Question: Consider the following project network with normal duration times provided for each task. Each task can be compressed by a maximum of two weeks; each
Consider the following project network with normal duration times provided for each task. Each task can be compressed by a maximum of two weeks; each weeks decrease will cost an amount that is equal to its estimated normal duration (for example, the duration of task A can be reduced to six weeks by spending an additional $7, or it can be reduced to five weeks for an additional cost of $14).
- Which tasks should be compressed if we want to reduce the project makespan by three weeks at the smallest possible total direct cost? What is the marginal increase in total direct costs for each week that we decrease the project duration?
- If the project is completed after 20 weeks, a penalty fee of $9 per week is assessed for each week late. However, if the project is completed before week 20, there is a $5 bonus paid for each week early. Find the project duration that minimizes total cost (where total cost includes direct labor costs, late fees, and earliness bonus).
| Task | Normal Duration | Predecessor (s) |
| Start | 0 | - |
| A | 7 | Start |
| B | 10 | Start |
| C | 7 | B |
| D | 8 | A |
| E | 6 | A |
| F | 5 | E |
| G | 10 | C, D, F |
| H | 11 | E |
| End | 0 | G, H |
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