Buffer sizing determines the overall duration of your project and the degree of overall contingency included in the plan. The buffer thresholds for action determine the frequency with which you will act. We usually
the(single-project)criticalchainplan165
ID Task
name Duration Pred.
1 A-1 5 days
2 A-2 10 days 1
3 A-3 15 days 2
4 A-4 10 days 3
5 A-5 20 days 4,9
6 A-6 15 days 5
7 B-2 10 days
8 B-3 10 days 7
9 B-4 5 days 8,4
10 C-3 15 days 8
11 C-4 10 days 10 12 C-5 15 days 11,15,6
13 C-6 5 days 12
14 D-3 20 days
15 D-4 5 days 14
16 Comp. 0 days 13
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Figure 6.13 Resolving other resource contentions.
CriticalChainProjectManagement
ID Task
name Duration Predec.
1 A-1 5 days
2 A-2 10 days 1
3 A-3 15 days 2
4 A-4 10 days 3
5 A-5 20 days 4,10
6 A-6 15 days 5
7 B-2 10 days
8 B-3 10 days 7
9 FB 10 days 8
10 B-4 5 days 4,9
11 C-3 15 days 8
12 C-4 10 days 11
13 FB 12 days 12
14 C-5 15 days 6,13,18
15 C-6 5 days 14
16 D-3 20 days
17 D-4 5 days 16,12
18 FB 12 days 17
19 PB 50 days 15
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1/18 R
R R
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1 8 15 22 29 5 12 19 26 3 10 17 24 31 7 14 21 28 5 12 19 26 2 9 16 23 30 Mag
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Critical chain
Figure 6.14 Identification of the critical chain and the addition of feeding and resource buffers create the critical chain plan.
set buffer thresholds as a percentage of the buffer, so the buffer size influences the actual sensitivity of the buffer triggers.
6.4.1 Statistical background
Recommendations on buffer sizing use statistics to develop relatively simple rules with a supporting theoretical basis. Dr. Goldratt recommends sizing the project buffer and feeding buffers to one-half the buffered path task length. That is, do not include gaps in the chain when you are sizing buffers. The buffers are there to protect the project from uncertainty in performing the tasks on the chain.
Goldratt’s method considers the statistical rule governing the addi- tion of uncertainties that are independent events. The statistical rule says that the uncertainty of the sum of the events is much less than the sum of the uncertainty for each event. That is sensible, because you should expect some variations to be positive and some to be negative. Consider Dr. Goldratt’s recommendation in context with his recommendation to simply cut activity times in half. Mathematical justification of his recom- mendation requires several additional assumptions, some of which we highlight here. His recommendation usually will lead to larger buffers than the method described next, a reasonable thing to do when you are beginning to deploy critical chain.
The spread in a distribution is proportional to the standard deviation, σor sigma. The spread of the distribution representing the sum (in our
A-6 Red 15
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Project complete B-3
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F-9 Red 10 Figure 6.15 Large exercise.
case, the buffer) equals the square root of the sum of the squares of the individual distributions. (Do not worry if you are not a statistics buff and cannot follow this. You can do fine with critical chain using Goldratt’s simple recommendation or simply by following the procedure we give below. You do not have to know this theory to have it work for you.)
If you make a few assumptions, you can come up with a relatively simple way to make use of your knowledge of the variation in estimates to size the project and feeding buffers. Projects usually do not have much information about the actual distribution of the task performance time.
(Exceptions might include repetitive projects, such as construction, in which extensive cost data exist.) However, you can usually place bounds on the task time, corresponding to some upper and lower limits of the time it will take. If you assume your estimating method yields about the same meaning for the upper and lower limits on most of the project tasks, you can then say that the difference between the upper and lower limits, D, is some multiple of the standard deviation. You may not know if it represents two or six standard deviations; you are only assuming that whatever it is, it is about the same for all the tasks you estimate with the same method. Then, without even having to define the limits precisely, you can size the buffer to protect the whole chain of tasks to the same degree we previously were protecting each activity. You take the square root of the sum of the squares of the Ds. The result is always less than adding the Ds.
For example, consider a chain of four tasks, each two weeks long. Two weeks is our standard low-risk estimate. One week is our 50-50 estimate.
So D equals 1.
The critical path chain is, therefore, eight weeks. The critical chain tasks add up to four weeks. Because D equals 1, D squared also equals 1.
The sum of D squared is then 4, and the square root of 4 is 2. Adding the two-week buffer to the four-week task chain gives a project duration estimate of six, compared to eight for the critical path. In this case, the square root of the sum of the D-squared method gives the same result as Dr. Goldratt’s simplified method. That always happens for four equal- length tasks, where D is half the task duration, that is, not very often.
6.4.2 Project buffer size
Size the project buffer using the square root of the sum of the squares method. Determine the D value for each task as the difference between
the initial task duration estimate and the reduced estimate. The following guidelines will help ensure an effective buffer:
◗ Seek to have at least 10 activities on the critical chain. Reason: The more activities in the critical chain, the more effective the sum of the squares and central limit theorem.
◗ Do not allow any one activity to be more than 20% of the critical chain. Reason: The uncertainty of one large activity will dominate the chain, leaving little possibility for the other tasks in the chain to make up overruns on the dominant task.
◗ Do not allow the project buffer to be less than 25% of the critical chain. Reason: Chains with many tasks of uniform length may calculate a relatively small buffer, providing inadequate protection.
6.4.3 Feeding buffer size
Size the feeding buffers using the square root of the sum of the squares method. Determine the D value for each task as the difference between the initial task duration estimate and the reduced estimate.
If there are fewer than four tasks in the feeding chain, make sure the feeding buffer is at least equal to the longest activity in the feeding chain.
6.4.4 Buffer trigger points
We set the buffer trigger points to plan for management control action and to initiate the action. Both trigger points must be set to minimize false signals and to ensure that action is taken when needed. It does not damage project performance directly to plan for project changes that are not made. Thus, there is less negative impact from too low a threshold for the project plan (yellow) trigger point. You may do significant damage to your project, however, if you set the action (red) trigger too low and take unnecessary control actions. Project changes, which include control actions, will likely cause confusion and delay the project.
We suggest setting the triggers at one-third and two-thirds of the buffer. Because project tasks are not always in a provable state of statisti- cal control, we recommend that you track buffer penetration over time. If you are tracking the buffer over time, you may want to institute some additional control chart triggers, such as four points in a row tending toward the trigger point. Do not make the trigger logic too complex.
Some people suggest that the trigger points should be relative or dynamic. That is, the triggers should require less penetration early in the project. The logic is that early in the project people may be inclined to use up the buffer. That fear, however, most often is baseless. Usually, there is negative buffer penetration early in the project. We suggest you trend the buffers and make decisions as you deem necessary. Be mindful that too many control actions have a negative effect on project performance.
Set the buffer triggers for feeding buffers at the same percentage of buffer penetration as for the project buffer.
6.4.5 Resource buffer size
Size resource buffers to the needs of the resource provider. The size should depend on the quantity of the resource, the length of the resource’s usual task, and special considerations such as required train- ing, travel, or other lead time.
For subcontractors, consider making the resource buffer a financial incentive to ensure a lead time. Because profits are a small percentage of revenue, you are often able to greatly increase delivery reliability by doubling the suppliers’ profit if they deliver on time, which should cost only a small percentage of the subcontract. A recent public example is that of the contractor who rebuilt an overpass on the Santa Monica Freeway, that was destroyed in an earthquake, and finished over a month early due to a significant reward.