Little's Law and Lead Time: Where Your Operation Is Leaking Cash

Every process settles into a balance between how much work is inside it and how fast that work leaves. Little's Law describes that balance: lead time equals work in process divided by throughput. When an operation releases more work than its bottleneck can finish, output stays the same while inventory and lead time climb, and both cost money. Many manufacturers and shippers carry far more work in process than their operations need. This article shows how to find the right level for yours and put a dollar figure on the excess.

What lead time means

Lead time is the time an item spends in a system, from the moment it enters to the moment it leaves. The system can be any part of your supply chain:

• Customer order: from order receipt to delivery
• Production job: from release to the shop floor to finished goods
• Purchase order: from placing the order to receipt at your dock

Value-added time, also called touch time, is the part of lead time when the item is being changed in a way the customer would pay for, such as cutting, welding, or assembly. The rest of lead time is waiting: in queues, in batches, in storage, in transit, or for an approval.

A note on terms. In Lean, cycle time usually means the time between finished units, or the time one step takes per unit. Many companies use the same words for lead time. Agree on definitions before you compare numbers across teams or suppliers.

Little's Law

John Little published the proof in 1961. The law holds for averages over a long enough period in any stable system, meaning work enters and leaves at about the same rate. It makes no assumptions about demand patterns or process times, so it works on a single machine or on an entire supply chain.

Keep units consistent. If WIP is counted in jobs and throughput in jobs per day, lead time comes out in days.

What it means in practice: at a given throughput, lead time moves in direct proportion to WIP. Double the work on the floor without adding capacity and lead time doubles. Releasing jobs early to get a head start adds WIP, so every job in the shop waits longer while output stays the same.

Every process has an equilibrium

A process reaches full output at a certain level of work in process. Below that level, the bottleneck sometimes runs out of work and output drops. Above it, output stays flat because the bottleneck is already busy, and every extra job only adds waiting time.

You can estimate that balance point from two numbers:

Hopp and Spearman call this critical WIP in Factory Physics. The fabrication shop in the worked example below finishes 10 jobs a day at its bottleneck, and each job needs 8 hours, or one shift, of processing. In an ideal line it reaches full output with about 10 jobs on the floor. It carries 200.

Real operations need some work in process above the minimum to absorb variation in arrivals, process times, and breakdowns. The leak is the work in process far beyond what that buffer requires. It buys no extra output.

Where the money leaks

• Cash on the floor. Every job in a queue holds material and labor you have paid for and cannot bill yet.
• Carrying cost. Capital, space, handling, insurance, and obsolescence typically run 20 to 30 percent of inventory value per year.
• Longer quoted lead times. Customers who need it sooner buy elsewhere, or you pay for overtime and expedited freight to hit the date.
• Bigger safety stocks. Long, uneven lead times force larger buffers of finished goods and purchased parts.
• Defects found late. A quality problem discovered after 20 days of queue has already reached every job behind it.

For a shipper, the same math applies on the water. Inventory in transit equals daily volume times transit days, so every extra day in the pipeline is another day of goods you have paid for and cannot sell.

Flow efficiency

Lean Six Sigma measures how much of lead time adds value with process cycle efficiency (PCE), also called flow efficiency:

How do you know if your number is good? Michael George published typical and world-class flow efficiency by process type in Lean Six Sigma (2002). The fabrication shop in the worked example below starts at 5 percent, half the typical level.

The gap between typical and world class is almost all waiting. A fabrication shop at 10 percent has parts sitting still 90 percent of the time. Raising it to 25 percent cuts lead time by 60 percent with the same machines and people. That is the opportunity: shorter lead times and less cash tied up in work in process.

Worked example: a fabrication shop

A manufacturer of steel store fixtures runs one 8-hour shift. Jobs move through cutting, bending, welding, powder coating, assembly, and packing.

These figures are illustrative.

Step 1. Calculate lead time

Step 2. Calculate flow efficiency

Each job gets 8 hours of work and spends 152 hours waiting. That is half the 10 percent typical for fabrication.

Step 3. Cap WIP

The shop starts releasing a new job only when a finished job leaves, and holds WIP at 100 jobs. That is still ten times the ideal minimum of about 10 jobs, which leaves a generous buffer for variation. Throughput stays at 10 jobs per day as long as the bottleneck always has work.

WIP value falls from $500,000 to $250,000. That frees $250,000 of cash and saves about $62,500 a year in carrying cost. Sales can quote two weeks instead of four.

Protect the bottleneck. Find the step with the highest utilization, often welding or powder coating in a shop like this. Keep a small buffer of jobs in front of it so it never sits idle, and cut WIP at the other steps first. If throughput drops after a WIP cut, the buffer in front of the bottleneck is too small.

Shrink batches. Large batches add WIP, because each unit waits for the rest of its batch at every step. The EOQ article balances order cost against holding cost. Little's Law adds the time cost of a large batch. Shorter changeovers make smaller batches affordable.

Why busy equipment creates long waits

Little's Law gives you the average lead time. Queueing theory explains where the queues come from. When jobs arrive at uneven intervals and take uneven times, the average wait at a step climbs steeply as the step gets close to 100 percent busy. Kingman's approximation estimates the wait:

Raising the powder coat line from 80 to 95 percent busy moves about 19 percent more work through it and makes each job wait almost five times as long. Two levers bring the curve down:

• Plan the bottleneck at a utilization you can sustain. Loading it to 100 percent on paper creates queues in practice.
• Reduce variation. Stable release schedules, standard work, steady batch sizes, and reliable maintenance all lower V. Cutting variation in half cuts the wait in half at every utilization. This is where Six Sigma variation reduction shows up as shorter lead time.

Little's Law across the supply chain

On the balance sheet: days of inventory

Days of inventory is Little's Law measured in dollars. Inventory is the WIP, cost of goods sold per day is the throughput, and the result is the average number of days a dollar of stock waits before it sells.

Bringing inventory down to $900,000 at the same sales cuts days of inventory to 45, frees $300,000, and saves about $75,000 a year at a 25 percent carrying rate.

In the import pipeline

In the EOQ example, a manufacturer uses 2,000 units a month and waits 2.5 months from purchase order to receipt. On average, 5,000 units are on order at any time, about $150,000 of open purchase orders at the $30 supplier price. This is the same demand-during-lead-time term that sits inside the reorder point. A supplier with a 1-month lead time would cut average stock on order to 2,000 units, about $60,000, and lower the safety stock you need. Compare total landed cost before switching, since a closer supplier may charge more per unit.

How to measure your own lead time and flow efficiency

1. Pick one product family and map its flow. List every step from order receipt to shipment. A value stream map works well for this.
2. Count WIP. Count jobs or units at each step, including those sitting in queue. Repeat on a few different days and average the counts.
3. Measure throughput. Use average completions per day over the last 4 to 8 weeks.
4. Calculate lead time as WIP ÷ throughput. Check it by tracking start and finish dates for 10 to 20 jobs, and compare both with the lead time you quote customers.
5. Add up value-added time from routings or a time study, and calculate flow efficiency in working hours.
6. Improve. Set a WIP cap so new work is released only as finished work leaves. Protect the bottleneck with a small buffer. Cut batch sizes and changeover times.
7. Review weekly. Track the numbers below and adjust the WIP cap as throughput changes.

KPIs to track

• Lead time: WIP ÷ throughput, by product family
• Flow efficiency: value-added time ÷ lead time
• WIP: in units and in dollars
• Throughput: completions per day or week
• Bottleneck utilization: share of available time the constraint is running
• On-time delivery: against the lead time you quoted
• Days of inventory: inventory ÷ daily cost of goods sold

Common mistakes

• Mixing units. Calendar days for lead time and working hours for value-added time understate flow efficiency. Use working time for both.
• Measuring during a surge or ramp-up. Little's Law needs work entering and leaving at about the same rate over the period you measure.
• Counting WIP once. A single count on an unusual day can be far from the average.
• Cutting WIP everywhere at once. A starved bottleneck lowers throughput, and lead time stops improving.
• Treating cycle time and lead time as one number. Define both before you set targets.

Related: Economic Order Quantity for Importers: How Much to Order · How the Producer Price Index Affects Your Input Costs