The Hungarian Assignment method
Step 1: Develop the Cost Table from the given Problem:
If the no of rows are not equal to the no of columns and vice versa, a dummy row or dummy column must be
added. The assignment cost for dummy cells are always zero.
Step 2: Find the Opportunity Cost Table:
(a) Locate the smallest element in each row of the given cost table and then subtract that from each element
of that row, and (b) In the reduced matrix obtained from 2 (a) locate the smallest element in each column
and then subtract that from each element. Each row and column now have at least one zero value.
Step 3: Make Assignment in the Opportunity Cost Matrix:
The procedure of making assignment is as follows: (a) Examine rows successively until a row with exactly
one unmarked zero is obtained. Make an assignment to row/column with single zero by making a square
around it. (b) For each zero value that becomes assigned, eliminate (Strike off) all other zeros in the same
row and/ or column (c) Repeat step 3 (a) and 3 (b) for each column also with exactly a single zero value all
that has not been assigned. (d) If a row and/or column has two or more unmarked zeros and one cannot be
chosen by inspection, then choose the assigned zero cell arbitrarily. (e) Continue this process until all zeros
in each row / column are either enclosed (Assigned) or struck off (x)
Step 4: Optimality Criterion:
If the number of assigned cells is equal to the number of rows / columns then it is an optimal solution. The
total cost associated with this solution is obtained by adding original cost figures in the occupied cells. If a
zero cell was chosen arbitrarily in step (3), there exists an alternative optimal solution. But if no optimal
solution is found, then go to step (5).
Step 5: Revise the Opportunity Cost Table:
Draw a set of horizontal and vertical lines to cover all the zeros in the revised cost table obtained from step
(3), by using the following procedure: (a) For each row in which no assignment was made, mark a tick (√)
(b) Examine the marked rows. If any zero occurs in those columns, tick the respective rows that contain
those assigned zeros. (c) Repeat this process until no more rows or columns can be marked. (d) Draw a
straight line through each marked column and each unmarked row. If a no of lines drawn is equal to the no
of (or columns) the current solution is the optimal solution, otherwise go to step 6.
Step 6: Develop the New Revised Opportunity Cost Table:
