Question

Solve the following minimal assignment problem : 

Machines	Jobs
	I	II	III
M1	1	4	5
M2	4	2	7
M3	7	8	3

Answer 1

 Given cost matrix is 

	I	II	III
M1	1	4	5
M2	4	2	7
M3	7	8	3

Subtracting smallest element of each row from every element of that row. 

	I	II	III
M1	0	3	4
M2	2	0	5
M3	4	5	0

As each column contains a zero we do not subtract smallest element of a column from every element.

Hence allocation is as given below 

Hence assignment is 

M₁ → I  M₂ → II  M₃ → III

Minimum total cost = 1 + 2 + 3 

= 6 units.