### Lead time

Lead-time is a key performance indicator. This article will explain how lead-time is calculated and derive how it can be reduced.

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Lean in the Line

Lead-time is a key performance indicator. This article will explain how lead-time is calculated and derive how it can be reduced.

July 22, 2021

Playing the “Airplane game” gave you a first idea of how the number of unfinished products in a line (“work in process” or WIP) can hold up production and increase “lead time”. We now want to look into the concept of “lead time” more carefully.

There is no accurate, general definition of “lead time”, but a universal desire to decrease it. As the term is used loosely, it is important that you do understand what it means for your business when evaluating tools to decrease “it”. Generally, lead time refers to a subset of the time from when an order comes in till when it is shipped. There are many details here, for example an order might not directly make it from your sales time to your production line or does not immediately ship after it is done. In this book, we are using the terms manufacturing lead time for the time an order hits the manufacturing floor till it is complete.

You can think about your manufacturing line like a queue in front of a coffee shop such as shown in Figure 8.1. Akin to having a production order for 10 items let’s say 9 people are waiting in front of you — the tenth person — for getting a coffee. How can you tell when you will be done?

The first thing that comes to mind is to simply queue up and take the time. Let’s say it takes 15 minutes until you exit the store. You know now, that every customer spent an average of 1.5 minutes (15 minutes divided by 10 customers) until they were served. We can therefore say: The Manufacturing Lead Time (*MLT*) is approximately the amount of work in process (*WIP*) times the time needed to make one (*Tone*). Or, as an equation

Using our example here 15 minutes (MLT) is approximately 10 customers (WIP) times 1.5 minutes/customer. Instead of using the actual time servicing one customer (or making one part), it is customary to use its inverse, the production rate or

You can easily measure it by counting the number of customers that are being served in a given time interval. In most instances, this is actually easier than waiting for a complete cycle to complete.

In the coffee shop, we would hence talk about a production rate of 2/3 customers per minute (1/1.5). With this, our equation becomes

This equation is known as “Little’s law”. It has initially been developed to predict the amount of customers waiting in a store at the same time, but was found to apply equally well to manufacturing processes.

Example 1: Identical Products

A rubber boat manufacturer completes six identical boats per day. They have 180 pending orders. What is the lead time for a new order coming in?

With a WIP of 180 and a production rate of 6, their manufacturing lead time is approximately 30 days (180 boats / 6 boats per day).

Little’s Law has been developed to estimate wait times and queue lengths in a retail setting. As so often, the devil is in the detail. In the example above, the detail was the word identical. Let’s say, it takes a minimum of 14 days to make a rubber boat. Can the lead time for a made-to-order boat ever go below 14 days? Of course not, but actually: maybe. It depends on where in the process customization starts.

The reason is that Little’s Law assumes that production time is just the time needed to make one. This can be seen when plugging in one for WIP into the equation above — the manufacturing lead time is 1.5 minutes, exactly what it takes to serve you. How to factor in the actual production time of an entire process consisting of multiple stations working in parallel depends on a case-by-case basis. In the rubber boat example, the lead time can indeed go down to zero days, namely when the line is running uninterrupted at six boats per day and there are only five or fewer orders in front of the new order. Yet, Little’s law fails when predicting the lead time for a custom order, which should take at least 14 days.

It turns out Little’s Law is still helpful here, we only need to make sure that we factor in actual the actual duration of the production process (DPP):

Here, the “-1” ensures that the manufacturing lead time comes out to at least the duration of the production process. We can now try this equation for a make-to-order process.

Example 2: Make-to-order products

A rubber boat manufacturer is capable of completing six custom-made boats per day. They have 180 pending orders. What is the lead time for a new order coming in? With the amount of work going into a single boat 14 days, WIP of 180 and a production rate of 6, their manufacturing lead time is 44 days (14+179/6).

Little’s Law works great if the production rate is constant. This is fine, if the time scale at which lead time is computed is chosen so that the production rate actually is constant on average. For example, if the production rate fluctuates between 10 and zero items per hour due to scheduled breaks, it might still be reasonable to say “the production rate is 8 items per day on average” and predict lead time hence. Similarly, a facility might only perform certain tasks on Mondays and Tuesdays and others on Wednesday to Friday. In this case, lead time might be expressed in weeks, using the average weekly production rate in Little’s Law.

What, if we do need more precise lead time estimates or fluctuations do not follow predictable patterns? Consider our coffee shop example, but now imagine the booth is staffed by two people. You are putting in an order and pay with the first person, which takes on average one minute, and then wait to receive your order from person two, who completes an order every 1.5 minutes. Now imagine, the person actually preparing the orders to take a 5-minute bathroom break once every hour. Just decreasing the production rate by roughly 10% would overestimate the lead-time for a majority of the customers, while doing a huge disservice to those customers who’s lead time effectively increases by 5 minutes. In order to predict lead-time in such an environment, you therefore need to accurately track down time and update lead-time manually.

Little's law tells us all the possible ways how we can bring lead time down:

- Decrease the length of the overall production process by identifying waste,
- increasing the production rate,
- decrease the amount of WIP by introducing a pull-system.

As the duration of the production process is a lower bound on lead time, it should be the first one you optimize. This can be done by identifying the seven deadly wastes and implementing lean continuous improvement. You should then aim at increasing the rate at which goods are produced. You will quickly find that the production rate is related to the cycle time of the slowest operation in your process. Specifically, the production rate *Prate* is the inverse of the longest cycle time.

For example, if your manufacturing line is able to finish six boats per day on average, at least one of the stations in your process needs 1/6th of a day to add value. Decreasing the cycle time of these stations will eventually increase your production rate.

Although you can (and should) implement a “pull system” to keep the amount of WIP in your line constant and make manufacturing lead time more predictable, rate-limiting your intake will not change overall lead-time, but push it to your sales team. It is likely, however, that reducing your WIP will — in addition to saving money on inventory, labor, and storage — also positively affect the length of the overall production process by reducing waste.

The key to understand lead time is the rate at which goods leave your process. This rate is directly related to the step of your manufacturing process that takes the longest time. “Little’s Law” provides a good approximation to estimate lead time, in particular when you are making identical goods. Make-to-order products require to take the length of your manufacturing process into account as well.

Tracking WIP and production rate using pen-and-pencil and calculating the lead time for every order might be cumbersome. It is therefore a standard feature in Optio™.

1. What is usually described as “lead time”?

- The time needed from start of production till delivery
- The time needed from receiving an order till the end of production
- The time needed for manufacturing a product
- All of the above

2The production rateis the…

- inverse of the time interval at which products leave your line
- inverse of the total time it takes to make a product in a line
- inverse of the lead time
- All of the above

3. A factory makes 400 pairs of shoes a day, and currently has pending orders for 10000. What is the lead-time for a red pair of sneakers, size 11?

- 25 days
- 50 days
- Not enough information provided

Solutions: 1-4, 2-1, 3-3

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