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In terms of creating a timeline, what is meant by the critical path of a PERT chart
PERT is fundamentally a statistical method of analyzing the combined work packages along the critical path in order to calculate the probability of success with the goal of completing the project provided a given network schedule. Mathematically, the critical path is the path through successive dependent nodes from start to finish with the longest duration. In theory, the timeline cannot be completed any sooner than the items on the critical path are completed.
How would the manager go about prioritizing correction of the problem existing in B, C, or D?
In the critical path step B is an activity which is delaying in solving the problem, therefore step B needs to be made a higher priority. Delays in step C or D are acceptable because they don’t impact the total duration of the project, since those tasks are not on the critical path.
Should the manager address the issue in step B first, step C first, or step D first; why?
Step B needs to be addressed first, since it’s first in the chain along the critical path.
For more information, see James M. Anthill & Ronald W. Woodhead’s 1990 book, Critical Path Methods in Construction Practice.