# Bill Fennema, a president of Fennema Construction. 3-Time Exercise to calculate the critical pathExample of the Critical Path - PERT Method

### Problem Data

It is required to calculate the critical path of the project, using the PERT method according to the following data:

- Number of Activities
- 11
- Time Unit
- Weeks
- Chart Type
- Activities-on-Nodes
- Description
**Bill Fennema, a president of Fennema Construction. 3-Time Exercise to calculate the critical path**Bill Fennema, a president of Fennema Construction, has developed the tasks, durations, and predecessor relationships in the following table for building new motels. Draw the AOA network and answer the questions that follow. a. What is the expected (estimated) time for activity C? b. What is the variance for activity C? c. Based on the calculation of estimated times, what is the critical path? d. What is the estimated time of the critical path? e. What is the activity variance along the critical path?- Table of Activities
Activity Immediate Predecessor(s) Optimistic Time Mean Time Pessimistic Time A 4 8 10 B A 2 8 24 C A 8 12 16 D A 4 6 10 E B 1 2 3 F E,C 6 8 20 G E,C 2 3 4 H F 2 2 2 I F 6 6 6 J D,G,H 4 6 12 K I,J 2 2 3

## Solution

The following are the calculations and detailed graphs to obtain the **critical path** according to the data provided:

### Step 1: Evaluation of the relationships between activities

In order to be able to plot the Network diagram (Activity-on-node), it is necessary to know the precedence and descent relationships of each activity; that is why the following table shows the relationships of each activity so that we can create our graph. Two fictitious “Start” and “End” activities are included.

Predecessor | Activity | Successor |
---|---|---|

Start → A | A | A → BA → CA → D |

A → B | B | B → E |

A → C | C | C → FC → G |

A → D | D | D → J |

B → E | E | E → FE → G |

C → FE → F | F | F → HF → I |

C → GE → G | G | G → J |

F → H | H | H → J |

F → I | I | I → K |

D → JG → JH → J | J | J → K |

I → KJ → K | K | K → End |

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