Question

To state whether the following is true or false with a short proof or a counter example in support of the answer :

The following 4/3/F/F_ max problem can be reduced to a machine problem:

Job Processing time (in hours) on

M₁ M₂ M₃

1 8 6 10

2 5 2 13

3 4 11 11

4 6 7 10

Answer 1

Yes The following max problem can be reduced to a machine problem.

Consider we have 4-job, 3-machine shop as shown in the diagram below-

$x_i=m_1+m_2\\y_i=m_3+m_2$

Idle time of machine 1 =46-25=21 min

Idle time of machine 2=46-24=22 min

Idle time of Machine 3=46-38=12min

So, Above problem can be reduced to machine problem.