Note on Assignment Algorithm with Easy Method of Drawing Lines to Cover All Zeros

Note on Assignment Algorithm with Easy Method of Drawing Lines to Cover All Zeros

Sarbjit Singh (Institute of Management Technology, Nagpur, India)
DOI: 10.4018/joris.2012070106
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Abstract

The Assignment algorithm is around 54 years old and a lot of work has been done on this algorithm. In this study various aspect of assignment algorithm has been considered. The endeavor of this note is to make solution of assignment problem so simple that even class tenth student can easily solve it. One of the most important aspects of assignment algorithm (Hungarian Algorithm) is to draw lines to cover all the zeros, in this study a new and easy method has been proposed to cover all the zeros, which helps to make this algorithm easy.
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Introduction

The assignment problem is a special type of linear programming problem where assignees are being assigned to perform task. It can also be defined as a special type of transportation problem in which each source should have capacity to fulfill the demand of any of the destinations. In other words, any operator should be able to perform any job regardless of his skills, although cost will be more if the job does not match with the worker’s skill. An example of assigning workers to jobs in a factory is given in Table 1.

Table 1.
Generalized format of assignment problem
JobWorker
1
2
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i
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N
1 2 j n


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