Question

A company is putting together an assembly combination. The table below provides the best time (in seconds) for each operator and assembly. Find the best assembly assignment that minimizes the total operation total time.

A B C D Employee 1 28 28 25 27 Employee 2 13 22 17 17 Employee 3 18 20 22 24 Employee 4 3 3 31 32 30

Answer 1

This is the original time matrix:

28	28	25	27
13	22	17	17
18	20	22	24
33	31	32	30

Subtract row minima

We subtract the row minimum from each row:

3	3	0	2	(-25)
0	9	4	4	(-13)
0	2	4	6	(-18)
3	1	2	0	(-30)

Subtract column minima

We subtract the column minimum from each column:

3	2	0	2
0	8	4	4
0	1	4	6
3	0	2	0
	(-1)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

3	2	0	2	x
0	8	4	4
0	1	4	6
3	0	2	0	x
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 1. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

4	2	0	2
0	7	3	3
0	0	3	5
4	0	2	0

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

4	2	0	2	x
0	7	3	3	x
0	0	3	5	x
4	0	2	0	x

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

4	2	0	2
0	7	3	3
0	0	3	5
4	0	2	0

This corresponds to the following optimal assignment in the original time matrix:

28	28	25	27
13	22	17	17
18	20	22	24
33	31	32	30

The optimal value equals 88.