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.
Table 2: Machine-dependent production costs and durations
|
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 |
Table 3: Release dates and due dates of products
| 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 |
