Throughput: The Rate the System Actually Produces

Throughput is the rate a whole system turns raw material into finished, saleable output, and the slowest stage sets it. Anjani Stationers Private Limited, an invented manufacturer, cuts 150 registers an hour, prints 125 and binds 100, so the works makes 100 an hour and no more. A second rate sits beside it: of the paper that went in, 70.42 per cent came back out as registers.

Two things already established carry everything below. The first is the order the work runs in: paper is cut, then printed, then bound, and a register that has not been bound is not a register anybody can invoice. The second is Anjani Stationers Private Limited's money, set out in full elsewhere in these notes: revenue of Rs 2,70,00,000/-, contributionWhat one unit brings in once the costs that move with that unit have been taken out, and before any cost that stands still is touched. of Rs 1,15,50,000/-, fixed costA cost whose total stays put whether the works makes one register or four lakh of them. Shed rent, the works manager's pay and the insurance all sit here. of Rs 74,00,000/-, and Rs 41,50,000/- left at the operating line.

Underneath those rupees sits a machine. Anjani Stationers Private Limited made 2,50,000 hard-bound registers of 200 printed sides in the published year and realised Rs 108.00/- on each. Rs 59.40/- of that went on paper and Rs 2.40/- on carriage and packing, leaving Rs 46.20/- of contribution, and Rs 29.60/- of standing works cost against it leaves Rs 16.60/-. Every one of those per-register figures multiplies back to a published total to the paisa, and a per-register figure that will not multiply back is not worth accepting. Rs 46.20/- multiplied by 2,50,000 comes back to Rs 1,15,50,000/-. Rs 16.60/- multiplied by 2,50,000 comes back to Rs 41,50,000/-. Both multiplications are worth doing once. Everything that follows leans on them.

What does throughput measure, and why is it not a property of any one machine?

Throughput is the rate at which finished output leaves the far end of the line. Not sheets cut, not sheets printed, not work started: registers bound, countable and ready to invoice. The measuring point matters more than it sounds. Everything upstream of the last stage can be running flat out and producing nothing a customer can be charged for. Throughput is a property of the whole system and never of any machine inside it, so a specification sheet for a press is not an answer to the question and never was.

Think of a busy sweet shop on the morning of a festival. Three counters are packing boxes at speed, and one person at the door is checking every bill before a customer may leave. However fast the three counters work, customers leave the shop at the rate the person at the door can check bills. Put a fourth packer behind the counter and the queue at the door simply gets longer. The shop's rate was never the packers' rate. It was the door's.

Which stage sets the rate the whole works runs at?

Anjani Stationers Private Limited runs three stages on the same registers, one after another. Cutting takes reams down to finished size at 150 registers' worth an hour. Printing runs at 125. Binding, the stage where loose printed sections become a hard-bound book, runs at 100. The same register has to pass through all three stages in order, so the three rates are not averaged and not added. A chain of stages runs at the rate of its slowest stage and at no other rate, so the works makes 100 registers an hour.

The idea has a name and an owner worth stating. Eliyahu Goldratt set it out in The Goal in 1984: in any system that produces something, one step is the constraint, and the output of the whole system is the output of that step. Everything else in the line is faster than the step holding things up, so everything else has spare capacity by definition. Anjani Stationers Private Limited's constraint is binding.

Turning an hourly rate into a yearly one takes three counts and one multiplication. Anjani Stationers Private Limited runs two lines, eight hours a day, across 250 working days. Multiply the three counts and the works has 4,000 line-hoursOne hour of one production line running. Two lines working an eight hour shift give sixteen line-hours that day, which is how a works counts the time it actually had available rather than the time on the calendar. of available time. At the system rate of 100 registers an hour, that is a rated capacity of 4,00,000 registers a year. The works made 2,50,000 registers against that rating, or 62.50 per cent of it. How such a percentage is built, checked against a second route and misread is a separate subject, covered under Capacity Utilisation: How to Compute It and What It Hides.

What happens when a stage that is not the slowest is made faster?

The answer is stronger than most people expect. Form the prediction before reading on. Printed sections visibly pile up in front of the binder, so printing is the stage the shop floor complains about. Suppose Anjani Stationers Private Limited buys a faster press and printing goes from 125 registers an hour to 150.

Binding still takes 100 registers an hour, so the works still makes 100 registers an hour and still makes 2,50,000 registers in a year. The only thing the new press changed is how quickly the pile in front of the binder grows. Money spent anywhere except the slowest stage buys nothing at all, and the strong form is the whole point: the return is zero rather than small. Take cutting from 150 an hour to 200 and the same nothing happens, for the same reason.

Now move the stage that is actually holding the line. Take binding from 100 registers an hour to 125 and the system rate goes to 125. Cutting at 150 and printing at 125 can both keep up. The 4,000 line-hours have not changed, so rated capacity moves from 4,00,000 registers to 5,00,000. The same rupee of spending buys 1,00,000 registers of rated capacity at binding and exactly nothing at printing, and nothing about the two machines explains that difference. Only their position in the order does.

Where does the constraint go once the slowest stage has been fixed?

It moves. Once binding runs at 125 registers an hour, printing also runs at 125 and binding is no longer the slowest on its own. The two now tie, and the works cannot pass 125 an hour until both of them move: raise binding again by itself and printing holds the line, raise printing by itself and binding holds it. Fixing a constraint does not remove it, it relocates it, so which stage is slowest is never answered once and for all. The ranking has to be redone after every improvement, and a capacity plan built on last year's answer buys the wrong machine at exactly the moment the business can least afford it.

The practical instruction is therefore a loop rather than a decision. Rank the stages by units an hour. Spend at the slowest. Re-rank. Spend again at whatever is slowest now. Buying at the stage that used to be the problem is the most expensive habit on a shop floor. Every rupee of it lands in the standing cost and none of it lands in output.

What is the second rate, the one from paper in to registers out?

How fast the works runs is only half of what a rate can mean. The other half asks how much of what went in came back out, and it is a completely different quantity with a completely different fix. Anjani Stationers Private Limited's lead product is a hard-bound register of 200 printed sides, and 200 sides are 100 sheets of paper. A reamThe paper trade's counting unit, five hundred sheets to the ream. Paper is bought, stored and invoiced in reams rather than in single sheets. is 500 sheets. So at perfect conversion, one ream becomes five registers and nothing is left over.

The works consumed 71,000 reams in the published year. At five registers a ream that is 3,55,000 registers. The works made 2,50,000. A works has two rates, how fast it runs and how much of what went in comes out, and the two have different fixes. Speeding up binding does nothing for the second one; a sharper blade, a better nesting layout on the sheet or fewer mis-printed signatures do nothing for the first. Anjani Stationers Private Limited got 3.5211 registers out of a ream against a possible five, a yield of 70.42 per cent.

A tailor cutting shirts from a bolt of cloth lives with the same two accounts. How many shirts he finishes in an afternoon is one number. How much cloth ended up on the floor as offcuts is another, and a fast tailor who wastes cloth and a slow one who wastes none are failing in ways that no single figure can describe. Anjani Stationers Private Limited's offcuts are called trimThe strip cut away to bring a sheet down to its finished size, together with everything torn, mis-printed or rejected along the way. It leaves the works as scrap rather than as product., and they leave on a scrap cart.

Why does the largest improvable number appear in no statement?

The waste is 21,000 reams, 29.58 per cent of the paper consumed, and at the Rs 210.00/- weighted average purchase priceOne price standing in for several separate buys, each buy weighted by how much was bought at it. A large lot pulls the average towards its own price far harder than a small lot does. that paper cost Rs 44,10,000/-. Not one statement Anjani Stationers Private Limited published carries that number, or any number from which a reader could work it out. The profit statement carries paper consumed as a single cost line, Rs 1,48,50,000/-, with no unit count behind it. The balance sheet carries the paper still on hand. The accounts record what the paper cost and never what the paper became, so nothing anywhere counts registers against reams.

Silence in the accounts is the whole reason the trim goes unchased. A works chases what its reporting shows it. Sales are reported weekly, the wage bill monthly, the paper price every time a lot is bought, and the biggest single improvable quantity in the building is reported never. The trim sits on a scrap cart nobody weighs.

Now the trap that sits directly on top of this figure. The shortfall is 1,05,000 registers. Paper costs Rs 59.40/- a register. Multiplying the two gives Rs 62,37,000/-. The product looks like the value of the waste and is wrong. Rs 59.40/- is paper per register sold: it is Rs 1,48,50,000/- of paper divided across the 2,50,000 registers that actually came out, so the cost of every wasted ream is already sitting inside it. Applying it again to the registers the waste destroyed charges the same paper twice. The honest statement of the waste is in reams, 21,000 of them, and in rupees only at the raw paper rate, Rs 44,10,000/- at Rs 210.00/- a ream.

What is a tenth of the trim worth to Anjani Stationers Private Limited?

Take the smallest credible improvement: recover one tenth of the 21,000 reams. One tenth is 2,100 reams, and at five registers a ream that is 10,500 more registers. Nothing else changes, so each of them carries the full Rs 46.20/- of contribution. A tenth of the trim is worth Rs 4,85,100/-, or 11.69 per cent of the year's operating result, and nothing in the accounts would ever have pointed at it. Set that against Rs 41,50,000/- of earnings before interest and tax (EBIT) and divide it yourself.

Notice what makes those 10,500 registers unusually valuable. The works has 1,50,000 registers of rated capacity standing idle, so those 10,500 need no new machine. The price stays at Rs 108.00/- throughout, so they need no new customer at a worse price. The paper was bought, paid for and thrown away, so they need no extra paper. All that is required is that fewer sheets end up on the scrap cart. The number is therefore improvable rather than lost. A loss has already happened. The trim recurs every year until somebody counts it.

What does the whole works look like when it is laid out in one column?

Everything below belongs to Anjani Stationers Private Limited in one illustrative year. The rupee figures were published elsewhere in these notes and are quoted; the counts, rates and per-register figures belong to this sequence and are stated as such. The stage rates first.

One caution about a figure that will not add up if it is taken at face value. Chitra Binding Works Private Limited, 70 per cent held by Anjani Stationers Private Limited and bought at the start of year two for Rs 21,00,000/-, invoices Rs 3.20/- of binding on every register, and that Rs 3.20/- does not sit beside the Rs 59.40/- of paper and the Rs 2.40/- of carriage: it sits inside the Rs 29.60/- of works cost, and the works cost splits into Rs 3.20/- of binding and Rs 26.40/- of everything else. Paper plus carriage is the whole of the Rs 61.80/- that moves with a register. Adding all three figures together gives Rs 65.00/-. The total is more than the variable cost per register and looks like an error until the third figure's home is identified. Why a business buys a stage of its own chain is a separate subject, covered under Vertical Integration: Owning More of the Chain.

The available time, and what it rates the works at.

The three moves, done as arithmetic rather than asserted. Only one of them changes anything.

And the yield, from paper in to registers out.

How Capacity Utilisation Affects Margins and Returns: what would filling the idle machines do to the margin?

The works ran at 62.50 per cent of its rated capacity in the published year. Take that reading as given and put the idle 37.50 per cent to work: 4,00,000 registers instead of 2,50,000, at the same Rs 108.00/- and the same Rs 61.80/- of cost that moves with each one. Revenue becomes Rs 4,32,00,000/-. Contribution becomes Rs 1,84,80,000/-. The Rs 74,00,000/- of standing cost does not move, so the operating result becomes Rs 1,10,80,000/- and the margin climbs from 15.37 per cent to 25.65 per cent.

The margin rises because Rs 74,00,000/- of cost does not move when the volume does, not because anything was sold better or bought cheaper. The price is the same price and the paper is the same paper. Say the assumption out loud alongside the result: the split between cost that moves with volume and cost that stands still is an assumption these notes make about Anjani Stationers Private Limited, not something the accounts disclosed, and every figure in this section rests on it.

Why does a purely physical move land on 2.7831, a number the accounts already gave?

Look at the two changes rather than the two levels. Volume rose from 2,50,000 registers to 4,00,000, a rise of 60.00 per cent. The operating result rose from Rs 41,50,000/- to Rs 1,10,80,000/-, a rise of 166.99 per cent. The second divided by the first is 2.7831. That 2.7831 is the operating leverageHow hard the profit line reacts to a change in volume. A business carrying a large standing cost has a lot of it, because a small rise in units produces a much larger rise in profit. already published for Anjani Stationers Private Limited, worked out from two accounting figures with no machine in sight. Rs 1,15,50,000/- of contribution divided by Rs 41,50,000/- of operating result is the same 2.7831.

Two routes, arriving from opposite directions, land on one number. Coincidence does not explain that, and neither does any general law: what both routes measure is the same block of cost refusing to move while contribution climbs. The accounting route measures it by comparing contribution with what is left after the block. The physical route measures it by filling idle machines and watching what reaches the bottom line. Change the size of the block, or move a rupee of cost from standing to moving, and both routes shift together to a new figure.

And the return, a figure that needs a label attached before it is quoted at all. On the published capital employed of Rs 1,52,00,000/-, an operating result of Rs 1,10,80,000/- would read 72.89 per cent against the published return on capital employedOperating profit measured against the money tied up in the business, both the shareholders' part and the borrowed part. It answers what a rupee of capital is currently earning. of 27.3 per cent, and that 72.89 per cent is a ceiling on what filling the machines could do rather than a forecast of any year. The ceiling holds capital employed still at Rs 1,52,00,000/- while volume rises 60 per cent, and receivables running at 128 days would not stand still while 60 per cent more registers went out of the gate. More registers means more paper on the floor and more money owed by customers, and both of those enlarge the denominator the 72.89 per cent is computed on.

Which two rates should a reader ask a works manager for, and in what order?

Two questions, asked in this order, will tell an analyst, a lender or a buyer more about a manufacturer than most of what a factory visit produces. First: how many units an hour does the slowest stage run at, and which stage is it? A manager who cannot name the stage has not looked, and a manager who names a different stage every quarter is describing a queue that moves rather than a constraint that has been measured. Second: for every unit of raw material that goes in, how many finished units come out?

A works that can answer only the first question has never counted its own waste. Nothing in ordinary reporting asks for the second answer, so it is almost never volunteered. For a lender the two rates are collateral questions in disguise: the first says how much of the sanctioned working capital limit can actually be converted into invoices in a year, and the second says how much of the paper on the security of which money was lent will ever become a saleable product. For an analyst the pair explains a margin without needing anybody's opinion on it. A manufacturer running at a high yield and a low utilisation has idle machines, and idle machines are a spending problem. A manufacturer running at a high utilisation and a low yield has a scrap cart, and a scrap cart is a process problem. The process problem is usually cheaper to fix and much harder to see.