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part-time resources and the Chinese principle

Most people know the so-called "China" principle which says that more people can accomplish the same task in less time. The applicability of this principle is subject to some restrictions:

• First, it depends very much on the task, whether and how long the relationship is linear, so if twice as many employees actually need only half the time.
• Second, there are for most tasks, a saturation limit beyond which additional resources can not work faster profit more. Try, for example times, a lecture for two to keep them in half the time.

An interesting reversal this principle is the planning part-time resources, which - subject to similar effects - but for different reasons. This post describes a quantitative approach as these effects in scheduling can be considered.

The sand and the stones
part-time staff resources are not available during your entire time on the project are available but only a part of. This fact must be bridged into account in scheduling the tasks for these employees. But how?
Imagine a big pile of sand in front of which is to be moved to another location. Suppose it requires 100 days of work to transport the sand. Then, two full-time employees need to have 50 days time, two employees, who work need only every other day for 100 days and two employees only one day a week work required 250 days (equivalent to 100 / 20% / 2).

Now we imagine that the cluster contains, besides the sand and stones that are so serious that the workers, they can only carry together. How long will it take now? Well, as long as the workers (even if they work part-time) work simultaneously, changes in estimates of the time nothing. If workers, however, always working on different days, they are also never to wear to the stones and the work lasts forever. How easy it is for the workers to work on the same day depends (in addition to planning aspects) obviously depends on how high the availability of each worker, and how many workers are also required.

The realistic time estimate
Although this offers an interesting excursion into the world of applied statistics, I do without it (not least because the appearance of individual employees in the project is hopefully not a random event, but a pending planning to follow). Instead, I explain briefly the method of calculation and the analogy to the Chinese principle.
Suppose the cluster contains so many stones that 10% accounts for the overall work on the wearing of the stones. This means that 90% of the work still done independently can be. For this 90%, the invoice (work / capacity / Number of employees) as described above. For the remaining 10% of the work, the same calculation rule, but the capacity is reduced because the employee also must be available. Highly simplified, we assume the cooperation capacity is individual capacity ^ Number of employees * Number of employees. If all employees are required to always wear a stone, the following picture:

The duration initially decreases with increasing number of employees - this reflects the high (90%) share of the work again, which must be done independently can. The more employees are also required to complete 10% of cooperative work (in our example, also the stones heavier), the greater the effect on the total time.

the practical side
The stone from the example correspond to the operations that can carry the team was together (ie team meetings and other necessary votes). The sand is equivalent parallelizable tasks which the employees can perform independently of each other. Similar to the application of the Chinese principle of increasing the team performance linear if either is the only work of independent tasks, or all resources are available to 100%. Are the limited resources available, the overall productivity with increasing number of employees even fall, as the following graphic.

The graph assumes a cooperative of 10% of the total work and assumes that this ratio in the estimation of the total work has been taken into account (eg: one hour team meeting is 10 hours of work, if at 10 members) .