According to the PMBOK® Guide (Project Management Body of Knowledge), specifically within the Project Cost Management knowledge area and the Control Costs process, the Schedule Performance Index (SPI) is a measure of schedule efficiency expressed as the ratio of earned value to planned value.
To calculate the SPI for Task 4 using the data provided in the table:
Identify the variables for Task 4:
Earned Value (EV) = 10,000
Planned Value (PV) = 9,000
Apply the SPI Formula:
$$\text{SPI} = \frac{\text{EV}}{\text{PV}}$$
$$\text{SPI} = \frac{10,000}{9,000} \approx 1.111...$$
Option C (1.11): This is the correct calculation. An SPI greater than 1.0 indicates that the project is ahead of schedule because more work was completed than originally planned for that point in time.
Option B (0.9): This would be the result if you incorrectly divided PV by EV ($9,000 / 10,000$). This would represent a project behind schedule, which is not the case for Task 4.
Option A (0.83): This would be the result if you incorrectly divided EV by AC ($10,000 / 12,000$), which is the formula for the Cost Performance Index (CPI).
Option D (1.33): This would be the result if you incorrectly divided AC by PV ($12,000 / 9,000$), which is not a standard Earned Value metric.
In the PMI framework, the Schedule Performance Index (SPI) is used to predict the completion date of a project. While the SPI is a useful efficiency indicator, it must be analyzed alongside the critical path; a project can have a favorable SPI (greater than 1.0) while still being delayed if the work being performed ahead of schedule is not on the critical path.
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