There are 5 machines and 4 jobs to be performed. Each machine can perform only a particular set of jobs and not all jobs. Also, time taken by each machine for each job is different. See the table for hours taken by each machine to do the job. X means the machine can't do that job.
|
|
JOB 1
|
JOB 2
|
JOB 3
|
JOB 4
|
|
MACHINE 1
|
13
|
12
|
X
|
15
|
|
MACHINE 2
|
12
|
X
|
12
|
12
|
|
MACHINE 3
|
X
|
X
|
10
|
10
|
|
MACHINE 4
|
10
|
13
|
14
|
11
|
|
MACHINE 5
|
9
|
11
|
13
|
X
|
a. Each machine can do at most one job. Formulate an integer linear program to assign the four jobs to different machines with the goal of minimizing the total time.
b. Find the optimal solution using Solver. What are the optimal assignments? What is the total time spent processing the jobs?