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