Question

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

		Machine
		U	V	W
Jobs	A	17	25	31
	B	10	25	16
	C	12	14	11

(cost is in ₹ per unit)

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.

		Machine
Jobs		U	V	W
	A	2	0	16
	B	0	15	6
	C	1	3	0

Look for atleast one zero in each row and each column.

Here each and every row and columns having exactly one zero No need step 2 go to step 3.

Step 3:

		Machine
Jobs		U	V	W
	A	2	0	16
	B	0	15	6
	C	1	3	0

Mark the zero by □ Mark other zeros in its column by X.

Since each row and each column contains exactly one assignment, all the three machine have been assigned a job.

Job	Machine	Cost
A	V	15
B	U	10
C	W	11
Total Cost		46

The Optimal assignment (minimum) cost = 46