each is picked against how much physical volume each moves, and the finding is the whole case for COI:

Among these 25,000 skus there is little correlation between popularity and physical volume of product sold

Popularity and size are close to unrelated. Some of your most-picked items are big, and some of your bulkiest items barely move. So if you rank by popularity and start filling front locations, you will hand a prime slot to a popular item that happens to be enormous, and it will swallow the space that three smaller, equally busy items could have shared. You will have spent your scarcest real estate badly while feeling like you did the obvious thing. Dividing picks by the space they cost is what stops that, and it is the entire insight of the method. Popularity tells you how much an item is wanted. COI tells you how much walking you actually buy back per slot you spend, which is the thing you are trying to optimise.

The refinement that changes the answer: restocking

Here is where the naive version of COI gets someone into trouble, and where the textbook goes past Heskett into something more careful.

A front location is not free to keep full. Every time it empties, someone has to walk stock from bulk storage to refill it, and that restock is labour too, walking that does not show up when you only count picks. So the real question is not picks per unit of space, it is net labour saved per location, picks saved minus restocks caused. Bartholdi and Hackman call this an item’s labor efficiency, and they work an example that is worth sitting with, because it breaks the intuition that the busiest item wins.

Three items compete for a forward location. Picking from the front saves about a minute per pick against picking from bulk, and each restock costs about three minutes.

• Item A is picked 600 times, for a total demand of 20 pallets. Its labor efficiency works out to 180.
• Item B is picked 1,000 times, for a total demand of 100 pallets. Its labor efficiency is 140.
• Item C is picked 200 times, for a total demand of 2 pallets. Its labor efficiency is 97.

Item A wins, and the textbook flags exactly why this is surprising: "sku A has a stronger claim than sku B despite the fact that sku B is requested almost twice as frequently." B is picked far more often, yet it loses. The reason is restocking. B is picked in small amounts relative to how much of it moves, so it drains its front location constantly and racks up restock trips that eat the pick savings, and it needs several locations to keep up, each one earning less. The pure-popularity ranking would have put B in front. The net-of-restock ranking sends A instead, and A is the right answer.

It gets sharper. Imagine a fourth item so popular that a typical pick takes half a pallet at a time. It is picked constantly and everyone would swear it belongs at the front. But at half a pallet per pick, a forward pallet is exhausted in about two picks, so it saves roughly two minutes of picking and then costs three minutes to restock. Storing it forward is a net loss. In the textbook’s words, "such a sku should not be stored forward, even if it is very popular." The busiest item in the building can be one you specifically do not want in your best location.

That is the finding to carry out of this section. Popularity is not the ranking. Space-adjusted popularity, COI, is much closer. And net-of-restock labour efficiency is closer still, which is why the textbook’s own conclusion is stated as a theorem: "the skus that have strongest claim to the fast-pick area are those offering the greatest labor efficiency." COI is the readable first cut of that idea, and labor efficiency is the version that survives contact with a real forward pick area.

The one thing COI cannot see

Now the honest limit, and it is the reason COI is a starting point rather than a finish line.

COI scores each item on two things: its own size and its own pick count. So does labor efficiency, with restocks added. Every item is ranked as if it were the only thing in the building. And that is the blind spot, because the cost you are actually trying to reduce is the length of real trips, and a real trip collects several items at once.

Think about what makes a trip long. Partly it is that a busy item sits far from shipping, which COI addresses. But partly it is that two items which almost always leave on the same order are stored at opposite ends of the building, so every one of those shared orders drags a picker across the floor and back. COI has nothing to say about that, and it structurally cannot, because it never looks at two items together. It ranks A on A’s numbers and B on B’s numbers and never asks how often A and B appear on the same order. That relationship, which items get picked together, is called affinity, and it is real money in any operation where orders have more than one line.

Where does affinity live? Not in any item’s own statistics. It lives only in the order history, in the plain fact of which items keep showing up on the same order number. You cannot derive it from cube and pick counts no matter how carefully you combine them, because it is not a property of items, it is a property of the pairs and groups they travel in. This is the exact point where a per-item rule like COI runs out, and where reading a year of actual orders begins.

It is worth being fair about when this matters and when it does not. If your operation is single-command, one item fetched per trip, then affinity is irrelevant and COI, in its labor-efficiency form, is very nearly all you need, because there is no such thing as two items sharing a trip. The moment your orders routinely have several lines picked together, which is most distribution, affinity becomes a cost that sits right alongside travel distance, and COI can only see the one it was built for.

So is COI still worth using?

Yes, without hesitation, as the first cut. It is cheap to compute, it needs only data you already have, item sizes and pick counts, and it will move your genuinely mis-slotted items in the right direction faster than anything else you can do in an afternoon. For the narrow and common question of which items deserve a limited fast-pick area, the net-of-restock version is provably close to the best possible answer, which is a rare and comforting thing to be able to say about a warehouse decision.

What it is not is the ceiling. The ceiling has two more things in it that COI leaves out by design: the restock economics, which turn COI into labor efficiency, and affinity, which needs the order history and cannot be reached from item statistics at all. A placement worked out from a year of orders can hold all three at once, which item deserves a close slot, at what quantity, given restocking, and which items should be neighbours because they keep shipping together. COI is the one-number sketch of the first of those. It is a good sketch, and it is why the method endures, but you would not stop at the sketch if the finished drawing were available, and for most warehouses it is, sitting unread in the order history.

One scoped note on the system side, because it comes up. Chapter 1 of this cluster enumerated the eleven location directive strategies in Dynamics 365 and confirmed that none of them ranks by COI, velocity, or distance. That is not a criticism of the product. Computing a COI ranking, let alone a full placement from history, is analysis you run on your data, not a switch inside the ERP, and the ERP is right not to pretend otherwise. It will faithfully send pickers to whatever locations the ranking put items in. Working out the ranking is the part that is left to you.

How to try it this week

You can compute a first COI pass on your own floor without any special tools. Pull two columns for your active items: the physical volume each occupies in its location, and the number of picks each took over a recent representative period. Divide space by picks. Sort from low to high. Then walk the top of that list, your lowest-COI items, and check where they actually sit today. Every one that is not near shipping is a candidate move, and the ones near the top of the list are the ones worth moving first, because they buy back the most walking per slot.

Then do the thing COI cannot. Take a month of order lines and count, for your busiest items, which other items keep appearing on the same orders. Any pair that ships together often and sits far apart is a cost COI never reported to you. That second list is not something the index can produce, and noticing that is the whole point of understanding what COI is: a sound, durable, per-item rule, and a clear line where the per-item view stops and the order history has to take over. The payoff for getting both right is the same one every part of this shows up as in the end, more lines out the door per person hour with the crew you already have.

The short version

COI ranks items by space divided by picks and hands the closest locations to the lowest scores, which is a real and durable insight from the 1960s, because popularity and size are uncorrelated and dividing by space is what stops you wasting your best slots on bulky popular items. The sharper version nets out restocking, and it can rank the busiest item in the building below a quieter one, or out of the front entirely. But every version of COI scores each item alone, so none of them can see affinity, which items ship together, which lives only in the order history. Use COI as the first cut. Do not mistake it for the finished answer.

For how you put a number on the walking COI is trying to reduce, read How do you measure warehouse travel waste?.

For the data behind the restock economics that turn COI into labor efficiency, read What data do you need to optimize warehouse picking?.

For the full ground-up treatment of the problem this sits inside, read Warehouse Pickup Optimization: The Operator’s Guide.