Voltwise
Voltwise is an independent contractor company that provides services around the expansion and maintenance of electric grids in Colombia.
Every month, Voltwise has the opportunity to bid on major priority projects announced by the regulatory agencies. To be profitable and, at the same time competitive, Voltwise must be able to plan ahead for its operations in order to bid on the right price.
The project they are currently considering involves the completion of six major tasks, for which Voltwise has accurate costs and time estimates.
The table below contains the expected completion time of each task along with the execution cost. Taking less than the expected number of days to complete a task is acceptable, but it comes with an extra expedition cost, as informed in the Expedition Cost column. The maximum number of days each task can be expedited is also given.
For example, if Voltwise decides to complete Task 1 in 20 days, the corresponding cost will be:
| Task ID | Regular Completion Time (days) | Execution Cost ($/day) | Expedition Cost ($/days) | Max Expedition (days) |
|---|---|---|---|---|
| 1 | 23 | 270 | 340 | 3 |
| 2 | 15 | 165 | 225 | 2 |
| 3 | 27 | 270 | 370 | 5 |
| 4 | 9 | 158 | 170 | 2 |
| 5 | 19 | 146 | 195 | 3 |
| 6 | 5 | 80 | 150 | 0 |
In addition, some tasks can only be initiated upon completion of other tasks. For example, they can only install the electrical network after digging the ditches.
The table below shows all the precedence pairs.
| Predecessor Task ID | Successor Task ID |
|---|---|
| 1 | 3 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
| 4 | 6 |
The goal for Voltwise is to find a feasible schedule to complete the project at the minimum cost given that all tasks must be completed within 75 days.