Why 85% machine utilization can still mean late orders.

The monthly report says your mill ran at 85% utilization. It also says you shipped nine orders late. Both numbers are true, and the first one is why most people miss the second. Machine capacity planning that works from monthly averages will tell you there is room. The floor knows there was not, at least not on Wednesday.

This post explains why a machine that looks 15% open can still make orders late, using arithmetic you can repeat on a notepad. Then it shows a better way to look at load: by machine, by day, for one week at a time.

What 85% actually measures

Utilization is the share of available time a machine is busy.^[1] It is a ratio: hours of work divided by hours offered. Over a month, a mill with 160 available hours that logged 136 hours of work is at 85%.

That number hides three things.

First, it hides the shape of the load. A machine that ran 6.8 hours every day and a machine that sat half-idle Monday and ran 12 hours of demand on Wednesday both average 85%. Only one of them shipped on time.

Second, it hides variability. A queueing teaching example makes the point: if one job arrives exactly on the hour and takes exactly 59 minutes, the server is busy 98% of the time and nobody ever waits.^[1] That only works because arrivals and job times never vary. In a real shop they vary all the time, and the same notes show that when arrivals are random, the line ahead of a single machine grows as utilization divided by one minus utilization.^[1]

Third, it hides which day. An order is not late on average. It is late on a date.

The people who wrote Factory Physics put it this way in a presentation on their own site: average capacities don't mean much without knowledge of the distribution about the averages.^[2]

The queue math, in one line

Queueing theory has a standard approximation for how long a job waits in front of a single machine. It is Kingman's formula, usually written as the VUT equation: queue time equals a variability factor, times a utilization factor, times the average process time.^[3] The utilization factor is u divided by (1 minus u), where u is utilization.^[4] One lean columnist calls it one of his favorite equations from Hopp and Spearman's Factory Physics (Waveland Press, third edition, 2011).^[5]

You do not need the full formula to see the problem. Work out the utilization factor alone:

The arithmetic: 0.85 divided by 0.15 is 5.67. Multiply by a 2-hour job and a variability factor of 1, and the average job waits more than 11 hours before a 2-hour cut. Go to 95% and the wait more than triples again. The lesson from VUT, as one Quality Digest column put it: "if a station increases utilization without making any other change, average WIP and cycle time will increase in a highly nonlinear fashion."^[5] The curve climbs toward infinity as utilization approaches 100%.^[1]

The same math is why one operations science journal warns that pushing a bottleneck much beyond 80 to 85% makes a cycle time explosion very likely.^[6] And it is why a university queueing course calls an old hospital guideline of aiming for 85% utilization a bad one.^[1]

Now notice what the monthly report did. It handed you a single number, 85%, that already sits on the steep part of that curve. And because it is an average, some days were far worse.

Variability makes every day worse

The V in VUT is the variability factor. In the standard form it is the average of two squared coefficients of variation: one for how jobs arrive, one for how long they take.^[4] Rush orders, a hot job pulled ahead, a batch of 40 arriving at once, a setup that ran long, a bad bar of material: each one pushes V up, and queue time goes up with it even when utilization does not move.

Variability is also why Goldratt's The Goal (North River Press, first published 1984) argues against the "balanced plant," where every resource is trimmed to exactly match demand.^[7][8] The novel's point is that dependent events plus statistical fluctuations push throughput down and inventory up when there is no slack to absorb the swings.^[7] The lesson that stuck with readers: "an hour lost on a bottleneck machine is an hour lost for the entire system."^[7]

Hopp and Spearman state the same trade-off as a law. Systems with variability must be buffered by some combination of inventory, capacity, and time.^[2] If you will not pay to reduce variability, you pay with high WIP, idle capacity, or late deliveries.^[2] A shop that insists on 85% on every machine and refuses to hold any buffer has chosen, without saying so, to pay in late orders.

In my shops, that choice was never made on purpose. It was made by a schedule that only looked at the month.

Load by machine by day, not by month

Here is a worked example. One mill, one shift, 8 hours a day, 5 days a week. The month shows 136 hours of work against 160 available: 85%. Take week one and spread the booked hours across the days the jobs must run to make their ship dates.

The week averages 85%. Wednesday is 150%. Now follow the hours. Wednesday can only do 8 of its 12, so 4 hours slip to Thursday. Thursday now holds 13 hours, so 5 slip to Friday. Friday finishes everything with no overtime. By Friday night the mill has done all 34 hours, the month-end report still says 85%, and every job that needed to run Wednesday or Thursday shipped a day or two late.

Then look downstream. Weld was waiting on the Wednesday mill parts. It had nothing to do Wednesday afternoon and a pile Friday morning. Weld's utilization for the week also looks fine. Weld's Friday does not. That is dependent events in practice: the slip at one machine becomes a peak at the next.^[7]

The queue math says the slow days were not free either. On Monday at 50% the utilization factor was 1. On Wednesday the daily load passed 100%, and at that point the formula stops applying because the queue does not reach an average at all. It just grows until demand falls off.^[1] The average of a calm day and a buried day is not a normal day.

This is the view HixonOps builds into the scheduling and capacity screen of its MES: hours booked against hours available, by work center, by day. The arithmetic is the same as the table above. The difference is that nobody has to rebuild it by hand every Friday.

What to do with a 150% day

You have five moves, and they cost different amounts.

1. Pull work ahead

Thursday is not the problem. Monday is. Monday had 4 open hours. If the material and the drawing for one of Wednesday's jobs were in the building on Monday, run it Monday. Pulling 4 hours from Wednesday to Monday turns 150% into 100% at no cost beyond a decision. This only works if you see the week before it starts, which is the point of the worksheet below.

2. Use an alternate routing

Most shops have a second machine that can run the job slower or with a longer setup. Say Mill 1 is loaded 2 hours on Wednesday and can run one of Mill 2's 4-hour jobs with an extra hour of setup. Move it. Mill 2 drops to 8 hours. Mill 1 goes to 7. Both ship on time, and the only cost was one hour of setup on a machine that was idle anyway.

The catch is that the routing has to exist, in writing, before Wednesday. In an Ohio MEP project with an exhaust manufacturer, the MEP center found the ERP routings were not giving the system the correct information, fixed the routings, set up work centers for scheduling, identified welding as the main bottleneck, and switched that department to forward scheduling. Lead time went from 12 to 14 weeks down to 5.^[9] Routings were the first fix, before any scheduling logic.

Alternate routings do not have to be in software. A one-page table on the scheduler's wall listing each operation, its primary machine, its backup machine, and the time penalty is enough to start.

3. Level the arrivals

The Lean Enterprise Institute defines heijunka as "leveling the type and quantity of production over a fixed period of time."^[10] Their worked example is close to the mill above: a producer gets 500 orders a week, but 200 arrive Monday, 100 Tuesday, 50 Wednesday, 100 Thursday, and 50 Friday. The lean answer is a small finished-goods buffer near shipping and a level plan of 100 a day.^[10]

Job shops cannot always buffer finished goods. But most can level the release of work into the floor. If you release everything the day the order lands, Monday's pile becomes Wednesday's 150% day two operations later. Release at the pace the bottleneck can take and the peaks flatten on their own.

Jim Womack of LEI makes a sharper point about where peaks come from. Much unevenness, which lean calls mura, has nothing to do with customers. It comes from month-end pushes to make the numbers, where sales writes too many orders at the end of the period and production goes too fast to fill them.^[11] His advice: "Ask why there should be any more variation in your activities than called for by customer behavior."^[11] A lot of 150% days are self-inflicted.

4. Add capacity on the right day

Overtime on Wednesday is cheaper than overtime all month. Four hours of overtime on one machine on one day, planned a week out, is a different animal from a standing Saturday shift because "we're behind." The first costs four hours. The second costs capacity you then fill with work that did not need to be early, and the average climbs back to 85%.

5. Reset the promise

Sometimes the honest move is a different date. A New York MEP case shows what happens when sales grow and nothing else changes: lead time went from about 15 weeks to over 19, on-time delivery sat at 30%, and it took a value stream map to find the bottlenecks before on-time delivery rose above 70%.^[12] A promise made against a monthly average is a guess. A promise made against a daily load is a commitment.

What to watch after the first month

Two numbers tell you whether the daily view is working.

The first is WIP in front of each machine, counted the same time every day. Little's Law ties WIP, throughput, and cycle time together: throughput equals WIP divided by cycle time, as long as you use long-run averages and the system is stable.^[6] If throughput is flat and WIP in front of the mill is falling, cycle time is falling with it, and the orders that used to wait 11 hours now wait less. You can watch that happen without any new formula.

The second is the number of over-100% cells per week. It should fall, and the ones that remain should land on the same machine. That is the machine where capacity, a second shift, or a real alternate routing pays for itself.

I spent 13 years fixing late orders by walking the floor and asking why. What I found, over and over, was good people, scattered data, and nobody looking at the same numbers. The scheduler had a monthly load report. The lead on the mill had a stack of travelers. The customer had a date. None of them agreed on what Wednesday looked like. At one steel products maker, more than $700,000 was tied up in late orders. Six months later it was under $50,000. No new system. Everyone looked at the same numbers every day.

If you want that view without building it in a spreadsheet forever, the HixonOps MES reads your routings and open orders and lays out the week by work center. If you are not there yet, the worksheet above does the same job for an hour a week.

Either way, stop trusting 85%. Ask what Wednesday looks like.