Little’s Law and Measuring Productivity

LITTLE’S LAW AND MEASURING PRODUCTIVITY

Chip Chapados

 John D.C. Little developed what we call Little’s Law to describe the predictability of movement inside a queue. In manufacturing operations the law is usually described to show the relationship between the amount of WIP, cycle time, and throughput. The law is usually stated as:

T =  WIP / CT

Throughput = WIP divided by Cycle Time

DEFINITIONS:

WIP – Work In Process: The amount of material in the process of being worked on but has not yet become a saleable product.

Throughput (sometimes called Total Operation Cycle Time): The amount of time it takes for an item to be made from beginning its processing to its completion.

Cycle Time – The amount of time it takes to do one specific operation.

For example:  In a cable manufacturer

 If the WIP was 3600 cables and the cycle time was 6 minutes then throughput would be 600 minutes or 10 hours, meaning it would take 10 hours for the last cable of the 3600 to be completed.

These calculations demonstrate the relationship of these variables at any moment in time on the production floor. The same calculations can be done by taking the average of the variables over time to give you an provide an average description of these variables over time.

The most important thing about Little’s Law is that it doesn’t matter what happens once work enters the queue. There could be more than one work station, or more than one path the work can travel, but the average outcomes remain the same. Little’s Law is the cornerstone understanding how things flow through queues.

SOME EXAMPLES OF WHAT LITTLE’S LAW CAN TELL US:

1. Little’s Law can be a tool to help understand the time and material relationships associated with operations. Little’s Law can be used as a snapshot in time or it can be used to study the average performance of an operation over time. It can also be used to measure changes in performance.

2. If you know any of the two variables, it allows you to calculate the third

Throughput = WIP divided by cycle time

or

WIP = Throughput times cycle time

or

Cycle Time = WIP divided by Throughput

For example:  If we look at a circuit board manufacturer and we know that the plant’s throughput is 45 days and its Cycle time is 10 minutes, or 6 per  hour, or 60 boards a day, then we can figure out the amount of WIP in the manufacturing queue:

45 * 60 = 2700 boards in WIP

If we look at a manufacturer of control panels and we know that they work 1  shift.  The plant’s throughput is 16 days and that its WIP in the manufacturing  queue is 400 control panels:

400 /16 = 25 panels a day or 3 hours and 71/2 minutes of cycle time

3. Little’s Law demonstrates how too much or too little WIP slows throughput. It provides the foundation for recognizing the optimal limits to WIP. If there is too little WIP then all available work stations are not being used and Throughput slows. If there is more WIP than work stations available then WIP collects in queues on the production floor and Throughput slows.

4. Little’s Lae demonstrates how “one piece flow” results in optimal throughput. The ideal level of  Throughput is what is known as “One Piece Flow.” One Piece Flow happens when on the production floor no more than one item is being worked and no items are waiting in queues to be worked on at any given time. This means that as one piece is finished another is begun to be worked on.  For One Piece Flow to be optimal the following conditions need to be met:

Same cycle time at each work station

Work can be handed off between work stations with no traveling

Zero defects

All work stations manned at the same times

All equipment same OEE and in same time windows

Material for work at each workstation available

5. Demonstrates that “batch and store” produces worst case throughput.

Make all subassemblies ahead of time and store slows throughput

Finished goods inventory slows dock to dock throughput

6. Provides critical metrics that can help measure operational performance.

Throughput is a critical operational measure that tells the speed if the production process

WIP tells the amount of raw materials tied up in the production process and allows you to calculate the cost of materials in production and then holding costs of the material in WIP.

Cycle time tells the time it takes to make any one item which provides information that can be used for deciding what improvements should be made on the production floor.

7. Little’s Law provides a way of testing the effectiveness of different production system designs. It can also be used to measure improvement initiatives by determining if Throughput is improved and by how much.