A job-shop needs to assign 4 jobs to 4 workers. The cost of performing a job is a function of the skills of the workers. The below table summarizes the cost of the assignment. Worker 1 cannot do job 3 and worker 3 cannot perform job 4.
a. Formulate this problem using a general LP model to minimize the total cost of this assignment problem.
b. Determine the optimal assignment using Solver via a generalization of a transportation problem.
| Worker |
jobs |
| 50 |
50 |
- |
20 |
| 70 |
40 |
20 |
30 |
| 90 |
30 |
50 |
- |
| 70 |
20 |
60 |
70 |