## Project Time Cost Trade-off

The cost of a project comprises of two components – direct cost and indirect cost.

Direct costs include the cost of materials, labour and equipments etc. direct cost of a project is the sum total of direct costs of all the activities contained in the project. It is inversely proportional to the project duration means the direct cost of any project reduces with the duration of the project.

Indirect costs are the cost associated with sustaining a project. Indirect costs include the cost of supervision, overheads, facilities, penalty cost and lost incentive payments. Project indirect cost is dependent upon the length of the project duration. A project having longer duration will have higher indirect cost.

Project Time Cost Trade-off Project Time Cost Trade-off

The normal and crash times and direct costs for the activities are shown below:

- Draw the network diagram.
- Determine the critical path.
- Find the minimum cost project schedule if the indirect cost is Rs. 150 per day.

Learn What is **Critical Path Method (CPM)** and **Programme Evaluation And Review Technique (PERT)**

Step I Calculate the slope using the formula slope = Crash Cost – Normal Cost/ (Normal time – Crash time)

Step II Construct the network and find out the critical path.

Critical path (longest normal duration) is 1-3-5-6. Project duration is 16 days. It can be crashed to 11 days (Maximum in crash time).

It is the critical path which decides the duration of the project so we will crash the activities of critical path only. So the eligible activities for crashing are

Activities | Slope |

1-3 | 100 |

3-5 | 100 |

5-6 | 200 |

As Activities 1-3 and 3-5 have the least cost slope, we can select any of the activity for crashing.

Step I: Crash activity 1-3 by 1 day. The project duration is 15 days.

Total cost = Normal cost + crash cost of activity 1-3

= 10,600 + 100 = Rs. 10, 700

After crashing the project by 1 day, the length of each path is checked to find out the critical path. It is observed that the same path 1-3-5-6 is still the longest duration path and the same activities are eligible for crashing.

Step II: Crash activity 1-3 by 1 day. The project duration is 14 days.

Total cost = Normal cost + crash cost of activity 1-3

= 10,700 + 100 = Rs. 10, 800

After crashing the project by 1 day, the length of each path is checked to find out the critical path. It is observed that the same path 1-3-5-6 is still the longest duration path. The activity 1-3 is completely crashed and it can not be reduced further. The eligible activities for crashing are 3-5 / 5-6.

Activities | Slope |

3-5 | 100 |

5-6 | 200 |

Step III: Crash activity 3-5 by 1 day. The project duration is 13 days.

Total cost = Normal cost + crash cost of activity 3-5

= 10,800 + 100 = Rs. 10, 900

After crashing the project by 1 day, the length of each path is checked to find out the critical path. Now there are two critical paths – 1-3-5-6 and 1-2-4-6. Now we have to crash both the paths together. We can one common activity in both the path or combination of two activities be selecting one from each path. We can compare the cost of the alternative options for crashing.

Activities | Slope |

1-2, 3-5 | 300 |

1-2, 5-6 | 400 |

2-4, 3-5 | 300 |

2-4, 5-6 | 400 |

4-6, 3-5 | 600 |

4-6, 5-6 | 700 |

Step IV: Crash activities (1-2) and (3-5) by 1 day. The project duration is 12 days.

Total cost = Normal cost + crash cost of activities 1-2 and 3-5

= 10,900 + 300 = Rs. 11, 200

Activity 3-5 and 1-2 are completely crashed now. After crashing the project to 12 days, again we check the duration of different alternative paths. It is observed now that all three paths are critical, that’s why needs to be crashed together.

Step V: Crash activities 4-6 (which is common in two paths) and 5-6 by 1 day. Project duration is 11 days.

Total cost = Normal cost + crash cost of activities 4-6 and 5-6

= 11,200 + 700 = 11,900 Rs.

Answer:

The minimum time for project completion is 11 days and associated cost is Rs. 13550.

The minimum cost for project completion is 12850 and associated time is 13 days.

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Project Time Cost Trade-off Project Time Cost Trade-off Project Time Cost Trade-off Project Time Cost Trade-off