The Reliance manufacturing Company produces an aircraft part. The company can produce the part entirely at a flexible work center with multiple computerized machines.
The company has 4 work centers, all of which are different because they were purchased at different times. Each work center has a single operator; however the company's operators have different skill levels, resulting in different levels of daily output and product quality.
The following tables show the average daily output and average number of defects per dayfor each of the company's 5 operators who are capable of producing the aircraft part:
|
Average Daily output per machine |
| Operator |
A |
B |
C |
D |
| 1 |
18 |
20 |
21 |
17 |
| 2 |
19 |
15 |
22 |
18 |
| 3 |
20 |
20 |
17 |
19 |
| 4 |
24 |
21 |
16 |
23 |
| 5 |
22 |
19 |
21 |
21 |
|
|
|
|
|
|
Average # of defects daily per machine |
| Operator |
A |
B |
C |
D |
| 1 |
0.3 |
0.9 |
0.6 |
0.4 |
| 2 |
0.8 |
0.5 |
1.1 |
0.7 |
| 3 |
1.1 |
1.3 |
0.6 |
0.8 |
| 4 |
1.2 |
0.8 |
0.6 |
0.9 |
| 5 |
1 |
0.9 |
1 |
1 |
|
|
|
|
The company wants to determine which operator to assign to each machine to maximize daily output and keep the percentage of defects to less than 4%.
a) formulate a 0-1 integer programming model for this problem
b) solve the model through excel step by step with formulas