Resolving the core conflict requires identifying one or more assumptions that can be invalidated by changing the system. Assumptions underlie each arrow of the core conflict. The critical-chain method arises from attacking the assumption that adding contingency to each task is the only way to manage uncertainty.

Goldratt was uniquely positioned to develop the critical-chain solution for projects. The critical-chain solution comes from recognizing that the variation in task performance and dependent events is at the root of the behavior of the present system. He had tremendous success in applying the solution for production management described in The Goal [2]. He knew that, in most cases, the uncertainty in project-duration estimates is much larger than the variation in production processes. He also knew that in many cases the task dependencies in projects were equal to or greater than the dependencies that exist in production. It is natural that he would look at projects from this perspective to find the assumption to attack.

Goldratt describes the impact of variation and dependent events using the saga of Herbie in The Goal. He uses the scenario of a troop of Boy Scouts on a hike through the woods. The trail is narrow, so the scouts cannot pass one another and must walk single-file. As they hike, the line grows longer and longer. Alex Rogo, our hero in The Goal and the troop leader for this weekend, realizes what is happening. The speed of the individual Boy Scouts is not the same. There are statistical fluctuations in how fast they walk. Each is dependent on the Boy Scout in front of him, and the one in front of that Boy Scout, because they cannot pass each other. These fluctuations cause the length of the line to grow continuously. Herbie turns out to be the slowest Boy Scout: the constraint. The gaps in the line compare to inventory in a manufacturing plant, which piles up while a machine is working on the parts in front of them (in the line).

For a project, the gaps in the line of Boy Scouts compare to time. If the next resource is not ready to start when a predecessor activity completes early, the project loses time. We lose the positive variances in statistical fluctuations. This is like a faster boy walking behind a slower one; he can catch up but not pass. The line grows in length. This scenario is worse than the manufacturing case. In manufacturing, eventually the inventory is used. In a project, we lose the time forever. There is no conservation of time.

The direction of Goldratt's solution follows from his TOC production solution. The first step is to identify the constraint of the project system. His focus on throughput led him to focus on the time it takes to complete the project. The longest path through the project is the evident constraint. At first look, this is the critical path.

How then to exploit the critical path? Goldratt is a Ph.D. physicist. He knows statistics, and he knows a lot about the cloudy behavior of much of reality. He knows that the only way to take advantage of our statistical knowledge is through dealing with numbers of events. Dr. W. Edwards Deming and Walter Shewhart before him had pointed out that science can't make predictions about a single instance of a statistical event. This leads to a very simple (in retrospect) insight: concentrate the uncertainty for many of the tasks of the project at the end of the project in a buffer. The buffer has a direct counterpart in Goldratt's production solution, where buffers of in-process inventory are strategically placed in front of machines to prevent them from running out of work.

Concentrating contingency in the buffer brings along two significant bonuses. The first bonus is a shorter plan. The variance of the sum of samples from a series of independent distributions is the sum of variances for the populations that samples come from. The variance is the square of the standard deviation. The standard deviation is proportional to the amount of variation in a single task. In other words, the uncertainty in the sum of tasks is the square root of the sum of the squares of the individual variation. While attempting to protect the completion date of each task in a project, each task has to include its own allowance for uncertainty. These allowances add up down the path. When we take these allowances out of each task and put them at the end of the path, they add up to the square root of the sum of the squares of the amount removed from each task; a much smaller total amount. Figure 3.15 illustrates how this works for a very simple case. The reason for this is evident.

Task 1

Task 2

Task 3

Task 4

We need less time this way because of our profound knowledge understanding of variation!

Figure 3.15 Concentrating contingency at the end of the path requires less total project time.

We need less time this way because of our profound knowledge understanding of variation!

Figure 3.15 Concentrating contingency at the end of the path requires less total project time.

Some of the tasks should overrun; some should underrun. The distribution of the sum need not be as large as the sum of the individual variations because some will cancel out.

A second statistical fact comes into play with this strategy. The central-limit theorem of statistics states that the distribution of samples from a variety of independent distributions tends toward a normal distribution. A normal distribution is a symmetrical distribution. It does not have the long tail to the right that many individual task distributions may have. This means that concentrating contingency at the end of a path reduces the likelihood that it will be overrun by a large amount.

A key part of the direction of the solution Goldratt proposed, then, is to use "average" task completion times in the plan and to add an aggregated buffer at the end of the plan for overall project contingency. Mathematically, the mean for each task duration is the average duration that sums a long a path.

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What you need to know aboutâ€¦ Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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