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**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 = LS-ES or LF-EF*

**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

- Benefit measurement method
- Murder board
- Scoring model
- Peer review
- Economic model

- Constrained optimization method (Mathematical )

- Linear programming
- Dynamic programming
- Integer programming
- Multi-objective programming

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.