Question

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

	Programmers
		P	Q	R
Programmers	1	120	100	80
	2	80	90	110
	3	110	140	120

Assign the programmers to the programme in such a way that the total computer time is least.

Answer 1

Here the number of rows and columns are equal.

∴ The given assignment problem is balanced.

Step 1: Select the smallest element in each row and subtract this from all the elements in its row.

	Programmers
		P	Q	R
Programmers	1	40	20	0
	2	0	10	30
	3	0	30	10

Step 2: Select the smallest element in each column and subtract this from all the elements in its column.

	Programmers
		P	Q	R
Programmers	1	40	10	0
	2	0	0	30
	3	0	20	10

Step 3: Examine the rows with exactly one zero, mark the zero by □. Mark other zeros in its column by X.

	Programmers
		P	Q	R
Programmers	1	40	10	0
	2	0	0	30
	3	0	20	10

Step 4: Now examine the columns with exactly one zero mark the zero by □.

Mark other zeros in its row by X.

	Programmers
		P	Q	R
Programmers	1	40	10	0
	2	0	0	30
	3	0	20	10

Thus all the three assignment have been made.

The optimal assignment schedule and total cost is

Programmers	Programmes	Cost
1	R	80
2	Q	90
3	P	110
Total Cost		280

The optimal assignment (minimum) cost = ₹ 280.