Critical Path : is a combination of activities that, if any are delayed, will delay the project’s finish date.
Purpose of critical path method:
1. To calculate the project’s finish date.
2. To identify how much individual activities in schedule can slip with delaying project
3. To identify the activities with the highest risk that cannot slip without changing the project finish date.
Float Calculation using CPM
● Float is the amount of time an activity can be delayed without delaying the project end date.
● Float is always Zero on Critical Path activities.
● Critical Path is longest path of network diagram.
Each activity have same box
ES : Early Start
EF : Early Finish
LS: Late Start
LF : Late Finish
Float = LSES or LFEF
Float Calculation
Late Start(LS) – Early Start(ES)
OR
Late Finish(LF) – Early Finish (EF)
Example
You are the project manager of project at SkillsMag and following activities are identified along with the activity effort.
Project A  
Activity  Preceding Activity  Duration (Wks) 
Start  None  0 
A  Start  1 
B  Start  3 
C  Start  5 
D  A  9 
E  B,C  2 
F  C  3 
G  D  4 
H  E  8 
I  F  2 
End  G,H,I  0 
First prepare schedule network Diagram
Step 2:
Calculate the ES and EF of each activity using forward pass technique.
Remember the following formulas for calculation.
Early Start (ES) = Early Finish(EF) of Predecessor activity. If no predecessor activity exists then 0.
Early Finish (EF) = Early Start (ES) + Activity Duration
Activity E is highlighted as it has 2 predecessor activities. we take higher one.
Step 3:
Under this technique, we will start calculating the value from last activities on the path i.e. from G,H and I.
Thumb Rule : Take highest EF.
Our case we have EF 15 is highest for activity H.
The formula for LS(Late start) is
Late Start (LS) = Late Finish – Activity Duration
Activity c has 2 successor activity,take lowest one.
Step 4 : Float calculation
Project selection methodsThere are various project selection methods. They are divided in two categories
Let’s have some introduction of different project selection methods.
Benefit cost ration (BCR):
It is a ratio of benefit over cost. If the Value of benefit cost ration (BCR) is grater then 1 (one) it is good.
Example 1: If project one is having BCR ratio of 1.9 and project two is having BCR ration of 2.2.Which project you will you choose?
Solution:
Project two as it has a greater BCR Value than project one.
Example 2:
If you expect cost of project is $90,000 and you expect to gain $1,80,000 from complete project. Calculate BCR for that.
Solution:
Benefit cost ratio (BCR): benefit over cost= benefit/cost
Here benefit is $1,80,000 and cost is $90,000
So BCR= 180000/90000=2
Internal rate of return (IRR) :
It means project’s return as an interest rate. Bigger internal rate of return (IRR) is always better.
Example: You have two projects, Project one has IRR of 10% and project two has IRR or 20%. Which one will you choose?
Solutions:
Project two as it has bigger IRR(20%) than project one (10%).
Present value (PV) & Net Present value (NPV) :
present value means current value today of future cash flow. You can calculate with the help of
PV=FV/ (1+r)^{ n}
Here
PV= Present value
FV= future value
R= rate of return
N=number of time period.
Bigger PV or NPV is better.
Example: You have two projects. Project one has NPV of $90,000 and project two has NPV of $60,000. Which one you are going to choose from those?
Solution:
Project one as it has greater NPV.
Opportunity cost:
It means selecting one project over another by giving up opportunity. Smaller opportunity cost is better for project selection.
Example:
If you have two projects project one has NPV of $38000 and project two has NPV of $90000.What is opportunity cost for selecting project two.
Solution: $38000 is opportunity cost.
Payback period:
It measure time that how long it will take to get an investment back from project.
Example: You have two projects project one have payback period of 3 months and project two has payback period of 6 months. Which one you choose?
Solution: It is project one as it has less payback period.
Return on investment (ROI):
It shows how much percentage you make by investing in project. Bigger ROI is always better.
Returned on individual capital (ROIC):
It shows how money is used in invested project. We display this as a percentage.
ROIC= Net income/total investment
Economic value added (EVA):
It represent how much value a project has truly created for its stakeholders. In other words we can say whether project returns to the company more value than its cost.
pmp formulas
PERT = (P+4M+O)/6
P = Pessimistic M= Most Likely O= Optimistic 
Standard deviation = (PO)/6 
Variance = {(PO)}/6 
Project PERT = Sum of PERT value of each task

Project Variance = Sum of variance of each task 
Normal distribution (sigma)
6 sigma = 99.99% 3 sigma = 99.73% 2 sigma = 95.46% 1 sigma = 68.26% 
No of communication channel = N*(N1)/2
Here N is number of member in project team If team have 10 member then =10 *(101)/2 =>10*9/2=>45 Communication channel 
Float = LF – EF = LS ES
LF = Late finish EF = Early finish LS = Late start ES = Early start Float value is 0(zero) on critical path. 
Schedule variance (SV) = EVPV (Positive variance is good)
EV = Earned value PV=Planned value 
Cost Variance (CV) = EV AC (Positive variance is good
EV = Earned value AC= Actual cost 
Cost performance index (CPI) = EV/AC
(>1 are good) 
Schedule performance index (SPI) = EV/PV
(>1 are good) 
Estimate at complication (EAC) =
1. Estimating assumptions are not valid = AC+ETC 2. Current variance are atypical = AC+BACEV 3. Current variance are Typical =AC+(BACEV)/CPI 4. Variance to continue at current rate = BAC/CPI 5. EAC = AC + [(BAC EV)/(CPI*SPI)] 
Estimate to complete (ETC) = EACAC 
Variance at complete (VAC) = BACEAC 
TCPI =
1. TO Complete performance index based on BAC= (BACEV)/(BACAC) 2. To complete performance index based on EAC= (BACEV)/(EACAC) 
Percentage complete of budget=(EV/BAC)* 100 
Benefit Cost Ratio (BCR) = Payback/project cost
Bigger is better 
Net present value (NPV) bigger is better
Internal Rate of Return (IRR) bigger is better 
Present Value PV= FV / ((1 + r)^term) 
Expected Monetary Value = Probability * Impact 
Procurement related
Actual cost (AF) ={(TCAC)*SSR}+TF TC = target cost AC = actual cost SSR= Sellers share ration TF= target fee 