(Numerical 1) Based on Hungarian Method from Balanced Minimization type Assignment Problem in Hindi

Описание: #EducatorAdda #HungarianMethod #AssignmentProblem #OperationResearch #BalancedMinimizationType #Hindi

"Hungarian Method Procedure"

Steps:
(1) Check, if the total number of rows is not equal to the total number of columns, then add a dummy row or a dummy column with cost 0, to make it a square matrix.

(2) Scan each row, find the lowest element, and subtract it from each element in that row.

(3) Similarly, scan each column, find the lowest element, and subtract it from each element in that column.

(4) Identify rows with exactly one unmarked 0. Make an assignment to this single 0 by making a square around it and cross off all other elements in the same column.

(5) Similarly, identify columns with exactly one unmarked 0. Make an assignment to this single 0 by making a square around it and cross off all other elements in the same row.

(6) If a row or column has two or more unmarked 0 and one cannot be chosen by inspection, then choose the cell arbitrarily.

(7) Continue the scanning process until all 0 in rows and columns are either assigned or cross off.

(8) If the number of assigned cells = the number of rows, then an optimal assignment is obtained and In case you have chosen a 0 cell arbitrarily, then there may be an alternate optimal solution exists.

(9) If an optimal solution is not obtained, then select the smallest element of the whole matrix, which is NOT COVERED by lines. Subtract this smallest element with all other remaining elements that are NOT COVERED by lines and add the element at the intersection of lines. Leave the elements covered by a single line as it is.

(10) Again repeat the step-5,6,7 until all the assignments have been made.

(11) If an optimal solution is obtained, write down the assignment results, and find the minimum cost/time.

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