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# PERT Cost Analysis

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The most important feature of network analysis is the activities cost projection (Pinto, 2015), and is done using Project Review and Evaluation Techniques (PERT). The primary jobs of a PERT starts after the network is drawn, all the activities duration and the “critical path” identified. For the project, “the critical path is A-C-D-F.” Again, tasks, not along the “critical path,” will not affect the project completion time even if they fall below the determined schedule. However, due to the importance of the critical activities on the project completion, assessment and adjustments must be made on their time to ensure that the tasks are accomplished as planned. According to Nafkha (2017), PERT cost matches activities cost and time for the allocation of least cost to the “project activities along the critical path.”

The duration and cost relationship for the estimated projection involves the normal estimate and crash estimate. The normal estimate of time is equivalent to the expected time estimate. In addition, the normal cost is the cost relating to finishing the project within the normal time. The crash cost estimate is the amount of the resources required to complete the project in a shorter time without sparing any cost within the project.

The PERT cost analysis assumes that for any unit reduction in time there is an equivalent increase in the cost. According to Appendix B, the weekly incremental cost (maximum cost) is the “crash cost minus the normal cost divided by the normal time minus the crash time.” Hence the relationship, incremental cost= {(Crash cost-Normal cost)/ (Normal time-Crash time) = (∆ Cost)/(∆ Time)}

The cost and time relationship presented is vital in determining how the incremental cost can be used to reduce the project duration with the least cost possible. For the project, the incremental cost is represented as cost per day. The critical path duration is calculated by adding the task duration, along the critical path A-C-D-F. Therefore, the critical path duration is 19 days, which is also its normal completion duration. To crash the project, activities along the critical path with least cost are crashed first. Tasks, C, and D, are the identified with the least cost of \$ 450 and \$ 750 respectively, with a maximum crashable time of 1 day for A and 2 days for B. It is observed that the project duration is shortened by 3 days with an incremental cost of \$ 1,500. To this end, the project duration is reduced to 16 days instead of completing it in 19 days, and the project cost has increased from \$ 14,750 to \$ 16,700.

According to Appendix B, the activities for crashing are C, D, and G, since they have the least-incremental cost of \$ 450, \$ 750 and \$ 900 respectively. When the critical path is identified as A-C-D-F, The activities for crashing are C and D because they have the lowest cost along the path. The critical network path has changed the decision rule in that only the critical activities are the path are crashable leaving out activity G, the assumption is based on the fact that crashing any activity other than the once along the critical path may make all the paths to be critical hence subjecting the activities to unnecessary crashing.

PERT cost analysis is very critical aspect crashing a network, most project managers’ use the knowledge of PERT to allocate cost project activities and the same time determine minimum period that the project can take to completion at the least cost possible.

References

Nafkha, R., & Wiliński, A. (2016). The critical path method in estimating project duration. Information Systems in Management, 5(1), 78-87.

Pinto, J.K. (2015). Project management: achieving competitive advantage. Upper Saddle River, NJ: Prentice Hall.

Appendix A

Project Gantt chart

Appendix B

Project cost crashing summary

Activity

Normal duration

crash duration

maximum  time

Normal cost

crash cost

crash cost per day

A

4

3

1

1000

2000

1000

B

5

3

2

2500

5000

1250

C

3

2

1

750

1200

450

D

7

5

2

3500

5000

750

E

2

1

1

500

3000

2500

F

5

4

1

2000

3000

1000

G

9

7

2

4500

6300

900

October 30, 2023
Category:
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Number of pages

3

Number of words

624