Capacity Utilisation: How to Compute It and What It Hides

Capacity utilisation is what a system actually produced divided by what it was rated to produce, over the same period. Anjani Stationers Private Limited made 2,50,000 registers against a rated 4,00,000, so utilisation is 62.50 per cent. Work it a second way, from the rate achieved per line-hour, and the two must land together. One figure on its own cannot tell an idle line from a slow one.

Worked at the settings the panel above opens on, in ordinary words: two lines, eight hours a day and 250 working days give 4,000 line-hours in the year. No hours were booked out for planned maintenance and none were lost to breakdowns, so all 4,000 line-hours were available and all 4,000 were run. At the rated 100 registers a line-hour the works was rated for 4,00,000 registers, and because nothing was booked out, the capacity available after planned downtime is that same 4,00,000. Against it the works produced 2,50,000 registers. Utilisation is 62.50 per cent on either denominator, the gap is 1,50,000 registers, and while running the lines turned out 62.5 registers a line-hour against the rated 100. Every available hour was run, so the whole of that gap is speed and none of it is time.

Anjani Stationers Private Limited is an invented manufacturer of hard-bound school registers, used all through these notes so that one set of arithmetic can be followed from one topic to the next. Its worksThe place where making happens: the sheds, the lines and the machines, as against the office in front of them or the warehouse behind them. An old word kept alive by cost accounting, which needs production held apart from everything around it. runs two lines. Registers are cut, then printed, then bound, and the whole arrangement is rated at 4,00,000 registers a year. The rated figure is taken here as given. Binding is the slowest of the three stages, so binding sets the rate, and why the slowest stage sets the pace for the other two is settled under throughput rather than argued again here.

Reading a profit statement, and what a ratio is, are taken as known here, so neither is rebuilt. The same year is computed twice instead, from two different starting points, and then taken apart. The interesting property of a utilisation figure is not how hard the figure is to work out but how much of the situation survives the working out, and the honest answer is: less than most readers assume.

Which two numbers does capacity utilisation need?

A utilisation figure is one division and nothing more: what the system actually turned out, over what the same system was rated to turn out, multiplied by a hundred. Anybody can do the sum. The care lives entirely in what the two numbers are allowed to be.

The stretch of time behind the top number has to be the stretch of time behind the bottom one, the machines behind each have to be the same machines, and a reported utilisation fails right there more often than it fails anywhere else. A year of output over a rated figure struck for one quarter produces a number four times too large that still looks like a percentage and still sits in a table like one. Output from three lines over a rated figure built for two does the same thing more quietly. Nothing about the arithmetic looks wrong, and the mismatch is buried in a note somebody else wrote.

The everyday version runs like this. A clinic has four consulting rooms and opens them six hours a day. Somebody reports that it saw nine hundred appointments last month. Is that a busy clinic or an empty one? The question cannot be answered, and not for want of a technique. The second number is missing: how many room-hours were on offer for those same appointments to be seen in. Until the room count and the opening hours are on the table beside the appointment count, the appointment count is a fact about nothing.

How is it worked out from what came out of the door?

The slow version of the route almost everybody uses is where the checks live, so take that route slowly. Anjani Stationers Private Limited made and despatched 2,50,000 registers in the year. The works was rated at 4,00,000 registers for that same year. Dividing 2,50,000 by 4,00,000 gives 0.625. Multiplied by a hundred, the utilisation is 62.50 per cent.

Then the same arithmetic run backwards. The reverse takes two seconds and catches a slipped decimal place before it reaches anybody else. The rated 4,00,000 multiplied by 0.625 returns 2,50,000. The working started there. If it does not return the output figure, one of the two numbers divided was not the number it was taken to be.

Now write down the part the percentage buries. The unused share is 100 less 62.50, or 37.50 per cent, and 37.50 per cent of 4,00,000 registers is 1,50,000 registers. A percentage is not something anybody on a factory floor can act on, and the gap of 1,50,000 registers is. Nobody schedules a shift against 37.50 per cent. A shift is scheduled against a number of registers, and 1,50,000 of them is the size of the thing being discussed. The percentage can be reported, but never alone.

What is the second route, and where does it start?

The first route counted registers. The second one counts time, and it starts from the shop floor rather than from the despatch book. Anjani Stationers Private Limited runs two lines. Each line runs an eight hour shift patternThe arrangement of who works when: how many shifts a day are staffed, how long each one runs, and on which days. It is decided by the business rather than fixed by the machines., and the works runs 250 working daysDays on which production is actually staffed and run, so weekly offs, holidays and planned shutdowns are already out of the count. A production year and a calendar year are rarely the same length. in the year. Two lines multiplied by eight hours multiplied by 250 days is 4,000 line-hoursOne line running for one hour. Counting in line-hours rather than clock hours keeps two lines running side by side from being counted as one, which is the commonest slip in a capacity sum..

Now divide the output by the time rather than by another quantity of registers. 2,50,000 registers over 4,000 line-hours is 62.5 registers a line-hour. 62.5 registers a line-hour is the rate the works actually achieved. Set it against the rate the works was rated for, 100 registers a line-hour, and 62.5 over 100 is 62.50 per cent.

The second route asks how fast rather than how much, and it lands in exactly the same place. Notice what changed on the way. The first route never mentioned an hour. The second route never mentioned the rated 4,00,000. The two routes start from different records kept by different people, they use different units in the middle, and they finish on the same two digits after the decimal point.

Why do the two routes agree here?

Do not call that agreement a confirmation, because the two routes could not have disagreed. Look at where the rated 4,00,000 came from: it is 4,000 line-hours multiplied by 100 registers an hour. So the first fraction is 2,50,000 over 4,000 times 100, and the second fraction is 2,50,000 over 4,000, all over 100. The second fraction is the first with the 4,000 cancelled from the top and the bottom. Nothing independent has been brought in.

A check that cannot fail has checked nothing, and treating this one as a confirmation is the first quiet error available in a capacity sum. If the output had been recorded wrongly, both routes would carry the identical wrong output. If the rated rate of 100 an hour had been set too high, both routes would carry that too, because the rated capacity is built out of it. Two ways of writing one relationship agree by construction, and agreement by construction is not evidence.

So what does the match earn? One real thing: it proves the rated 4,00,000 and the working year of 4,000 line-hours are consistent with each other. If both figures are handed over and they do not reconcile at 100 an hour, then one of the two was struck on assumptions the other does not share, and that has been found out before either percentage is written down.

When do the two routes actually part?

They part the moment the rated figure stops being built from the works' own hours. Somebody reads a rating off the plate on a machine, or carries forward a figure struck when the works ran a different shift pattern, or uses a rated capacity set for a year with a different count of working days in it. Now the denominator in route one no longer equals the line-hours in route two multiplied by the rated rate, and the two percentages separate.

A disagreement between the two routes is not a rounding error, it is a denominator nobody read. The output is the one number both routes share, so the output cannot be the source of the difference. The difference has to be in the rated figure, and specifically in the hours and the speed that were assumed when it was struck. Averaging the two percentages is the instinct, and it produces a number describing no works that has ever existed.

The practical rule is short. Before either percentage is written down, the question to ask is what the rated figure was built from. If it opens up into a count of machines, a count of hours and a rate, it can be tested. If it does not open up at all, the honest thing is to say so rather than to divide by it and report two decimal places.

What does one utilisation figure hide?

A utilisation percentage is not one thing. A utilisation percentage is two things multiplied together: the share of the available hours that were actually run, and the share of the rated speed that was actually achieved while running. Only their product is reported, and a product can be reached from more than one pair.

Take Anjani Stationers Private Limited's 2,50,000 registers and produce them two ways. In the first, every one of the 4,000 line-hours is run, and the lines turn out 62.5 registers an hour. The first works ran 100 per cent of the time available at 62.50 per cent of the rated rate, and 100 multiplied by 62.50 per cent is 62.50 per cent. In the second, only 2,500 line-hours are run, but every one of them at the full rated 100 registers an hour. The second works ran 62.50 per cent of the time at 100 per cent of the rate, and the product is the same 62.50 per cent. Both produce exactly 2,50,000 registers. Both report exactly 62.50 per cent.

One works ran every hour it had and ran slowly, the other ran at full speed and stood idle for 1,500 line-hours, and the percentage cannot tell them apart. These are not two shades of the same situation. Idle hours and slow hours are opposite situations wanting opposite responses. The first is a line speed problem, and the answer lives in the machines, the changeovers and the way work moves between stages. The second is an order bookThe work a business has already been asked to do and has not yet delivered. A thin one leaves machines standing whatever their condition; how a business fills it is a selling question rather than a production one. or a scheduling problem, and the answer lives outside the works entirely. Spending on one when the trouble is the other buys nothing.

The published year was the first of the two. Anjani Stationers Private Limited ran all 4,000 line-hours and achieved 62.5 registers an hour. A reader handed only the 62.50 per cent could not have known that, and would have had no way of finding out from the percentage alone.

What is actually inside the rated figure?

Open the rated 4,00,000 and four things fall out. Two lines. Eight hours a day. 250 working days. One hundred registers a line-hour. Multiply the four together and the rated capacity comes back exactly. Now look at them again and sort them, because they are not the same kind of thing at all.

One hundred registers a line-hour is a fact about machines, set by the slowest stage the work passes through. The other three are decisions. How many lines to keep running, how long a shift to staff, how many days a year to open: each of those was chosen by somebody, is written down somewhere, and could be changed next quarter by a meeting.

Changing the shift pattern changes the reported utilisation while nothing on the factory floor changes at all. Shorten the working year and the denominator shrinks under an unchanged numerator, so the percentage climbs. The registers going out of the door are the same registers, made by the same machines, at the same speed. A works reporting a rising utilisation may have improved. The works may equally have redefined what it counts as available, and the percentage cannot distinguish those two either.

The same reading disposes of a target that gets set far too often. One hundred per cent utilisation is not something to aim at, because the rated figure ignores things that are real. Machines need maintenance. A changeoverThe stop between two different runs, while settings, plates or materials are swapped so the next batch can start. The time it takes is real production time and no rated figure includes it. between one specification and the next takes time that produces nothing. A rated figure that assumed neither is not a ceiling anybody can touch, and a works pressed to reach it gets there by deferring the maintenance rather than by making more.

One choice about the denominator is still open, and the choice is genuinely a choice rather than a convention. Subtract the hours a works books out in advance for maintenance and changeovers, and a second denominator appears underneath the first: the capacity available in the hours the works was actually open. Book 400 of the 4,000 line-hours out and the same 2,50,000 registers read 62.50 per cent against the rated 4,00,000 and 69.44 per cent against the 3,60,000 available. Neither is wrong. The first asks how much of what the works was built to make it made, the second how much of what it could have made while it was open, and a figure quoted without saying which one it used is a way to make a works look busier than it is.

What does a utilisation percentage not establish?

Be clear about how little the finished number claims. The percentage does not establish that the idle capacity is worth filling. Filling 1,50,000 registers of capacity requires 1,50,000 registers of demand at a price that covers what making them costs, and the utilisation figure knows nothing about either. Nor does it establish that filling the gap is even possible: the paper has to be there, the people have to be there, and the buyers have to want registers in the months the works can make them.

The percentage does not establish that a higher figure is a better business. A works running at 95 per cent on work it priced badly is in more trouble than one running at 62.50 per cent on work it priced well, and the percentage is silent on price. Nor does it establish anything about what a business is worth. Worth is a different subject with different inputs.

A utilisation figure measures use and says nothing whatever about whether the use is worth having. The silence is not a weakness in the measure. The measure is precisely that: a description of how much of a rated ability was drawn on, held deliberately clear of every question about whether drawing on it was a good idea. The effect on margin of filling the gap is worked through separately.

What is the most that filling the gap could be worth?

A reader who has just computed 62.50 per cent asks the obvious next question immediately: what is the missing 37.50 per cent worth? There is an honest answer and it arrives with a label welded to it. Push the works to its rated 4,00,000 and the return on capital employedOne year of operating result, stated as a percentage of the funds locked into the business to produce it. How it is built and read is covered in the accounting notes rather than here. Anjani Stationers Private Limited published at 27.3 per cent comes out at 72.89 per cent instead, a figure marking the outer edge of what better use of the machines could reach on its own, and not a prediction of anything.

Look at what has to be frozen for those two digits to arrive. The capital employedThe total money tied up in a business, counted as the funding put in by owners and long term lenders, or equivalently as the fixed assets plus the working capital it needs to run. Where the figure comes from is covered in the accounting notes. stays exactly where it was, Rs 1,52,00,000/-, even though three fifths more registers are leaving the door. Receivable daysHow many days of sales are sitting unpaid with customers on average. A higher number means money is tied up for longer between despatching goods and being paid for them. stay at 128 too, when a works despatching three fifths more registers is waiting on three fifths more unpaid invoices and needs more paper standing on the floor besides. Neither of those would sit still in practice, and both of them move the wrong way for the number.

The ceiling rests on one more thing worth naming. The split between costs that move with volume and costs that do not is an assumption made for teaching here rather than something the business disclosed, and a different split gives a different ceiling. So the figure answers how far this could possibly go and not what will happen. The arithmetic behind it is worked through separately in these notes.

Which three questions come before writing a utilisation figure down?

A lender sizing a working capital facility, an analyst building a view of how much a manufacturer can grow without spending on new machines, and a works manager deciding what to do on Monday all reach for the same percentage, and all three should ask the same three questions of it first.

First: what period is the output measured over, and does the rated figure cover the same one. The period question is the mechanical check, and it catches the crudest errors. Second: what was the rated figure built from. If it opens up into machines, hours and a rate, it can be tested, and tested against the second route. If it arrived as a single number from a nameplate or a previous year's file, then the divisor is something nobody can inspect.

Third: is the gap made of idle time or of slow running. The percentage never answers the third question by itself, and of the three it is the one that settles what happens on Monday. The lender learns from it whether more volume needs money spent on machines or only more orders. The analyst learns whether the growth on offer is nearly free or expensive. The works manager learns whether Monday's problem is on the shop floor or in the sales office. Same percentage, three readers, and none of them can get what they came for without splitting it in two.

The everyday version is a truck. A household moving house is told the truck was used at sixty per cent. Sixty per cent of what: sixty per cent of the days it could have run, or sixty per cent full on every trip it made? The first means hiring the same truck for more days. The second means packing better. Nobody would confuse those two about a truck, and everybody confuses them about a works, because the works reports a percentage and the truck is sitting in the street where it can be looked at.

Anjani Stationers Private Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.