Cut the (s)crap

[I had to edit this post on April 01, 2008. And no, it’s not April Fool’s Prank] 

Have you ever wondered how manufacturing scrap works? Or what it really is? It’s an interesting topic, and yet a very confusing one. It has caused so many headaches to the project team I worked on recently, because nobody really understood it. So, what is manufacturing scrap?

Every manufacturing (or production) process produces scrap. It’s a given. The reason there is scrap is imperfection, and it’s mostly not about machines themselves. Even if you had the most perfect machines run by Star Trek computers, you couldn’t possibly eliminate the imperfection. Imagine you manufacture furniture. Your wood cutting machines work around the clock, blades wear off and get overheated, a careless worker forgets to change the blade when he should, and the blade breaks, destroying an otherwise perfect piece of wood. Or a grain of sand makes its way to the polishing machine, and you find it out only after five hundred panels, which instead of being mirror-polished, look as if a cat with mad cow disease danced flamenco over them while being electrocuted. Scrap happens.

What’s the big deal about it? You simply throw away the scrap, attribute the costs of scrapped quantity to good quantity, and that’s it. From accounting perspective alone, this works allright. But from supply chain management perspective, scrap is a big issue. In order to be able to meet your demand, you must be able to predict the scrap. You must be able to plan for it.

How do you plan for scrap? In manufacturing, there are several kinds of scrap, which you must take into account when planning your supply chain. You may have scrap related to preparing the machine, or scrap related to calibrating it. You can do almost nothing about it, because every time you start the machine, to get it properly running you might need to throw some of the products away. This kind of scrap is called fixed scrap. This kind of scrap is similar to fixed costs, because no matter how big the volume, fixed scrap remains the same per production process. For example, if you are printing newspaper, you might simply need to use first two hundred meters of paper roll to calibrate the printing machine, regardless of whether you print ten or hundred thousand copies. Fixed scrap is expressed as a number of units, and normally can’t be influenced too much. In our example, fixed scrap would be two hundred meters.

Another important type of scrap is called running scrap, or operation scrap, which amounts to certain percentage of whole input quantity. Because it is tightly related with input quantity of materials, it varies as quantity varies, therefore it is very similar to variable costs. Running scrap is expressed in percentage. If your printing machine scraps 2% during operation, you will scrap 200 copies of newspaper if you print ten thousand copies, but you will scrap 2,000 copies if you print a hundred thousand copies.

What causes this running scrap? Running scrap normally has nothing to do with preparation of machines, but it has a lot to do with human error, or machine imperfection. Anyone, or any machine, performing an operation, is likely to screw up every once in a while, and as a result, you get scrap. If you have bad machines or you don’t maintain them, or have unskilled personnel, you are likely to have more running scrap. If you have cutting-edge machinery and highly skilled operators, you can reasonably expect to have very little scrap. While fixed scrap in most cases can be determined very precisely, running scrap can be only estimated.

So far, it has been pretty simple. But now for something completely different.

Manufacturing process is rarely simple, and it usually consists of several operations, which may run in parallel, or sequentially, or both. If there was only one operation, scrap would be simple. If you printed posters, and your printing machine scrapped one hundred sheets of it up front for preparation, and then scrapped 10% during processing, how much paper sheets should you put into the machine to get one thousand sheets out? The answer is simple:

1,000 + 10% + 100 = 1,200

But add another operation, cutting for example, which also has one hundred meters fixed scrap, and also 10% running scrap. Now, how much paper should you put into the printing machine to get one thousand sheets out of the cutting machine? If you think this is correct answer:

(1,000 + 10% + 100) + 10% + 100 = 1,420

You’ve just wasted 10 good sheets of paper. Why? Because fixed scrap is more fixed than your hunch tells you. It is not just fixed per operation, meaning that no matter whether your operation consumes 1,000 sheets or 10,000 sheets, fixed scrap is the same. It is also fixed across operations, meaning that fixed scrap used on one operation stays the same throughout the manufacturing process, regardless of number of operations. When you pay closer attention to the last formula above, you can clearly see that fixed scrap on last operation is affected by running scrap percentage of 10% of the previous operation. When you complete the formula above, you can see that it consists of 210 sheets of fixed scrap (100 of the last operation, increased by 10% of the running scrap of the first operation, plus fixed scrap of the first operation). However, the total fixed scrap per whole process should be 100 + 100 = 200 sheets of paper.

So, fixed scrap is fixed throughout manufacturing process, but running scrap accumulates for each operation. So, correct formula for scrap calculation must calculate running scrap completely separate from fixed scrap. Something like this:

(1,000 + 10%) + 10% + 100 + 100 = 1,410

But fixed scrap gets funny. Try to calculate net output from 1,410 gross requirements. It’s easy:

(1,410 – 100 – 100) – 10% – 10% = 1,000

However, try to calculate the output from the first operation, which is also input for second operation. We know that fixed scrap should be fixed, however, if you try to calculate the output of the first operation based on known fixed scrap and running scrap, you get incorrect result:

(1,410 – 100) – 10% = 1,190.91

Manufacturing planning systems normally don’t do these things. Typically, you know your net requirements, then you go and calculate the gross requirements based on known variables. But what if you had a scenario where you had certain amount of raw materials, and you wanted to calculate how much net output you can get from them? In this case, you get to learn a funny fact about fixed scrap: it’s really not that fixed after all.

When you calculate backwards, fixed scrap really is fixed, you calculate it separately from running scrap, then add the sum of fixed scrap to the sum of the running scrap, and get your gross requirements. It works so well that you can calculate the gross requirements for any single operation directly. However, when you calculate forward, fixed scrap goes bananas if you need to calculate output of a single operation which is also not the last operation in the process.

In our example, we had gross input of 1,410, we needed to calculate the output of the first operation (which is also input to second operation). Obviously, we can’t calculate it directly, because if we did so, we’d get result of 1,190.91, which if fed to second operation wouldn’t give us the actual 1,000 of net output:

(1,190.91 – 100) – 10% = 991.73

Which I hardly need to tell you isn’t 1,000 which is actual net output of 1,410 gross input. So, where’s the catch? How do you calculate the output of a single operation, which is not the last operation, directly, without calculating total net output, and then calculating it backwards?

[Start of edited block] 

When calculating fixed scrap forward, in order for your output to match the required gross input for the next operation, your fixed scrap gets inversely affected by both total fixed scrap of subsequent operations and running scrap of current operations. Formula would go something like:

Gross Input – (Fixed Scrap – SUM(Fixed Scrap of subsequent operations) * Running Scrap %) – running scrap % = Net Output

So, in our example, for the first operation, fixed scrap was 100, and total fixed scrap of subsequent operations was 100. When this total scrap was multiplied by running scrap of 10% of current operation, and deducted from fixed scrap of current operation, you get 90, you get the result of 90. So, instead of calculating the fixed scrap in the first operation as 100, you calculate it as 90. In this case, you get correct results:

(1,410 – 90) – 10% = 1,200

I must be nuts, right? My customer thought it when I was explaining this to them last week. Read on. Imagine we had four operations, all having 100 sheets of fixed scrap and 10% running scrap. For 1,000 net output, gross requirements would be:

((((1000 + 10%) + 10%) +10%) + 10%) + 100 + 100 + 100 + 100 = 1,864.1

Now, if you need to calculate the net output of the first operation, in the formula above, it would be:

(1,864.1 – (100 – 300 * 10%) – 10% = 1,631

If you want to go forward operation by operation, you’d get this:

(1,631 – (100 – 200 * 10%) – 10% = 1,410

(1,410 – (100 – 100 * 10%) – 10% = 1,200

(1,200 – (100 – 0 * 10%) – 10% = 1,000

So, fixed scrap is not that fixed, is it?

[End of edited block] 

When you think what scrap is, it may be hard to understand why this has to be so complicated. Scrap may be regarded as some kind of safety against running out of raw materials, and helps you with planning. Why is it calculated this way, then? Why can’t it simply be calculated by applying the running scrap percentage of the next operation against the fixed scrap percentage from the previous operation, like this:

(((1,000 + 10% + 100) + 10% + 100) + 10% + 100) + 10% + 100 = 1,928.2

Because calculating net from gross is as straightforward:

(((1,928.2 – 100 – 10%) – 100 – 10%) – 100 – 10%) – 100 – 10% = 1,000

Isn’t this logical, after all? Well, not really. Imagine yourself working at the shop floor, operating the machines. Your first machine has 100 sheets of scrap, and 10% expected running scrap. After it has finished working, you don’t simply throw away those first 100 sheet, and you don’t stick your finger into the exit pile, peel off the top 1/10 of it, and throw it away. If you did so, then this last method of scrap calculation would work. But fixed scrap of one operation might be also good as fixed scrap of subsequent operations. If you need 100 sheets of paper to get the first machine running, and you need 100 sheets of paper to get the second one running, and this paper is scrap anyway, couldn’t you use same 100 sheets of paper as fixed scrap for both operations?

So, the reality at the shop floor really looks much different than the requirements calculation, which will never give you the exact and precise results, but your goal should be to try to keep it as accurate as possible, by tracking scrap, planning for it, then improving your processes, then repeating it over, and over, and over again.


Vjeko has been writing code for living since 1995, and he has shared his knowledge and experience in presentations, articles, blogs, and elsewhere since 2002. Hopelessly curious, passionate about technology, avid language learner no matter human or computer.

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