In earned value management, the schedule performance index (SPI) is a key measure of schedule efficiency. How is the schedule performance index (SPI) calculated?

Introduction / Context:
Earned value management provides a set of integrated measures that combine scope, schedule, and cost performance. The schedule performance index, or SPI, focuses on how efficiently the project is using time relative to the plan. Knowing the correct formula for SPI is essential for interpreting project performance and answering exam questions correctly.

Given Data / Assumptions:
- The measure in question is the schedule performance index, SPI. - Planned value is abbreviated as PV and earned value as EV. - The question asks for the mathematical relationship between EV and PV in SPI. - Standard earned value management definitions apply.

Concept / Approach:
SPI is defined as the ratio of earned value to planned value. Earned value represents the value of work actually completed in terms of the approved budget, while planned value represents the value of work that should have been completed according to the schedule at a given time. An SPI greater than 1 indicates that more work has been completed than planned, suggesting the project is ahead of schedule. An SPI less than 1 indicates the project is behind schedule. Therefore, we must identify the formula SPI = EV / PV.

Step-by-Step Solution:
Step 1: Recall the definitions of EV and PV in earned value analysis. Step 2: Remember that SPI compares earned work with planned work using a ratio. Step 3: Identify that SPI uses EV as the numerator and PV as the denominator, SPI = EV / PV. Step 4: Select the option that correctly states SPI = EV / PV.

Verification / Alternative check:
One way to verify is to consider a simple example. If the project should have completed 100 units of value (PV = 100) but has only completed 80 units (EV = 80), the SPI should be less than 1 to show a delay. Using SPI = EV / PV gives 80 / 100 = 0.8, which correctly indicates a schedule shortfall. Using PV / EV would give 100 / 80 = 1.25, which would incorrectly suggest the project is ahead of schedule. This confirms that the correct formula is EV divided by PV.

Why Other Options Are Wrong:
Option A is wrong because PV / EV inverts the ratio and would misrepresent schedule status. Option C is wrong because it introduces project duration into the formula, which is not part of the SPI definition. Option D is wrong because EV - PV is a difference, not an index; it corresponds more closely to schedule variance than to SPI. Option E is wrong because BAC - EV is related to remaining work or cost to complete, not to SPI.

Common Pitfalls:
A frequent mistake is to confuse SPI with schedule variance or to invert the ratio. Students may also mix up SPI with the cost performance index, which uses EV / AC. Another pitfall is to misinterpret SPI values greater or less than 1, so it is important to remember that SPI is a ratio of earned to planned value and that its value directly shows schedule efficiency.

Final Answer:
The schedule performance index is calculated as earned value divided by planned value, SPI = EV / PV.