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# Unbalanced Assignment Won’t Seem to be a Problem Henceforth. Here’s What You Need to Know

05 September,2017

“Believe it can be done. When you believe something can be done, really believe, your mind will find the ways to do it. Believing a solution paves the way to solution.”

- David Joseph Schwartz

Last weekend I came across this beautiful quote which has so much positivity instilled in it. And today, to begin with a positive note I just thought of sharing this quote with you all. If there is a problem, a solution won’t be too hard to find. All you need is a bit of dedication, investing sufficient time on research and planning a constructive way to get the problem solved in a smart and rather easier way.

Anyway, today’s topic might seem to be a bit complex to some of you and that’s the reason I am here to suggest you ideas and information that can actually come into play. Talking of unbalanced assignment and the concept of this terminology, it is to be mentioned for your information and reference if the number of jobs is not equal to the number of operating executives, then the problem that tends to appear is referred as “unbalanced assignment”. In a pay-off matrix of assignment issues and potential problems if the total number of columns and rows are not equal then it is considered as unbalanced assignment problem.

## Solving Unbalanced Assignment Problem

Now, in order to solve and find effective solution to the unbalanced assignment problem, I would suggest readers to use the Hungarian method. It is also referred to as “combinatorial optimization algorithm” which can solve the unbalanced assignment problem in polynomial time. For example, there are three workers Allen, Robert and Mark. One of them has to do the housekeeping, another wash dishes and the third one cleans bathroom. However, each of them asks for different payment for the various tasks assigned. Now the problem is to look for the lowest cost method to assign the individual task. We can represent this problem in a matrix of the costs of workers executing the tasks.

For instance:

 Housekeeping Dish washing Bathroom cleaning Allen \$2 \$3 \$3 Robert \$3 \$2 \$3 Mark \$3 \$3 \$2

The minimum cost, which is \$6, can be derived by applying Hungarian method to the aforementioned table. Allen does the housekeeping, Robert wash dishes and Mark cleans bathroom.

Matrix interpretation is widely practiced across the globe in order to solve certain complex situations on managerial grounds, in case an unbalanced assignment problem emerges. While this is just an instance shared hypothetically with you all, I hope applying this method in real time will be useful and certainly effective.

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