5 Ways Little's Law is Applied to Manufacturing

Little's Law is a fundamental equation used in operations management to analyze systems with queues. It relates the number of items in a system (Work in Progress) with its input rate (Throughput) and time spent in the system (Cycle Time):

WIP = TH ⋅ CT

Where:

• WIP = average number of items in a system [units]
• TH = average arrival rate [units/s]
• CT = average time a unit spends in the system [s]

At first glance, Little's Law can seem like a tautology that simply defines throughput. However, as you will see below, the equation can be used to make predictions in various situations where you have incomplete information.

Here are five applications Little's Law can be used for in manufacturing, from analyzing individual workstations up to entire supply chains:

1) Determine the queue length at any station (WIP = TH*CT)

Used to calculate the actual unit capacity of a station.

1. Fully saturate the input to the station so that the station is never waiting for parts
2. TH = count the number of units input into the station over some time (such as a minute)
3. CT = with a stopwatch, press lap every time a unit exits the station, and find the median of the measurements
4. Calculate the queue length of the station using WIP = TH * CT

2) Calculate the required inventory capacity based on planned inventory time (WIP = TH*CT)

Used to determine the required inventory capacity of a station or waiting area, based on a specified dwell time for processes such as curing liquid adhesive on a unit or discharging its battery.

1. CT = required dwell time
2. TH = the rate at which units will be taken from the inventory
3. Calculate the required inventory capacity using WIP = TH * CT

3) Find a station that requires CT reduction (TH = WIP / CT)

Used to quickly find a station that needs attention during a line walk.

1. Walk a production line and find a station with a high number of parts awaiting input
2. High WIP before a station is indicative that the station is a bottleneck based on TH = WIP / CT

4) Determine the actual throughput of a production line (TH = WIP / CT)

Used to calculate the output rate of a production line after yield loss and downtime.

1. Fully saturate the production line input if it is a push system. Ensure enough material is available for a pull system.
2. WIP = the number of units output over some duration
3. CT = the duration the units were counted over
4. Calculate actual production line throughput using TH = WIP/CT

5) Indirectly measure the cycle time of an entire production line (CT = WIP / TH)

Used when a part's entry and exit times cannot be registered (such as if MES is not yet set up to automatically measure a unit's input and output times from the line).

1. WIP = input qty - output qty
2. TH = count the number of units at the end of the line over some time
3. Calculate the cycle time of the entire line using CT = WIP / TH

Note:

• For applying Little's Law with yield loss, check out this article
• The total line CT will take into account downtime

Bonus: Calculate the dollar inventory cost of a multi-product system

Used to calculate how much inventory costs your organization. This is a cool example that shows that your unit of WIP can be changed to currency to directly measure business metrics.

1. TH = the daily sales of all products
2. CT = number of days of inventory needed across all products
3. Calculate WIP = TH * CT

Here is an example:

1. TH = daily sales of products A, B, and C is $500/day
2. CT = the distribution center needs 7 days of inventory because the factory shuts down for a week during holidays
3. WIP = $500/day * 7 days = $3,500 (the inventory cost to the business of maintaining a 7 day inventory of products A, B, and C)

Note:

• We don't care about what proportion of products A, B, and C are sold as long as we know that the total sales volume is $500/day
• There are also other costs to maintaining inventory such as facility costs

References:

Hopp, W.J. and Spearman, M.L. (2012). Factory Physics. Milano: Mcgraw Hill.