Example: Machine assignment and sequencing
We need to produce 12 products on a set of three machines. Each machine may produce all of the products but processing times and costs vary (Table Machine-dependent production costs and durations). Furthermore, for every product we are given its release and due dates (Table Release dates and due dates of products). We wish to determine a production plan for all products that minimizes the total production cost.
| Production costs | Durations | |||||||
|---|---|---|---|---|---|---|---|---|
| Prod. \ Mach. | 1 | 2 | 3 | 1 | 2 | 3 | ||
| 1 | 12 | 6 | 7 | 10 | 14 | 13 | ||
| 2 | 13 | 6 | 10 | 7 | 9 | 8 | ||
| 3 | 10 | 4 | 6 | 11 | 17 | 15 | ||
| 4 | 8 | 4 | 5 | 6 | 9 | 12 | ||
| 5 | 12 | 6 | 7 | 4 | 6 | 10 | ||
| 6 | 10 | 5 | 6 | 2 | 3 | 4 | ||
| 7 | 7 | 4 | 5 | 10 | 15 | 16 | ||
| 8 | 9 | 5 | 5 | 8 | 11 | 12 | ||
| 9 | 10 | 5 | 7 | 10 | 14 | 13 | ||
| 10 | 8 | 4 | 5 | 8 | 11 | 14 | ||
| 11 | 15 | 8 | 9 | 9 | 12 | 16 | ||
| 12 | 13 | 7 | 7 | 3 | 5 | 6 | ||
| Product | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Release | 2 | 4 | 5 | 7 | 9 | 0 | 3 | 6 | 11 | 2 | 3 | 4 |
| Due date | 32 | 33 | 36 | 37 | 39 | 34 | 30 | 26 | 36 | 38 | 31 | 22 |
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