Homework SourseFibrous Incorporated makes products from rough tree fibers I
Fibrous Incorporated makes products from rough tree fibers. Its product line consists of five items processed through one of five machines. The machines are not identical, and some products are better suited to some machines. Given the following production time in minutes per unit, determine an optimal assignment of product to machine:
Machine
Product
A
B
C
D
E
1
17
10
15
16
20
2
12
9
16
9
14
3
11
16
14
15
12
4
14
10
10
18
17
5
13
12
9
15
11
|
Solution
Solution :
The assignment is as follows :
Product 1 - Machine B
Product 2 - Machine D
Product 3 - Machine A
Product 4 - Machine C
Product 5 - Machine E
The calculation is as shown below :
| Machine | ||||||
| Product | A | B | C | D | E | |
| 1 | 17 | 10 | 15 | 16 | 20 | |
| 2 | 12 | 9 | 16 | 9 | 14 | |
| 3 | 11 | 16 | 14 | 15 | 12 | |
| 4 | 14 | 10 | 10 | 18 | 17 | |
| 5 | 13 | 12 | 9 | 15 | 11 | |
| Machine | ||||||
| Product | A | B | C | D | E | |
| 1 | 7 | 0 | 5 | 6 | 10 | |
| 2 | 3 | 0 | 7 | 0 | 5 | |
| 3 | 0 | 5 | 3 | 4 | 1 | |
| 4 | 4 | 0 | 0 | 8 | 7 | |
| 5 | 4 | 3 | 0 | 6 | 2 | |
| Machine | ||||||
| Product | A | B | C | D | E | |
| 1 | 7 | 0(A) | 5 | 6 | 10 | |
| 2 | 3 | 0(X) | 7 | 0(A) | 5 | |
| 3 | 0(A) | 5 | 3 | 4 | 1 | |
| 4 | 4 | 0(X) | 0(A) | 8 | 7 | |
| 5 | 4 | 3 | 0(X) | 6 | 2 | |
| Machine | ||||||
| Product | A | B | C | D | E | |
| 1 | 7 | 0(A) | 5 | 6 | 10 | |
| 2 | 3 | 0(X) | 7 | 0(A) | 5 | |
| 3 | 0(A) | 5 | 3 | 4 | 1 | |
| 4 | 4 | 0(X) | 0(A) | 8 | 7 | |
| 5 | 4 | 3 | 0(X) | 6 | 2 | |
| D | E | |||||
| 8 | 7 | |||||
| 6 | 2 | |||||
| D | E | |||||
| 1 | 0 | |||||
| 4 | 0 | |||||
| Machine | ||||||
| Product | A | B | C | D | E | |
| 1 | 7 | 0(A) | 5 | 6 | 10 | |
| 2 | 3 | 0 | 7 | 0(A) | 5 | |
| 3 | 0(A) | 5 | 3 | 4 | 1 | |
| 4 | 4 | 0 | 0(A) | 1 | 0 | |
| 5 | 4 | 3 | 0 | 4 | 0(A) |
