MACFAST ASSIGNMENT

1. Assignment problem

2. What is assignment problem?
 Assignment problem refers to special class of linear
programming problems that involves determining
the most efficient assignment of people to projects.
 It is often used minimize total cost or time of
performing task.

3. Methods of solving AP in Hungarian method
 Step 1:check whether the problem is balanced or
not. if yes, move to next step otherwise provide
dummy row or column and make it balanced.
 Step 2: subtract the smallest element of each row
,in the cost matrix ,from every element of that job.
 Step 3:find the minimum element in each column
and subtract it from all the elements of that
particular column.
step 2 and step 3 creates at least one zero in each
row and column.

4.  Step 4:starting with row 1 of the matrix, if there is
exactly one zero, make an assignment and cancel
all zero’s in that column and then draw a vertical
line. similarly starting with 1st column, if there is
one zero make an assignment and cancel that row
with horizontal line. continue this step till all zeros
are allocated or cancelled.
 If optimal assignment is not formed go to step 5.

5.  Step 5: ensure all zeros are covered with minimum
line.
Find the minimum element not covered by any
line.
 Step 6: subtract the elements not covered by line.
Also add the same element which are at
intersection.
 Step 7:now reapply the steps 4 to 6