13 de jan. de 2013

Fundamentals of The Theory of Constraints

In his book The Goal, Eliyahu Goldratt presents Alex Rogo, a plant manager who received the task of improving a plant’s results in no more than three months, otherwise it will be closed. What to do in such a short schedule? He found the answer while accompanying his son's Boy Scout troop in a 20-mile hike, where he faced the following problem:
Ahead of the group, fast-walking Andy was trying to set a new speed record. Behind, fat Herbie was setting the slowest pace. So, the group started to spread in the woods (like an increasing inventory level in a plant). They were supposed to cover 10 miles in five hours, but they are going just half the necessary speed. What to do to improve their efficiency?
To solve the Boy Scout troop problem, Alex Rogo asked the group to stop and join hands. Than, like dragging a chain, he passed through the line until the entire troop had exactly the opposite order they had before. They started walking again with the condition that nobody could pass anybody.
This time the group stuck together, but some of the boys started to complain that they were going too slow. In fact, keeping that pace they couldn’t accomplish the planned schedule. So it was necessary to elevate the constrain, the first boy in the line, the fat Herbie. They realized that Herbie’s pack was too heavy, full of things like soda, spaghetti, candy bars, pickles, and even an iron skillet. Then they decided to split the load among others members of the team and, this time, they really improved their performance as a group.
In The Goal, the company’s traditional cost accounting and variance reporting system was responsible for many of the problems the factory was experiencing. Instead of focusing efforts on activities that would increase profits, the company’s traditional management accounting system focused attention mainly on counterproductive efforts to reduce unit product costs. If real improvements had been made in operations, the management accounting system almost invariably would have sent inappropriate signals in the form of unfavorable cost variances. Therefore, as a precondition to improving, Alex had to throw out the old cost accounting and variance reporting systems. He then completely redesigned the accounting and performance reporting system from the ground. (Noreen et al., 1995, pp. 2-3)
Israeli physicist Eliyahu Goldratt notice that there was plenty of room to improve the exploitation of resources in manufactures plants. With his associates he created a company named Creative Output, in the beginning of 1980’s, developing a software to schedule jobs through manufacturing processes, focusing on bottleneck operations.
(...) Goldratt has a doctorate in physics and became involved in business almost accidentally. A friend was having difficulty scheduling work at a plant that built chicken coops. Goldratt was intrigued by the problem and conceived an innovative scheduling system that permitted a dramatic increase in completed chicken coops with no increase in operating expenses. Goldratt discovered that there was no satisfactory job shop scheduling software available on the market, so he incorporated his ideas in a software product called OPT that was launched in 1978. (Noreen et al., 1995, pp. 2-3)
The Theory of Constraints is the result of broadening this scope, applying a problem-solving approach which seeks to improve the global objective of a system through the understanding of the underlying causes and effects dependency and variations.
The core idea in the Theory of Constraints (TOC) is that every real system such as a profit-making enterprise must have at least one constraint. If it were not true, then the system would produce an infinite amount of whatever it strives for. In the case of a profit-making enterprise, it would be infinite profits. Because a constraint is a factor that limits the system from getting more of whatever it strives for, then a business manager who wants more profits must manage constraints. There really is no choice in this matter. Either you manage constraints or they manage you. The constraints will determine the output of the system whether they are acknowledged and managed or not. (Noreen et al., 1995, p. xix)
At first glance it may looks like simple, but this is not exactly the case considering the way people used to think and evaluate problems, as stated by Peter Senge:
From a very early age, we are taught to break apart problems, to fragment the world. This apparently makes the complex tasks and subjects more manageable, but we pay a hidden, enormous price. We can no longer see the consequences of our actions; we lose our intrinsic sense of connection to the larger whole. (Senge, 1990, p. 3)
The first step is to break the current view (focusing on local optima) and start to consider the effects of local changes in the whole results.
This is exactly the same principle created by Justus von Liebig (1803-1873), known as the “Law of the Minimum”, which states that the yield potential of a crop is determined by the poorer of all nutrients. If a nutrient is deficient or lacking, plant growth will be poor even if all the other nutritive elements are abundant. The growth of the crop can only be improved by increasing the amount of the limiting nutrient. Goldratt’s original contribution was to emphasize the same principle to business management:
The first step is to recognize that every system was built for a purpose, we didn’t create our organizations juts for the sake of their existence. Thus, every action take by any organ – any part of the organization – should be judge by its impact on the overall purpose. This immediately implies that, before we can deal with the improvement of any section of a system, we must first define the system’s global goal; and the measurements that will enable us to judge the impact of any subsystem and any local decision, on this global goal. (Goldratt, 1990, p. 4)
This vision inspired the analogy of the system as a chain. If we imagine a system as a chain, the only way to increase its strength is to improve the weakest link. This is the point where the chain will broke soon or later. If we improve any other link, letting the weakest one aside, the strength of the chain will keep absolutely the same as before (as stated in the “Law of the Minimum”). Only when the weakest link is strengthen the overall system will be improved. And when the weakest link is strengthen to the degree that it is no longer the weakest link, there will be another weakest link limiting the system performance.
The concept behind the “Law of the Minimum” and the view of the system as a chain are the basis for the Theory of Constraints. This primary approach constitutes a valuable orientation defining which actions should be taken to improve the overall performance of a system. The constraint can be found inside the organization (lack of hardware, software, people, machines, etc.), can be the result of a controlling policy, or can be located outside the company (market, suppliers, infrastructure, etc.).
Focusing local optima, not considering the overall impact of compartmentalized efforts, is just waste of time and money. Unfortunately, focusing local performance, without identification of neither the weakest link nor the overall results, is common sense in organizations. That’s why managers are asked to improve local performance and demand the same to their subordinates. But the sad true is that the system will increase only at the same rate of improvement in its constrain (the weakest link). All other efforts, increasing output in non-constraint parts, will only result in waste of time and money. Instead of focusing on the best solution for each component it is necessary to look for the best possible solution for the entire system (global optimum), avoiding emphasis on local optimum. The overall result, in an ongoing system, is not exactly the sum of the results of each part, it is the result the weakest part makes possible in interaction with the others.
To make things clear, let’s consider a system of five resources (can be a production line, sales department, etc.), as presented in figure 1:

Figure 1: A linear system of 5 resources.
Now suppose, for simplicity, that this system produces only one item. Let’s say it can produce 10 units of item A per hour. But there is only market for selling 8 units. In this case, the system should produce only 8 items per hour, according to the constraint in this case (the market). Production above 8 units per hour will only represent cost since it cannot be sold, at least not without some kind of promotion which could affect profit margins. In a situation like that company’s efforts should concentrate in marketing and sales, not in improving the production output.
Suppose now the demand for product A increased to 12 units per hour. The system can only produces 10 units/ hour, so these 2 extra units will represent unsatisfied customers, damaging the image of the company and attracting new competitors to the market. A fast solution would be expand the working time with extra hours (which would be costly and can negatively affect productivity and quality) or even outsource part of the production (if possible). But suppose these alternatives are not available. What should be done?
Let's consider in more detail the capacity of each resource. The fact that the system is producing 10 units per hour doesn’t imply that each one of the resources produces exactly 10 units per hour. If this is the case, the system should be absolutely perfect, with each resource producing in a harmoniously constant way where each unit produced requires the same time (zero variations). There is no rework to be done, nor unexpected setups, problems in machines or with workers. But, if any variance occurs in one machine, all the sections downstream would be affected and the system could not produce 10 units per hour.
The fact that the system is able to produce 10 units/ hour doesn’t mean that all resources can (or should) produce only at this rate. In fact the system produces 10 units/ hour just because there might be one resource – and probably just one – that could not produce at a higher rate. And this one is the constraint, the weakest link of the system. A local analysis reveals the real capacity of each resource, as presented in figure 2:

Figure 2: Capacity level in each resource of a linear system.

As we see, only resource 4 has the capacity of 10 units/ hour. This is the resource which is limiting the system’s performance. If we want to increase the throughput it is mandatory to improve the capacity of resource 4. Any effort to improve capacity in other resource will only represents increasing costs, not affecting overall performance.
Before analyzing what could be done to improve capacity in resource 4, we should consider the flow of work through the system (how it is balanced). Imagine what would happen if the production schedule does not consider the impact of different capacity in resources? Unfortunately this is a common situation, because managers are asked to improve local optima. In fact, we are used to think the way that local performance anywhere improves overall results.
So, what would be the result of exploiting capacity in any resource of this system except resource 4? Probably only increase of inventory in process. The throughput rate will keep the same at 10 units per hour. There is absolutely nonsense trying to reach local optimum everywhere. But who never observed a manufacture plant piled up of material in process?
In our example, if we schedule production for 10 units per hour rate in each resource, the overall result will certainly be less than 10 units/ hour. Simply because any variance which results in less than 10 units/ hour in one resource would not be recovery by the others – this “balanced” system wouldn’t have any inventory in process for safety. And if at some time the system does not produce 10 units it also would not produce a higher rate afterwards in order to recover the production level.
In synchronous manufacturing thinking, however, making all capacities the same is viewed as a bad decision. Such a balance would be possible only if the output times of all stations were constant or had a very narrow distribution. A normal variation in output times causes downstream stations to have idle time when upstream stations take longer to process. Conversely, when upstream stations process in a shorter time, inventory builds up between the stations. The effect of the statistical variation is cumulative. The only way that this variation can be smoothed is by increasing work-in-process to absorb the variation (a bad choice because we should be trying to reduce work-in-process) or increasing capacities downstream to be able to make up for the longer upstream times. The rule here is that capacities within the process sequence should not be balanced to the same levels. Rather, attempts should be made to balance the flow of products through the system. When flow is balanced, capacities are unbalanced.
(...) Rather than balancing capacities, the flow of product through the system should be balanced. (Aquilano et al., 2001, pp. 668-669)
How can we balance the system? For that purpose Theory of Constraints has a methodology called drum-buffer-rope. Since we assume variability in the system as natural it should be important to keep inventory of finished goods, if possible. This inventory of finished goods, called shipping buffer, provides safety against problems in production line that could affect the sales of the company. This way the shipping buffer signals what level of output is necessary in the system. If finished goods inventory increases, than sales are decreasing and might not be necessary to keep the same production rate of 10 units/ hour. The shipping buffer dictates the output rate of the system (like a drum dictates the cadence for rowers on a boat), and signals how much material should be released into the system to accomplish the necessary output. Figure 3 exemplifies this drum-buffer-rope system:

Figure 3: Drum-buffer-rope system.

But there is still a missing point. As stated before, the market now is not the constraint of the system. In fact, if demand is higher than supply (as indicated by the fact that the system could sell 12 units/ hour if it would have productive capacity) it will not be possible to keep a shipping buffer, which would also not be necessary, since everything produced would sell immediately (output rate is not dictated by the market, but by resource number 4).
Next figure presents the situation where the drum is represented by resource 4, which determines the amount of material that should be released in the system (represented by a rope). But if there is a problem at resources 1, 2, or 3, resource 4 wouldn’t be able to keep the output rate of 10 units/ hour and the entire system would be affected. Resource 5 will suffer the lack of material and, without a good shipping buffer, the sales level will decrease.

Figure 4: Drum-buffer-rope system with constraint at resource 4.

Situation gets even worse when the market is seeking for more products than it is possible to produce. In this case there is not a shipping buffer, so any delay in production represents a real decrease in sales.
Since the market is buying, let’s forget the shipping buffer (otherwise we would keep it). Now we need to do something to protect the output rate of the system – and as the output rate is dictated by the constraint (drum), we should provide a shelter for the performance of resource 4. The solution is to keep inventory of material ready to use just in front of resource 4. If anything goes wrong at resources 1, 2, or 3, the system will not be immediately affected, since the constrained resource 4 could use this inventory to keep with the rate of 10 units/ hour. As soon as the problem is solved, the resources upstream should use their extra capacity (each of them can produce more than the constraint resource) to recover the previous level of the constraint buffer. When market is not the constraint, we should focus on keeping resource 4 producing without interruptions (the real problem is that if anything goes wrong exactly at resource 4).
In the same way, if something happens to resource 5 the constrained resource 4 should not stop. So it would be necessary to leave free space in front of resource 4 (space buffer) in order to place its completed parts. Afterwards, resource 5 can use its extra capacity to eliminate excess inventory. Now the system is balanced according to the drum-buffer-rope methodology. On one hand, the output rate is dictated by resource 4 (drum) which regulates the production of upstream resources and the quantity of material to be released into the system (this is also regulated by the level of the constraint buffer, in case of any problem). On the other hand, the market regulates the necessary output for the constraint (depending on the system it might be necessary a shipping buffer – probably not the case if market seeks to buy more than the system can produce).
Unfortunately, most systems are not simple as this example. There might be different products and occasions which could also imply in different constraints (keep the system balanced is not an easy task). But the point to highlight is that the overall system output rate is dictated by the constrained resource and not by the capacity of each resource individually.
For instance, consider again resource 1 in the example. It has capacity for producing 25 units per hour, even though the system output rate is only 10 units/ hour. So, we could say that resource 1 is working only at 40% of its capacity. What is the current view about it? Bad productivity, low efficiency. Let’s suppose one hour of resource 1 costs $50. Producing 10 units/ hour means that each unit costs $5 at this resource. It would cost only $2 if it produces at 100% capacity. Most managers would increase production rate in this resource concerned with “saving costs”. But what will be the result for the entire system? Sales will increase? No, the overall output rate will keep at 10 units/ hour due to constraint in resource 4. Costs will decrease? On the contrary, since certainly the inventory level throughout the system will be higher (more money invested to produce the same as before).
The local measure of cost per unit is just an illusion. But to overcome the assumption that a resource idle just represents waste is a heresy. It’s necessary to break a paradigm and states that if we want to exploit a system efficiently the first step is to forget local efficiency, then identify the constraint and work to elevate its output rate.
Appropriate performance measures are essential to organizational control. Production workers are typically evaluated by efficiency to standard time or rate. The use of these measures encourages workers to maximize output at each resource. Worse, these measures encourage a worker to make more pieces than are currently needed rather than to waste time setting up to make parts that are needed. Clearly, non-constraints should produce only in quantities sufficient to supply the constraint for short term requirements. Any additional production will be excess inventory that may never be sold. The assumption behind the use of local efficiency measures is that the system’s output will be maximize (or cost minimized) if each resource’s output is maximized. Local productivity measures, however, do not support the system’s productivity. In fact, the production of excess inventory increases expense and lead time and causes order due dates to be missed. Thus, these local productivity measures are not consistent with the firm’s financial objectives. (Gardiner et al., 2001, p. 15)

AQUILANO, N.J.; JACOBS, F.R; CHASE, R.B. Operations Management For Competitive Advantage. 10th ed. Irwin McGraw-Hill, 2001.
GARDINER, Stanley C.; BLACKSTONE Jr.; GARDINER, Lorraine. The Evolution of The Theory of Constraints. International Journal of Management, 2001, pp. 13-16.
GOLDRATT, Eliyahu M. What is This Thing Called Theory of Constraints. New York: North River, 1990.
OREEN, Eric; SMITH, Debra, MACKEY, James T. The Theory of Constraints And Its  Implications For Management Accounting. North River Press, 1995.
SENGE, Peter M. The Fifth Discipline: the art and practice of the learning organization. Randoum House, 1990.

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