# McGee Carpet and Trim - 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
- Days
- Chart Type
- Activities-on-Nodes
- Description
**McGee Carpet and Trim - 3-Time Exercise to calculate the critical path**McGee Carpet and Trim installs carpets in commercial offices. Andrea McGee has been very concerned with the amount of time it took to complete several recent jobs. Some of her workers are very unreliable. A list of activities and their optimistic completion time, the most likely completion time, and the pessimistic completion time (all in days) for a new contract are provided in a given table. (a) Determine the expected completion time and the variance for each activity (b) Determine the total project completion time and the critical path for the project (c) Determine Early Start (ES), Early Finish (EF), Late Start (LS), and slack for each activity.- Table of Activities
Activity Immediate Predecessor(s) Optimistic Time Mean Time Pessimistic Time A 3 6 8 B 2 4 4 C 1 2 3 D C 6 7 8 E B,D 2 4 6 F A,E 6 10 14 G A,E 1 2 4 H F 3 6 9 I G 10 11 12 J C 14 16 20 K H,I 2 8 10

## 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 → FA → G |

Start → B | B | B → E |

Start → C | C | C → DC → J |

C → D | D | D → E |

B → ED → E | E | E → FE → G |

A → FE → F | F | F → H |

A → GE → G | G | G → I |

F → H | H | H → K |

G → I | I | I → K |

C → J | J | J → End |

H → KI → K | K | K → End |

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