Question

A firm is required to procure three items (P, Q and R). The prices quoted for these items (in Rs.) by suppliers $S_1,S_2\text{and}{S}_3$ are given in the table. The management policy requires that each item has to be supplied by only one supplier and one supplier supplies only one item. The minimum total cost (in Rs.) of procurement to the firm is

Item	Supplier
	$S_1$	$S_2$	$S_3$
P	110	120	130
Q	115	140	140
R	125	145	165

• A. 350
• B. 395
• C. 360
• D. 385

Answer 1

The correct option is D 385



Step 1: Subtract minimum entry in each column from all the entries in that column,



Step 2: Subtract the minimum entry in each row of the job-opportunity cost matrix from all the entries of that row.

0	0	0
0	15	5
0	10	20

Step 3: Draw a minimum number of horizontal and vertical lines to cover all zeroes. This can be done in 2 lines, which is one less than the number of rows (which is 3). Thus the solution is yet not fixed. Hence go to step 4



Step 4: From the uncovered entries, the minimum is 5. Thus, subtract 5 from all the entries, which are uncovered. Add 5 at the junction of lines. We get the following matrix now, as the revised opportunity cost matrix.



$\text{The minimum cost = 120 + 140 + 125 = Rs. 385}$

$\text{Points to Remember}$

• It is a special case of transportation problem where in each row and column, 1-allocation is possible and the matrix should be a square matrix i.e. (m = n)
• The Hungarian method is used to solve assignment problems and it is developed only for minimization.