# to make an unbalanced assignment problem balanced, what are added with all entries as zeroes?

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## [Solved] To make an unbalanced assignment problem balanced, what are added with all entries as zeroes?

Q.

## To make an unbalanced assignment problem balanced, what are added with all entries as zeroes?

A. Dummy rows B. Dummy columns C. Both A and B D. Dummy entries

Answer» C. Both A and B

View all MCQs in: Operations Research

## Discussion

### Related Multiple Choice Questions

To make an unbalanced assignment problem balanced, what are added with all entries as zeroes?

Before starting to solve the problem, it should be balanced. If not then make it balanced by ‐‐‐‐‐ ‐‐‐‐‐‐ column incase demand is less than supply or by adding ‐‐‐‐‐‐‐‐‐‐‐‐ raw incase supply is less than the demand

Before starting to solve the problem, it should be balanced. If not then make it balanced by ‐‐‐‐‐ ‐‐‐‐‐‐ column incase demand is less than supply or by adding ‐‐‐‐‐‐‐‐‐‐‐‐ raw incase supply is less than the demand

If the number of rows and columns in an assignment problem are not equal than it is called problem.

When a maximization assignment problem is converted in minimization problem, the resulting matrix is called matrix.

When a particular assignment in the given problem is not possible or restricted as a condition, it is called a problem.

______method is used in Assignment Problem

The method used for solving an assignment problem is called method.

Assignment problem helps to find a maximum weight identical in nature in a weighted ‐‐‐‐‐‐‐‐‐‐‐‐

As for maximization in assignment problem, the objective is to maximize the ‐‐‐‐‐‐‐‐‐‐‐

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## UNBALANCED ASSIGNMENT PROBLEM in Quantitative Techniques for management Tutorial 19 March 2023

UNBALANCED ASSIGNMENT PROBLEM in Quantitative Techniques for management - UNBALANCED ASSIGNMENT PROBLEM in Quantitative Techniques for management courses with reference manuals and examples pdf.

## UNBALANCED ASSIGNMENT PROBLEM - QUANTITATIVE TECHNIQUES FOR MANAGEMENT

« Previous Topics

Hungarian Method For Solving Assignment Problem

Types Of Assignment Problem

Use Of Linear Programming To Solve Assignment Problem

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Restricted Assignment Problem

Multiple And Unique Solutions

Maximization Problem

Whenever the cost matrix of an assignment problem is not a square matrix, that is, whenever the number of sources is not equal to the number of destinations, the assignment problem is called an unbalanced assignment problem. In such problems, dummy rows (or columns) are added in the matrix so as to complete it to form a square matrix. The dummy rows or columns will contain all costs elements as zeroes. The Hungarian method may be used to solve the problem.

**Example :**A company has five machines that are used for four jobs. Each job can be assigned to one and only one machine. The cost of each job on each machine is given in the following Table.

## Unbalanced Maximization Assignment problem example

**Assignment Problem**

**Solution:**Convert the 4 × 5 matrix into a square matrix by adding a dummy row D5.

**Dummy Row D5 Added**

**Row-wise Reduction of the Matrix**

Column-wise reduction is not necessary since all columns contain a single zero. Now, draw minimum number of lines to cover all the zeros, as shown in Table.

**All Zeros in the Matrix Covered**

Number of lines drawn ≠ Order of matrix. Hence not optimal.

Select the least uncovered element, i.e., 1, subtract it from other uncovered elements, add to the elements at intersection of lines and leave the elements that are covered with single line unchanged as shown in Table.

**Subtracted or Added to Elements**

Number of lines drawn ≠ Order of matrix. Hence not optimal.

**Again Added or Subtracted 1 from Elements**

Number of lines drawn = Order of matrix. Hence optimality is reached. Now assign the jobs to machines, as shown in Table.

**Assigning Jobs to Machines**

**Example :**In a plant layout, four different machines M1, M2, M3 and M4 are to be erected in a machine shop. There are five vacant areas A, B, C, D and E. Because of limited space, Machine M2 cannot be erected at area C and Machine M4 cannot be erected at area A. The cost of erection of machines is given in the Table.

**Assignment Problem**

Find the optimal assignment plan.

**Solution:**As the given matrix is not balanced, add a dummy row D5 with zero cost values. Assign a high cost H for (M2, C) and (M4, A). While selecting the lowest cost element neglect the high cost assigned H, as shown in Table below.

**Dummy Row D5 Added**

- Row-wise reduction of the matrix is shown in Table.

**Matrix Reduced Row-wise**

**Note:**Column-wise reduction is not necessary, as each column has at least one single zero. Now, draw minimum number of lines to cover all the zeros, see Table.

**Lines Drawn to Cover all Zeros**

Number of lines drawn ≠ Order of matrix. Hence not Optimal. Select the smallest uncovered element, in this case 1. Subtract 1 from all other uncovered element and add 1 with the elements at the intersection. The element covered by single line remains unchanged. These changes are shown in Table. Now try to draw minimum number of lines to cover all the zeros.

**Added or Subtracted 1 from Elements**

Now number of lines drawn = Order of matrix, hence optimality is reached. Optimal assignment of machines to areas are shown in Table.

**Optimal Assignment**

## Solved I POLLS JUVCHIVCI "To make an unbalanced assignment

Answer to Solved I POLLS JUVCHIVCI "To make an unbalanced assignment

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