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Here's the Backward Pass.
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We start at the end of the project
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and scan backward to the beginning
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to find the latest everything can start and finish
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given the constraints of the logic.
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If a deliverable has more than one successor,
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we copy the least latest start of all the successors
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to the predecessor's latest finish.
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Then we subtract the duration from the latest finish
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to get the deliverable's latest start.
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And we write these numbers on the bottom
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of the deliverable to keep track of them.
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We start at the end of the project
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and already know the shortest schedule
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is 34 days in duration,
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so the latest day the training session can finish
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and preserve the critical path is day 34.
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Since we're going backward, we subtract numbers
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and the training session is one day in duration
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so the latest day it can start is 34 minus one or 33.
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We write the latest finish at the bottom right
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and the latest start at the bottom left of the deliverable.
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The implement new floor plan deliverable
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only has one successor, so the latest day it can finish,
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while preserving the critical path,
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is the latest start of that successor which is day 33.
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The implement new floor plan is two days in duration,
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so the latest it can start is 33 minus two or day 31.
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Since most deliverables only have one successor,
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we can just keep moving backward,
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copying the latest start to the previous
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latest finish for quite a while.
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The first time a deliverable has more than one successor
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is all the way back to the executive review
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with three successors: the new floor plan second draft,
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new department processes second draft,
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and training manual first draft.
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Since there is more than one successor
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we choose the least latest start to copy over
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as the latest finish, which is day 12,
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from the new department processes second draft.
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Given the logic of the project,
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as shown in the precedence diagram,
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day 12 is the latest the executive review can finish
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and maintain the 34 day schedule.
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We keep moving backward through the project.
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The next and only other time we have more
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than one successor is for the kick off meeting.
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So we choose the least of the successor's latest start,
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the least of seven, one, and 17.
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Copying over the one.
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We then subtract the kickoff meeting one day duration
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to determine the latest it can start, which is day zero.
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Since the early start and late start
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of the first deliverable both match at zero,
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this confirms we did all the arithmetic properly.
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Now, we've calculated the earliest everything
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can start and finish with the forward pass,
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and the latest everything can start and finish
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with the backward pass, which gives us everything we need
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to calculate the float of all the deliverables
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and confirm the critical path.
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Let's take a look.
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