Theory of Constraints (TOC)

In 1984 Eliyahu Goldratt published a book called The Goal. It teaches the principles of an emerging field called Theory of Constraints as they apply to business operations or plant management. These principles are taught using a business novel to show how the principles apply in these specific physical circumstances. It also contains a secondary plot involving the personal life of the primary character in the novel which establishes that the same principles can also be applied in our personal lives. By the time the story is concluded the reader has been thoroughly introduced to a new way of thinking. The basic concept is that our understanding of the world around us always rests on assumptions. We have no choice about whether we make assumptions. The only choice we have is which assumptions we choose. Our assumptions bind us thereby limiting our ability to act. There is not news, it is the basic process of perception! The author then shows how different assumptions can change what we perceive, the actions we can take, and the results of those actions.

He starts by introducting a new way to measure performance in plant operations. He teaches the protagonist the ideas of Throughput, Inventory and Operational Expense and the ramifications of these concepts in plant operations. The protagonist then extends those lessons to his personal life. It is these ramifications which constitute the revolution in thinking which is TOC. In the first edition the story ends with the protagonist saving his plant and earning a promotion. Later editions have been extended the story to introduce the next step in the process - understanding the thinking processes that underlay TOC principles. This synopsis is not a substitute for reading The Goal. I do not attempt here to fully explain the concepts and their background that Eliyahu Goldratt does in his novel. It is an absorbing story in itself and it is on my "A" list of books to read.

The Goal

Alex has been running his manufacturing plant for about 6 months. A series of incidents brings it to his attention that his plant is not making money. He receives an ultimatum from his boss that if he does not make significant progress in the next three months toward profitability, his plant would have to be shut down entirely. Natually Alex is panicked by this news. He contacts an old University teacher he had run into a few weeks previous to see if he could get some help with his problem. Jonah, as his former teacher is known, offers to assist but is unable to be a regular consultant due to his hectic schedule. Jonah asks Alex what the goal of a business is and Alex is having some difficulty answering Jonah's question. This is not as unreasonable as it might seem. When we are in the middle of the forest we most commonly see only trees and not the overall view of the forest itself.

The Plot

Alex finally concludes that the goal of a business is to make money. Naturally we then need a way to measure our progress toward the goal. At the senior management level the system of measurements is quite simple. It consists of three measurements used together to assess and control the financial health of an organization. These measurements are taught to all business students.The trouble is that they are not terribly relavent to some parts of business and certainly not the parts of a business that we work in after graduating from college or university. The high level measurements used to assess an organization's fiscal health are:

In using these measurements we want all of them going in the right direction all of the time. Profits should grow continuously larger, relative profits should grow larger with the the same assets, and we need to accrue cash and near cash resources so that we always have sufficient liquidity for our business purposes. This lesson liquidity is currently being reinforced as the world heads into a recession and many companies have discovered they have not done an adequate job of maintaining any of these measures but most especially liquidity.

The difficulty in an organization is: How does one know whether any particular action is moving us closer to the goal? You see the three measurements above are expressed in financial terms and it is often difficult for operations to be assessed in financial terms before they are implemented. This is particularly true in manufacturing plants. The financial measurements are not terribly helpful here so Jonah introduces Alex to a new measurement system which is much more functional for assessing whether any given action in a plant is moving the organization toward the goal. This system also requires three measurements and they are as follows:

These measurements are a tool which enables anyone to determine whether any action we want to take will move us toward the goal or away from it. They apply to the system as a whole not just to a part of the system! This point is very important. When we look at just a part of a system we refer to this as a 'localization'. With TOC we are not interested in localizations. We don't want to look at an individual tree we want to consider the forest as a whole. We want throughput to increase; we want operational expense to decrease; we want inventory to decrease. While we want all three measurements to improve at the same time, it is necessary to realize where the greatest improvement will come from. Relative magnitude of improvement over a year for each of these are:

This ought to suggest that our efforts need to be primarily focussed on increasing throughput. However, check out the business news stories and judge for yourself where companies are focussing most of their time and energy. Almost all of them are focussed in the areas where the least improvement is possible!

So the first fundamental lesson is to focus on throughoput. Any kind of an analysis of how to improve throughput reveals that we need to understand some basic concepts before we can come to grips with how throughput can be increased. The first two concepts are:

In a manufacturing operation, as in life, events occur in a sequence. They do not occur in isolation so thinking about them as if they are separate from all other events in the sequence is not only misleading but will harm the sequence itself! For example painting a part cannot occur until the part is first machined. So the later events are dependent on earlier events. If we are driving along a road following other vehicles then our driving is limited by, dependent upon, the behaviour of the drivers ahead of us. If we cannot pass the vehicles ahead of us then our speed is dependent on their speed. As much of an impact as this dependence has, it is the combination of that dependence and statistical fluctuations which really create the real havoc!

Statistical fluctuations mean that while we know how many parts are normaly be produced each hour, the actual number of parts fluctuates around an average. In any given hour we may produce more or less than that average. Using the car example in the previous paragraph we would say that our average speed fluctuates around the average of the slowest car ahead of us. This is because the slowest car effectively governs the speed at which all vehicles behind it may travel. It is a bottleneck to all trafic behind it. In a plant these effects are also observed. One of the steps in our system will be a bottleneck. This concept is central to understanding throughput. A bottleneck determines the throughput for the system and any given system only has one maybe two bottlenecks at any given time. There is a mathematical proof of this concept but if we pay attention to the things going on around us common sense will confirm this observation without resorting to reading the mathematical proof. If we look around us we can quickly find several examples of this behaviour in the organizational world around us both in our work worlds and in the wider world in which we life.

The last two paragraphs have just explained something very fundamental to understanding throughput in our organizations but, the reaction of most people to this information is: "So What?" This means they still don't understand: they don't get it! Let's look at some of the implications of the existence of bottlenecks. For example the cost, to the system, of a bottleneck not operating.

We might ask what is the cost of having a bottleneck go down, be non-operational, for an hour. Cost accounting experts will quickly answer with a number which they have calculated with great precision which represents the cost of operating that machine for an hour. The problem with their answer is that they have calculated the cost for the machine as if it was operating all on its own - in isolation or 'localized'. They are demonstrating their understanding of mathematical technique and their total ignorance of the fact that the machine does not operate in a vacuum. Do not misunderstand me, they are not ignorant, they are making an incorrect assumption. They are acting as if the context, the assembly line, is irrelevant when it is anything but irrelevant. The question was "What is the cost if that machine is a bottleneck and takes the whole system down for an hour?" The assumptions are very different. The cost of taking down the whole system for an hour is the total loss of productivity for the entire system for that hour. In other words the system loses one hour of productivity and the organization loses the sale of those products which were not produced. It is as if the whole plant is idle for an entire hour. That number is always substantially higher than the figure which the cost accountants will quote!

Alex and his group then spend quite a bit of time learning how to differentiate and manage bottlenecks. They first have to learn to see things in a new way. Then they learn how to properly manage their bottlenecks. As a result they dramatically increase their throughput and become the bright spot of the company for the next quarterly reporting period. In doing so the bottleneck shifts from being one of the machines in the plant, to being the market. This is the normal state of affairs for many of our business organizations. So they learn to dramatically increase their sales and how to manage their physical bottlenecks at the same time. This is not a trivial point and the know-how to do it is very precious!

The Process

In the Goal a process of ongoing improvment is followed. At first the participants do not realize they are following a process. However, when they analyse their actions they not only see and identify this process but they also realize that they have not done certain things to complete the process. The missed actions are causing problems for them and so the reflection helps them solve some of their residual problems. The process of ongoing improvement that they follow consists of the following five steps:

  1. Identify the system's constraint.
  2. Decide how to Exploit the system's constraint.
  3. Subordinate everything else to the above decision.
  4. Elevate the system's constraint.
  5. Warning!!! If in the previous step a constraint has been broken go back to step 1, but do not allow Inertia to cause the system's constraint.

In going through this process they are assistaed by Jonah who acts as a consultant and mentor to Alex and the others. He directs their attention to certain matters and asks questions that help the team to understand what is happening in their plant from a new perspective. While refusing to supply Alex with answers to his problems, Jonah does guide Alex to learn the things which enable Alex and his team to solve their own problems. The ideas are easy to understand because of the physicallity of a the example - a manufacturing plant. The things discussed are concrete not just abstract ideas, but the very nature of the concrete example also makes it difficult for people to transfer these principles to other areas. This has been a huge problem and is probably the primary cause for the time delay in implementing these ideas in other areas of business. I will explain this further when I discuss the It's Not Luck book.

Alex and his team are very successful, not only saving their plant from closure but setting records for profitability. Alex and his team have difficulty throughout the book because they, like all of us, have accepted things they have been taught without working them out for themselves. As a result of this, they accept many things in their world without having thought critically about them, and without having examined the consequences of those things for themsleves. We should not be surprised by this but most of us are surprised anyway when similar experiences happen to us.

Much of this comes down to the difference between Common Practice and Common Sense. As a result of actions taken in the past which become embedded in the system, Common practice is the way we do things around here. Actions become systematized and are then maintained by tradition and the inertia of the system. Common sense is our intuition about how some aspect of our world actually works. The two are quite different, and usually stand in stark contrast to each other. As people we have gotten used to compartmentalizing Common Practice and Common Sense as if they have no real connection with each other. An example from the book will illustrate. When Alex and his people learn what a bottleneck is their first step is to find out if they have any and where they are. By definition a bottleneck is an operation which has more demand on it than it can fulfill. If we try to get a machine to do more than it is capable of doing we will cause inventory to pile up around it. Common Sense tells us that the biggest piles of inventory will be found around the bottlenecks. Common Practice, however, has us diving into our records to find out what the capacity of our machines are, setting these up in a table and looking for the smallest number. Which method do you suppose yields results faster?

The successful adoption and use of these concepts result in a promotion for Alex. This terrifies him. He and his team did it, but he is not sure he can duplicate his reults in his new job. Jonah has offered to teach Alex the skills he needs, but asks Alex to come up with the list of the skills he needs to learn. In doing this Jonah is continuing his behaviour of getting Alex to understand and solve his own problems. Alex's wife assists him in this process. She became interested wondering what the skills could be. She is convinved that the needed skills are thinking skils and that they must be fundamental not just to managing a company, but fundamental to coping with life. At the end of the book Alex and one other protagonist are examining the five steps of ongoing improvement listed above to try and discern what skills are needed to accomplish that process. They come up with the following list of questions which the skills need to be capable of answering.

  1. How to decide what to change.
  2. How to decide what to change to.
  3. How to successfully plan and accomplish the change while avoiding all of the usual implementation problems.

Answering these questions requires methods of analysis - thinking skills, just as Alex's wife thought - which can be used to unequivically answer the questions. We need answers not guesses! We need to know that the answer we have will work. Jonah did not ask Alex to develop the thinking skills, just the questions which those skills needed to answer. So at this point Alex has his answer and indicates such to Jonah.


As a matter of interest, there are at least two methods used to answer these kinds of questions in our society. Since there is more than one method, we need to ask if either method is superior or are they both interchangeable. A partial list of the methods which are used is:

It turns out that the scientific method is superior in one very important way. The heart of the political method is compromise. In the accurate sciences there is no compromise with answers. For example, if we want to know the height of a building so we can send out two teams to find the answer. Most of us would think it ridiculous if they returned with different numbers. We would think it even more ludicrous if we then arbitrarily pick something between the two results to be the correct answer. This is exactly what we do when we use the Political method. The Political method assumes that the goals of both parties are mutually exclusive. The sad part is that we often do not even bother to verify this. We assume rhe objective is the same and start bargaining away what we want or need because something is better than nothing. This example also demonstrates that we have expectations about how many answers there should be to any given problem. When we think there is one right answer we use the scientific method. If agreement and participation are the most important aspects of an issue then we use the political method. This method acknowledges that the parties have different interests and we agree that there needs to be a negotiation for whose interests should take precedence. But this method almost always results in compromises being made by both parties. While this might be equitable - nobody gets exactly what they want, but everyone gets some of what they need - it overlooks the possibility that there might be a solution which could make all parties happy.

The scientific method provide us with the means to examine the assumptions and the consequences of our analyses and thus determine what our course of action should be without resorting to compromise. This is a marked departure from how we usually solve problems in the social and political arena! The point is we do not have to compromise; we have to find an answer which is acceptable to all of the constituents. These same thinking skills can be used in the social and political arenas to find and implement answers to problems which will solve our social and political problems without resorting to compromise. This makes the Scientific method approach superior to all others.

A dozen years later there had been so much demand for what comes next, that Goldratt wrote another book in which he articulates the thinking skills and explains how to use them to resolve complex problems. In the interim he was forced to develop Jonah's methods so that he could teach them as general principles and not just teach them 'by experience'.

It's Not Luck

The saga continues in Eliyahu Goldratt's next book called It's Not Luck. In this book the thinking skills are introduced and developed. These thinking skills are one of the three necessary things which enable a person to construct new common sense solutions to complex problems. One of the main things that normally makes this so difficult is that people and companies do not exist in a vacuum. They have a history and that history - traditions - constrain their thinking and approach to problems. To express it another way, common practice normally prevents us from seeing common sense! These Thinking Skills enable a person to systematically break free of the constraints of common practice. They comprise a system of constructing and communicating Common Sense.

The next necessary item for doing this is intuition. The Thinking Skills are no substitute for experience because experience is what enables us to develop intuition about a particular area. In our work life we often find ourselves fighting fires: trying to control a complex situation and prevent it from spinning out of control. The fact that a person has the ability to fight fires demonstrates that they have adequate intuition about a particular situation. However, while intuition is necessary for developing new solutions to complex problems, it is not sufficient all by itself.

The third necessary item to accomplish this analysis is the will to do it. You must believe there is a solution to be found or you will not try. Thus the will to do the analysis is the third necessary item. Together these three items are sufficient to find a solution. When intuition is combined with the Thinking Skills and the will to perform the analysis they are sufficient to solve complex problems in any area of human endeavour. This book shows us how this process works.

The protagonist is again Alex, who this time is the general manager of The Diversified Group. This group consists of three companies: a printing comapny, a cosmetics company and Pressure Steam. Acquired as a part of a diversification movement, these companies are in the diversified group because they have nothing in common with the main business of the organization. A decision is made by the board to sell these companies in order to improve the credit position of the organization. The companies' operational performance is exceptional, but their financial performance is marginal. Alex disagrees with the decision to sell but he cannot change it. He starts out as point person in assisting two of the board members with the sale. As the plot progresses his team figures out how to translate their exceptional operational performance into exceptional financial performance too.

There is also a side plot of applying the thinking skills in the personal arena and as the basis for Alex's wife, a marriage counsellor, who uses the thinking skills every day to help people work through their personal issues. By this time TOC was being applied in areas of business other than operations. This book teaches the thinking skills to show how TOC can be applied to solve complex problems.

Five thinking skills are introduced in the following order. They are:

Let me tie the three questions from The Goal to these five thinking skills. In the book the skills are presented, in the order shown above but that is not the normal sequence in which they are used. The following table shows the sequence in which the skills are normally applied in analyzing an issue.

QuestionThinking Skill SequencePurpose or Useage
What to ChangeCurrent Reality TreeTo create an accurate representation of the current situation in all of its complexity
Evaporating CloudTo verbalize an accurate and complete statement of the root cause of a problem
What to Change toFuture Reality TreeTo create an accurate and complete representation of the situation as we want it to be in the future
How to Plan the ChangeNegative Branch ReservationTo anticipate all the possible problems that might arise in the transition from Current Reality tree to Future Reality Tree and either prevent their occurrence or change their effect from negative to positive
Transition TreeTo create a step by step plan to move from the current situation to the planned situation

Evaporating Cloud

I presume that the author introduced the Evaporating Cloud tree first because it is the simplest of the thinking skills. In fact he introduces the Negotiating tree form first, but the two logic diagram are identical. They are, in fact, one and the same tool jut used for different purposes. The Evaporating Cloud form is shown in an example below. The first tool normally used in an analysis is the Current Reality Tree. Once a Current Reality tree has been created we trace the linkages back to find the root cause all the UDEs. If necessary we even rewrite the tree to show this root cause at the bottom of the tree. Then we write the root problem as a conflict between two necessary but conflicting requirements. This is the Evaporating Cloud. As the example shows there are five boxes linked by arrows. The top and the bottom paths represent the necessary but conflicting conditions. There can be more than two but that is rather unusual. The leftmost box presents the common objective. If there s no common objective, there is no conflict. The right side presents the conflict between the two necessary conditions. The diagram is always read from left to right using the following verbage. In order to... we must...

For the above example it would be read:

Cost Path
Throughput Path

Other than knowing the words which should be used to read these diagrams, no special training is needed to understand them. Constructing the diagrams is a bit more difficult. In my experience people make variations of these six mistakes when trying to construct Evaporating Cloud trees.

  1. They do not form a coherent cloud because they fail to make the correct logical connections between the boxes of the diagram. You must use the indicated verbage: In order to [contents of left box] we must [contents of right box] in order to tease out the meaning. Without these logical connections the cloud is not coherent. If the sentence doesn't feel right, it probably needs more adjusting and polishing.
  2. They formulate both necessary conditions coherently but fail to link them properly with a common objective. The problem cannot be solved unless there is an objective which is common to both necessary conditions. That is what 'necessary' means in this context. Furthermore if you are trying to resolve a conflict the common objective must be acceptable to both sides. You cannot impose an objective from one side on the other. It just doesn't work. The objective must be shared by both sides!
  3. The conflict of the cloud is not an apparent conflict. It is the fact that we are trying to solve a problem which has two conditions which cannot both be true at the same time which makes this a complex problem. It must at least appear that there is an initial conflict!
  4. We must specifically state the assumptions which are being made for each linking arrow. Stating the problem and then failing to verbalize the assumptions for each connecting arrow is a waste of time. Precisely stating the problem is a necessary first step, but it is only the first step. The cloud enables us to present a compact yet complete understanding of the problem, but why bother doing it if we don't perform the next step and solve the problem. In order to solve the problem we must know what assunption is being made for each link.
  5. Critical examination of the assumptions is at the heart of solving complex problems. We ask ourselves if these assumptions are really true in this situation, We can also ask whether there are any relevant limitations on these assumptions. A detailed examination of these assumptions will give us the leverage to spot which assumption(s) do not hold true for this particular situation. Once we know which assumption(s) is/are false we know which condition is really necessary and which one only appears to be necessary because we only made a superficial examination of the problem. When we know which assumptions are valid we have solved the problem!
  6. Some people immediately propose a compromise solution. Without the detailed examination of the assumptions (error 5 above), the problem looks insolvable. Some people do this because they don't know how to perform the analysis. Some do it because they are lazy. Some do it because it is the only method they know for dealing with complex problemsl. At this point compromise appears to be the only way out so they take it rather than doing the work of examining the assumptions. Never propose a compromise solution! Go figure out the assumptions and evaluate them.
The diagram above would look this with the assumptions filled in.

This is read using the method given above with the addition of a clause which specifies the basis for the linkage.

Cost Path
Throughput Path

For the above example we would examine each assumption to see if we believe it to be true. It appears that both the assumptions for the left links of the cost and throughput are okay. it is well documented in business that we can increase profits either by cutting costs or by increasing sales.

Currently Reality Tree

The second thinking tool that is introduced is the Current Reality Tree. It is much harder to perform and is far easier to learn if it is introduced in a structured learning environment. We create one of these because any complex situation is linked by many interdependent effects. However, all these effects are caused by only one or two underlying causes. A Current Reality tree helps us identify the underlying cause. When peoplae are intimately familiar with a given situation their intuition might allow them to forulate the Evaporating Cloud without creating the Current Reality tree, However, in order to user the thinking skills fully in creating new solutions to cmplex problems we must be able to explain what the root caause of the problem is. This requires us to create a current reality tree. Otherwise we are asking others to 'take our word for it' and no one is usually willing to do that where complex problems are involved. The process consists of the following steps.

  1. Write down a list of five to ten Undesireable Effects (UDEs). There is no set number but the more complex the problem you are analyzing the more UDEs you will notice.
  2. Review the list of UDEs and find two UDEs which are linked as cause and effect. Use your intuition about which UDE is linked to which other UDE. The link might be a long distance one, that is there may be intermediate effects between the UDEs. Don't be concerned with that at first, we will deal with that issue later. Write down the perceived link as a logic diagram like the one shown below.
  3. Once we have a link we examine it to make sure it satisfies the following conditions. These are called the Categories of Legitimate Reservation. They make sure that the links are systematicaly tested.
  4. Categories of Legitimate Reservation
    1. Clarity - Is the link we are proposing clearly stated?
    2. Entity existence - Is te proposed entity real and is its effects significant?
    3. Causality existence - Is the proposed cause really a cause and not an effect or independent entity?
    4. Cause insufficiency - Is te proposed cause sufficient all by itself to case the effect?
    5. Additional cause - Are there other contributing entities that are not yet listed which are necessary for suffciency?
    6. Cause-effect reversal - Do you have the cause and effects reversed?
    7. Predicted effect existence - Does the predicted effect actually exist? Has it been observed by anyone?
    8. Tautology - Is the cause and effect circular logic?

  5. Add any cause effect relationships you deem necessary to satisfy the above list of reservations. This often results in adding UDEs tothe diagram which you may not have initially listed. This is normal and it is the reason why the initial list of UDEs need not be either complete or exhaustive.
  6. Select another item from your list of UDSs which links to your existing diagram. Link it in using the categories of Legitimate Reservation to establish and firmly link the new entity.
  7. Continue this until all the UDEs have been linked to the diagram.
  8. When all UDEs have been linked in, review the diagram to locate the root case, the entity, that all other effects can be traced back to.
  9. If necessary redraw your diagram to place the root cause at the bottom of the logic diagram.
  10. Create an Evaporating Cloud by identifying the two necessary but conflicting conditions which are associated witht he root cause of the problem.

Future Reality Tree

This logic tree represents the reality we want to move to. The whole point in developing it is to gain more insight into the system of effects that must be created in order to create the desired reality. We start with our current situation. We place our objectives at the top and then contruct a logic tree from where we are to where we want to be.