(Solved Homework): Kelle Carpet and Trim installs carpet in commercial offices. Peter Kelle has been…
Kelle Carpet and Trim installs carpet in commercial offices. Peter Kelle has been very concerned with the amount of time it took to complete several recent jobs. Some of his 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 given in the following table: This exercise contains only parts b, c, and d. b) Activities on the critical path for the project are C-D-E-G-I-K. The total project completion time is 40.17 days. (Round your response to two decimal places.) c) For the given project, the earliest start (ES) and earliest finish (EF) are: (Round your responses to two decimal places.)
Expert Answer
You have computed the critical path and the project completion time correctly. You could have used those steps to calculate the earliest start and finish times for each task.
Let’s define the terms
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Earlist Start time is the earliest expected time an activity can start. Hence, it is the maximum of the expected finish times of its predecessors, or 0 in case there are no predecessors.
Earliest Finish Time is the earliest expected time that an activity can finish. Hence, it is the expected time to finish that task, plus (the maximum of the expected time to finish its predeeding tasks, or 0 in case there is no predecessor).
I used Excel to compute the Earliest Start and Earliest End times for your problem; unfortunately I am not allowed to attach the sheet. I have copied the table.
It is apparent from the table that for tasks, A, B, and C, the Earliest Start and Earliest End are 0, and the time taken for the task, respectively, because there are no preceding tasks. For the other tasks, the earliest start time is the end time of its critical predecessor task. To get the Earliest End time, just add the expected time to get their start time.
Hope this helps.
| Task | Optimistic | Mean | Pessimistic | Predecessors | Expected time | Earliest Start Time | Earliest Finish | Critical Predecessor |
| A | 2 | 6 | 8 | None | 5.6666666667 | 0 | 5.6666666667 | None |
| B | 3 | 4 | 5 | None | 4 | 0 | 4 | None |
| C | 2 | 3 | 4 | None | 3 | 0 | 3 | None |
| D | 7 | 8 | 9 | C | 8 | 3 | 11 | C |
| E | 1 | 3 | 5 | B,D | 3 | 11 | 14 | D |
| F | 1 | 2 | 3 | A,E | 2 | 14 | 16 | E |
| G | 7 | 10 | 14 | A,E | 10.1666666667 | 14 | 24.1666666667 | E |
| H | 11 | 12 | 13 | F | 12 | 16 | 28 | F |
| I | 5 | 7 | 9 | G | 7 | 24.1666666667 | 31.1666666667 | G |
| J | 13 | 15 | 17 | C | 15 | 3 | 18 | C |
| K | 5 | 9 | 13 | H,I | 9 | 31.1666666667 | 40.1666666667 | I |
