*Space*, *space*, *space*.

We need **space**.

If only we had more **space**…

Every warehouse manager has heard this at one time or another. It can be pretty frustrating to have too much product and nowhere to put it!

So if it’s so important, why do facilities run out of it?

A lot of times this issue is driven by production planning, batch-handling, or differences between forecasted product volumes & profiles and actual space.

But **process quality **assumptions can drive unexpected space requirements too.

Your site capacity was designed with an accuracy and quality assumption. Do you know what it is?

Let’s take a look.

## Little’s Law Drives Space Requirements

During the design process, the Industrial Engineers use assumptions on throughput—like inventory turns—volumes, and inbound and outbound order profiles. From those data points, they can assume the best storage media required and how much is needed. The calculation of “how much” storage comes from my favorite bit of industrial math, Little’s Law.

Little’s Law states that

“…under steady state conditions, the average number of items in a queuing system equals the average rate at which items arrive multiplied by the average time that an item spends in the system.”

or with:

L = average number of items in the queuing system,

W = average waiting time in the system for an item

λ = average number of items arriving per unit time,Little’s Law is stated as:

L= λ W

This is pretty straightforward! If I receive 100,000 units every 10-hour shift, and the dock-to-stock time is 2 hours, then my dock needs to accommodate:

L = 2 hours * (10,000 units / 1 hour) = 20,000 units

If units come in on 800 units / pallet, then the dock needs to accommodate 125 pallets plus travel aisles and so on. So far so good! It provides definite and easy-to-calculate answers. This can be applied to the whole building’s steady-state production.

But if it’s so easy to calculate, why do facilities run out of space?

## Quality Assumptions In Process Design

As with many things, the devil is in the details. The assumptions drive the math. If the receiving throughput time extends, for whatever reason, to 3 hours, then the dock needs to accommodate 30,000 units. If the receiving team exceeds its hourly goal, then the dock needs more space. And the effects compound, leading to teams being frustrated as they’re told to “keep receiving” outside of the engineered facility capacity calculations. This is why a metered takt-time approach and rigorous process consistency and quality are so valuable in planning facilities.

There is another key and usually unarticulated assumption—the **One Crazy Thing!**—built into facility designs:

**Process quality **affects space usage too. In our example above, we assumed *100% accuracy* and *no defects *in the 100,000 units coming in.

But suppose 1% of the units have some sort of problem or are received incorrectly. All of a sudden, the dock needs to accommodate its regular throughput flows *plus *1% * 100,000 *= *1,000 units of problem solving or defect resolution.

And problem solving units often take up more space than regular units. They need to be segregated and labeled for researchers to work with.

They also take longer to process due to research, filing tickets, or requesting required information. Where a regular unit’s dock-to-stock time might be two hours, a problem unit might sit in the problem-resolution area for half a shift, or a shift, or two shifts, or longer. This takes up footprint. And then we need to know how much space is required for those problem units.

We return again to Little’s Law with a 1% defect rate and a half-shift queue time. This means that:

λ = 1000 units arrive every shift, or 100 per hour

W = 5 hours waiting timeL = 100 units per hour * 5 hours =

500 units

So the inbound dock would need 500 units of storage to accommodate the problem resolution space. Unless defect rates or problem-resolution processing times change, this needs to be counted as a permanent storage requirement.

And that’s just the inbound dock. To be meaningful for a whole facility, the engineering needs to account for the defect rates of the major inbound and outbound processes.

## How Much Defect Rates And Volumes Matter

This analysis is sensitive to the problem-resolution queue waiting time and arrival rate, which is heavily influenced by process quality. In a high-volume facility, even small variations in quality add up to large amounts of rework. What does this look like in a large facility?

Wow! A facility processing 250,000 units daily with 1% defects (or a 99% first-pass yield) and problem-solving everything within a day still has to accommodate 2500 units of problem-solving. If the resolution time goes down or defect rates go up, so does the storage requirement.

But is this a concern? Best-in-class facilities run their processes at over 99.5% inventory and order accuracy. Surely, no one exceeds 1% overall defect rates.

Well, take a look at the table.

Let’s assume a 99.5% accuracy rate (or 5000 DPMO) for **each** of receiving, putaway, picking, and shipping. These are sequential processes, so the defect rates are multiplied by each other instead of averaged to find the actual first-pass yield.

99.5% may be good, but we’re already at 98% (or (99.5%)^{4}, 98.02%, to be precise) first-pass-yield for the facility. That just turned into **5,000 additional units of problem-solving space** required even at high levels of component process accuracy.

That can get big fast! More defects and higher resolution times equals more space needed.

## Conclusions And What To Do

The key takeaways from this are:

1) Account for problem-resolution areas in your facility planning. If you don’t, you’ll run out of space!

2) Articulate the assumptions—throughput and defect rates—driving those resolution areas. Check whether they are valid, and how sensitive they are to your operation’s success. Plan for larger queues earlier in the operation until you know you’ll have processes stabilized at high quality rates.

3) If you have a large problem-resolution queue, you can back out your **process quality **by determining how long the average parcel has been there, how many units are present, and, knowing your average daily volumes, using Little’s Law to check how many must have had problems.

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