## Assignment Problem: Maximization

There are problems where certain facilities have to be assigned to a number of jobs, so as to maximize the overall performance of the assignment.

The Hungarian Method can also solve such assignment problems , as it is easy to obtain an equivalent minimization problem by converting every number in the matrix to an opportunity loss.

The conversion is accomplished by subtracting all the elements of the given matrix from the highest element. It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem.

- Unbalanced Assignment Problem
- Multiple Optimal Solutions

## Example: Maximization In An Assignment Problem

How should the counters be assigned to persons so as to maximize the profit ?

On small screens, scroll horizontally to view full calculation

## Final Table: Maximization Problem

Use Horizontal Scrollbar to View Full Table Calculation

The total cost of assignment = 1C + 2E + 3A + 4D + 5B

Substituting values from original table: 40 + 36 + 40 + 36 + 62 = 214.

Operations Research Simplified Back Next

Goal programming Linear programming Simplex Method Transportation Problem

## Choose the correct alternative : To use the Hungarian method, a profit maximization assignment problem requires ______. - Mathematics and Statistics

Choose the correct alternative :

To use the Hungarian method, a profit maximization assignment problem requires ______.

Converting all profits to opportunity losses

Finding the maximum number of lines to cover all the zeros in the reduced matrix

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## Hungarian Method for Maximal Assignment Problem Examples

## Hungarian Method for Maximal Assignment Problem Example

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## Hungarian Method

## Hungarian Method to Solve Assignment Problems

## What is an Assignment Problem?

## Hungarian Method Steps

- Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.
- Examine the columns one by one until you find one with precisely one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.

Step 4 – Perform the Optimal Test

- The present assignment is optimal if each row and column has exactly one encircled zero.
- The present assignment is not optimal if at least one row or column is missing an assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and ensure that each column has at least one zero.

Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:

(a) Highlight the rows that aren’t assigned.

(b) Label the columns with zeros in marked rows (if they haven’t already been marked).

(d) Continue with (b) and (c) until no further marking is needed.

Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment.

## Hungarian Method Example

With 5 jobs and 5 men, the stated problem is balanced.

When the zeros are assigned, we get the following:

The present assignment is optimal because each row and column contain precisely one encircled zero.

Where 1 to II, 2 to IV, 3 to I, 4 to V, and 5 to III are the best assignments.

Hence, z = 15 + 14 + 21 + 20 + 16 = 86 hours is the optimal time.

## Practice Question on Hungarian Method

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## Frequently Asked Questions on Hungarian Method

## What are the steps involved in Hungarian method?

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## Hungarian Algorithm for Assignment Problem | Set 1 (Introduction)

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- Discuss(20+)
- For each row of the matrix, find the smallest element and subtract it from every element in its row.
- Do the same (as step 1) for all columns.
- Cover all zeros in the matrix using minimum number of horizontal and vertical lines.
- Test for Optimality: If the minimum number of covering lines is n, an optimal assignment is possible and we are finished. Else if lines are lesser than n, we haven’t found the optimal assignment, and must proceed to step 5.
- Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.

Try it before moving to see the solution

Explanation for above simple example:

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## COMMENTS

To use the Hungarian method, a profit-maximization assignment problem requires a. converting all profits to opportunity losses.b. a dummy agent or task. c. matrix expansion.d. finding the maximum number of lines to cover all the zeros in the reduced matrix. ANS: A PTS: 1 TOP: Hungarian method a. converting all profits to opportunity losses .

The Hungarian Method can also solve such assignment problems, as it is easy to obtain an equivalent minimization problem by converting every number in the matrix to an opportunity loss. The conversion is accomplished by subtracting all the elements of the given matrix from the highest element.

Using Hungarian method the optimal assignment obtained for the following assignment problem to minimize the total cost is: 1 - D, 2 - A, 3 - B, 4 - C. VIEW SOLUTION Miscellaneous Exercise 7 | Q 1.09 | Page 127 Choose the correct alternative : The assignment problem is said to be unbalance if Number of rows is greater than number of columns

To use the Hungarian method, a profit maximization assignment problem requires converting all profits to opportunity losses. Concept: Hungarian Method of Solving Assignment Problem Is there an error in this question or solution? Chapter 7: Assignment Problem and Sequencing - Miscellaneous Exercise 7 [Page 126] Q 1.07 Q 1.06 Q 1.08 APPEARS IN

To use the Hungarian method, a profit-maximization assignment problem requires a. converting all profits to opportunity losses The transportation simplex method can be used to solve the assignment problem. T The transportation simplex method is limited to minimization problems F

Find Solution of Assignment problem using Hungarian method (MIN case) Solution: The number of rows = 5 and columns = 5 Here given problem is balanced. Step-1: Find out the each row minimum element and subtract it from that row Step-2: Find out the each column minimum element and subtract it from that column.

9. To use the Hungarian method, a profit-maximization assignment problem requires a. converting all profits to opportunity losses. b. a dummy agent or task.c. matrix expansion. d. finding the maximum number of lines to cover all the zeros in the reduced matrix. ANS: A PTS: 1 TOP: Hungarian method a. converting all profits to opportunity losses .

The Hungarian method for solving an assignment problem can also be used to solve; a. A transportation problem b. A travelling salesman problem c. Both (a) and (b) d. Only (b) An optimal solution of an assignment problem can be obtained only if; a. Each row and column has only one zero element b. Each row and column has at least one zero element c.

To use the hungarian method a profit-maximization assignment problem requires How To Solve An Assignment Problem. #1 This video is private The crosses indicate that they are not fit for assignments because assignments are already made. Step 2 — Subtract the column minimum from each column from the reduced matrix.

Here is the video about Maximization Assignment problem by using Hungarian method, in this video we have solve the problem by using simple step by step procedure which includes, Row...

Use the Hungarian method to determine the optimal assignments. Solution In the given problem there are 5 operators and 5 Lathe. The problem can be formulated as 5 × 5 assignment problem with cij = weekly output (in pieces) from jth Lathe by ith operator. Let xij = {1, if jth Lathe is assigned to ith Operator; 0, otherwise.

The Hungarian method is defined as a combinatorial optimization technique that solves the assignment problems in polynomial time and foreshadowed subsequent primal-dual approaches. What are the steps involved in Hungarian method? The following is a quick overview of the Hungarian method: Step 1: Subtract the row minima.

The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.It was developed and published in 1955 by Harold Kuhn, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry.

The Hungarian algorithm, aka Munkres assignment algorithm, utilizes the following theorem for polynomial runtime complexity ( worst case O (n3)) and guaranteed optimality: If a number is added to or subtracted from all of the entries of any one row or column of a cost matrix, then an optimal assignment for the resulting cost matrix is also an …

Q2 List any three variations of assignment problem. Q3. To use the Hungarian method, a profit-maximization assignment problem requires I). Convening all profits to opportunity losses 2). A dummy agent or tack. 3). Matrix expansion 4). Finding the maximum number of lines to cover all the irons in the reduced metric Q4.

This is the video about Restricted assignment problemIn this we have solved restricted assignment problem with simple step by step procedure. Please try to w...

Q2 List any three variations of assignment problem. Q3. To use the Hungarian method, a profit-maximization assignment problem requires I). Convening all profits to opportunity losses 2). A dummy agent or tack. 3). Matrix expansion 4). Finding the maximum number of lines to cover all the irons in the reduced metric Q4.

Now use the Hungarian Method to solve the above problem. The maximum profit through this assignment is 214. Example 6. XYZ Ltd. employs 100 workers of which 5 are highly skilled workers that can be assigned to 5 technologically advanced machines. The profit generated by these highly skilled workers while working on different machines are as ...

Hungarian Algorithm Application. First, we want to turn our matrix into a square matrix by adding a dummy column with entries equal to 518 (the highest entry in the matrix). Now we have a 4 by 4 ...

In (1955), Kuhn developed the Hungarian method of the assignment problem, the reason for naming it with this name is because its basis liesby the effort of the Hungarian mathematician Egervàryin ...