Integer Programming
A workshop has 6 machines that can perform any job assigned to them. The workshop has 10 jobs that it needs to complete over two days. Jobs 1 to 5 must be finished on the first day and jobs 6 to 10 must be finished on the second day. Any of the machines will take a complete day to finish any of the jobs. The workshop manager requires that none of the machines stay idle for the two days. Write an integer programming model that would minimize the total costs of running the 10 jobs. The cost per job per machine is given in Table 2.
Table 2
Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 Job 7 Job 8 Job 9 Job 10
Machine 1 $85 $75 $80 $65 $80 $90 $85 $55 $60 $100
Machine 2 $82 $76 $78 $63 $80 $85 $82 $54 $58 $90
Machine 3 $87 $77 $82 $60 $82 $90 $87 $54 $62 $102
Machine 4 $79 $72 $76 $59 $78 $85 $77 $53 $56 $90
Machine 5 $90 $78 $84 $70 $85 $93 $90 $57 $64 $97
Required to write the decision variables, objective function, and constraints have to solve it using Solver in Excel.