Project scheduling example
A town council wishes to construct a small stadium in order to improve the services provided to the people living in the district. After the invitation to tender, a local construction company is awarded the contract and wishes to complete the task within the shortest possible time. All the major tasks are listed in the following table. The durations are expressed in weeks. Some tasks can only start after the completion of certain other tasks. The last two columns of the table refer to question 2 which we shall see later.
| Task | Description | Dur. | Prede- cessors |
Max. reduct. | Add. cost per week (in 1000€) |
|---|---|---|---|---|---|
| 1 | Installing the construction site | 2 | none | 0 | – |
| 2 | Terracing | 16 | 1 | 3 | 30 |
| 3 | Constructing the foundations | 9 | 2 | 1 | 26 |
| 4 | Access roads and other networks | 8 | 2 | 2 | 12 |
| 5 | Erecting the basement | 10 | 3 | 2 | 17 |
| 6 | Main floor | 6 | 4,5 | 1 | 15 |
| 7 | Dividing up the changing rooms | 2 | 4 | 1 | 8 |
| 8 | Electrifying the terraces | 2 | 6 | 0 | – |
| 9 | Constructing the roof | 9 | 4,6 | 2 | 42 |
| 10 | Lighting of the stadium | 5 | 4 | 1 | 21 |
| 11 | Installing the terraces | 3 | 6 | 1 | 18 |
| 12 | Sealing the roof | 2 | 9 | 0 | – |
| 13 | Finishing the changing rooms | 1 | 7 | 0 | – |
| 14 | Constructing the ticket office | 7 | 2 | 2 | 22 |
| 15 | Secondary access roads | 4 | 4,14 | 2 | 12 |
| 16 | Means of signaling | 3 | 8,11,14 | 1 | 6 |
| 17 | Lawn and sport accessories | 9 | 12 | 3 | 16 |
| 18 | Handing over the building | 1 | 17 | 0 | – |
Question 1: Which is the earliest possible date of completing the construction?
Question 2: The town council would like the project to terminate earlier than the time announced by the builder (answer to question 1). To obtain this, the council is prepared to pay a bonus of €30K for every week the work finishes early. The builder needs to employ additional workers and rent more equipment to cut down on the total time. In the preceding table he has summarized the maximum number of weeks he can save per task (column "Max. reduction") and the associated additional cost per week. When will the project be completed if the builder wishes to maximize his profit?
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