A Queueing (Queuing) System is a structure where things arrive (anything, including people), they join a line, wait for service. After being served, they exit the system. If this is true, then we can use the properties of Queueing Theory to help us better manage fulfillment centers, distribution centers, and any large facility that has the same properties as any line.

One result of Queueing Theory is Little’s Law:

Little’s Law: For a Queueing (Queuing) System in steady state, the average length L of the queue equals the average arrival rate λ times the average waiting time W.

Or,

L = λW

Given this definition, a warehouse (distribution center, fulfillment center) is a Queue in which Stock Keeping Units (SKU) are the customers that arrive at the receiving dock, where they join a queue (a line) to be processed and then wait for service (shipped). The processing in this case is the Pick, Pack, Ship part of the internal warehouse process.

Here’s a simple example of how to use Little’s Law to expose information that is not obvious.

Imagine a warehouse with 10,000 pallets, and the company has an average of 4 inventory turns per year. How much labor is needed to support this activity? Using Little’s Law, we get:

10,000 pallets = λ(1/4 year)

so,

λ = 40,000 pallets / year

Let’s assume an 8 hour shift and 250 working days per year and 2,000 working hours per year. Then, we get:

λ = 20 pallets / hour

Of course, most systems aren’t conveniently in a steady state, but the principle still applies. With the little information we had, we estimated the labor required to support the activity of this warehouse.

## Other Applications of Little’s Law

Little’s Law can be applied to many areas of business. Here are scenarios where Queueing Theory can be helpful:

- how to staff an emergency room (ER)
- how to staff a call center
- how many features a software engineering team can develop
- how many projects can be completed

There are more. Think about it – I bet you can find many applications of Queueing Theory. Think about your areas of responsibility – how might you apply Little’s Law?

TekGems says

This explains why Amazon would need to run 24 hours a day at certain times of the year (8 hour shift x 3?) to keep up with inbound receiving and outbound shipping. Since there are external dead lines Amazon has to meet with delivery carriers like USPS and UPS, they would need to work through the night to meet the next day’s deadline. Or perhaps increase capacity during certain shifts to meet those deadlines. I get the impression Amazon values exceeding expectations (happy customers) versus disappointing customers to save money in the short-term. This, I think, explains the motivation behind buyers liking FBA. Even though things might cost a few dollars more, but the great likelihood of receiving by the stated date is very comforting.