Define PV, EV, and AC in Earned Value Management (EVM).
PV (Planned Value): budgeted cost of work scheduled. EV (Earned Value): budgeted cost of work performed. AC (Actual Cost): actual cost of work performed. Example: If by week 4 you planned $80k of work (PV=80), completed $70k worth (EV=70), and spent $75k (AC=75).
Formula for Cost Variance (CV) and interpretation.
CV = EV − AC. >0 under budget, <0 over budget, =0 on budget. Example: EV=70, AC=75 → CV = 70−75 = −5 (over budget by 5).
Formula for Schedule Variance (SV) and interpretation.
SV = EV − PV. >0 ahead of schedule, <0 behind schedule, =0 on schedule. Example: EV=70, PV=80 → SV = 70−80 = −10 (behind schedule by 10).
Formula for Cost Performance Index (CPI) and meaning.
CPI = EV / AC. >1 cost efficient, <1 cost overrun. Example: EV=70, AC=75 → CPI = 0.933 (cost overrun).
Formula for Schedule Performance Index (SPI) and meaning.
SPI = EV / PV. >1 ahead, <1 behind. Example: EV=70, PV=80 → SPI = 0.875 (behind schedule).
Define BAC and EAC.
BAC (Budget at Completion): total planned budget. EAC (Estimate at Completion): forecasted total cost at completion. Example: BAC=$200k. If trends hold, you might forecast EAC based on CPI/SPI.
Formula for EAC when future work will continue at current CPI (most common).
EAC = BAC / CPI. Example: BAC=200, CPI=0.80 → EAC = 200/0.80 = 250.
Formula for EAC when original estimate is valid and only current variances were atypical.
EAC = AC + (BAC − EV). Example: AC=120, BAC=200, EV=100 → EAC = 120 + (200−100) = 220.
Formula for EAC when both cost and schedule performance impact the remaining work.
EAC = AC + (BAC − EV) / (CPI × SPI). Example: AC=120, BAC=200, EV=100, CPI=0.9, SPI=0.95 → Remaining = 100/(0.855) ≈ 116.96; EAC ≈ 236.96.
Formula for EAC when a new estimate is provided for remaining work.
EAC = AC + Bottom‑up ETC. Example: AC=120, new ETC=70 → EAC = 190.
Formula for ETC and VAC.
ETC = EAC − AC. VAC = BAC − EAC. Example: EAC=240, AC=120 → ETC=120. If BAC=200 → VAC=200−240=−40 (overrun).
Define TCPI and give formulas for TCPI(BAC) and TCPI(EAC).
To-Complete Performance Index (efficiency needed on remaining work). TCPI(BAC) = (BAC − EV) / (BAC − AC). TCPI(EAC) = (BAC − EV) / (EAC − AC). Example: BAC=200, EV=100, AC=120 → TCPI(BAC)=100/80=1.25.
Interpret TCPI values.
TCPI > 1 means you must perform more efficiently than so far; < 1 means required efficiency is easier than to date. Example: TCPI=1.25 indicates a very tough target.
Given EV=150, AC=120, PV=160, compute CV, SV, CPI, SPI.
CV=150−120=30 (under budget). SV=150−160=−10 (behind). CPI=150/120=1.25. SPI=150/160=0.9375.
Define critical path and its impact on project duration.
Critical path is the longest path through the network; it determines the shortest possible project duration. Activities on it have zero total float (in a typical case).
Define total float and give formulas.
Total float = amount an activity can slip without delaying project finish. Formula: TF = LS − ES = LF − EF. Example: If ES=4, EF=8, LS=6, LF=10 → TF=2.
Define free float and formula.
Free float = time an activity can slip without delaying the early start of its successor. FF = ES(successor) − EF(current). Example: Successor ES=12, current EF=10 → FF=2.
Define lag and lead with example.
Lag delays successor; lead accelerates successor. Example: Finish‑to‑Start with 3‑day lag: successor starts 3 days after predecessor finishes. Lead of 2 days lets successor start 2 days before predecessor finishes (negative lag).
PERT expected duration (triangular vs. beta/weighted) and variance.
Triangular mean = (O+M+P)/3. Beta (PERT) mean = (O + 4M + P)/6; variance = ((P−O)/6)^2. Example: O=4, M=6, P=10 → PERT mean=(4+24+10)/6=6.33; variance=((6)/6)^2=1; σ=1.
Probability of meeting a target using PERT (basic).
Z = (Target − TE) / σ (where TE is PERT mean, σ is standard deviation). Look up Z in normal table. Example: TE=20, σ=2, Target=23 → Z=(3/2)=1.5 → ~93.3% chance.
Communication channels formula.
Number of communication paths = n(n−1)/2, where n = team size. Example: n=8 → 8*7/2=28 paths.
Crash vs. fast-track: definitions and cost/schedule impact.
Crashing adds resources to shorten duration (↑ cost). Fast-tracking overlaps activities (↑ risk). Example: Overlapping design and build saves time but increases rework risk.
When is EV = AC and PV equal?
At project start EV=0 while PV may be >0; EV equals PV only if perfectly on schedule; EV equals AC only if perfectly on cost. Rare in practice. Example: If EV=PV=50 and AC=50 → on time and on budget.
SPI or CPI equals 1 — what does it mean?
SPI=1 means on schedule; CPI=1 means on budget. Example: EV=80, PV=80 → SPI=1; EV=80, AC=80 → CPI=1.
