Balanced and Unbalanced Assignment Problem – Importance And Difference

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In the world of trade, many business organizations aim for the optimal use of their limited resources among different activities. They can only achieve this by using the assignment problem method. It is a special case of transportation problems in the trade business, where the primary objective is to assign an equal number of origins to an equal number of destinations. This method involves the assignment of people to different projects, jobs to machines, and teachers to classes, etc.

The assignment problem is an effective way to minimize the assignment costs and utilize the limited resources properly. Many business researchers are unaware of this method, and it is not difficult to guess that you are one of them. Well, there is no need to worry. You have just come to the right place. In today’s article, we will discuss this method and its types. So, let’s get started with the topic straight away.

What does it mean by an assignment problem?

An assignment problem is a special case of transportation problems often solved in the field of project management. The main objective behind this method is to assign an equal number of resources to an equal number of jobs or activities. Why so? This is done to keep the cost low and maximize profits. The problem of assignment arises in businesses when there are various sources with different efficiencies for performing different tasks or jobs.


Suppose a manager has four people. What does it mean? It means he has four resources available to do a job. Let’s say he also has four jobs to do. Which job should he give to Which person? This is what the assignment problem is. The manager has to decide who can do which job so that the cost is very low and the person who has been assigned the job does it well. Hence, this is how the problem of assignment works.

Types of assignment problem

After reading the information above, you now have got a good idea of the assignment problem. Now, it is time to look at its types. In general, there are two types of problem assignments, i.e., balanced and unbalanced. A brief description of each type is as follows:

Balanced assignment problem

It is the first type of problem assignment. It is a problem assignment where the number of facilities or resources to do the work required is equal to the number of jobs. For example, if there are 5 jobs to do, then there are also 5 people or resources to do the job.

Unbalanced assignment problem

The second type of problem assignment is known as the unbalanced assignment problem. It is the opposite of balanced problems. What does it mean? It means that the number of resources is not equal to the number of jobs or vice versa. For example, there are 5 jobs to do, and you only have 4 people under your control. It means you are dealing with an unbalanced assignment problem.

Application areas of assignment problem

Assignment problems are not only limited to trade businesses. There are many ways in which they are used and help their users in assigning different people to different jobs or tasks. Some of its main application areas are as follows:

  • It is used in assigning machines to different orders in the factory
  • It can be applied in marketing businesses where the managers assign different salesmen to different areas.
  • Also used in assigning contracts to different bidders
  • It is also used in education. For example, assign teachers to different classes
  • In assigning different accountants to the account holders of a particular area

Hence, these are different applications of the assignment problem in another field. However, if you want to know about its applications in a particular field, do not hesitate to get help from assignment writing services.

Different methods of solving assignment problem

Until now, you have got an idea of the assignment problem, its types, and its applications in different fields. However, do you know how to assign different people to different jobs? Simply put, do you know the methods of solving the problem of assignments? NO! There are 4 methods of doing this. They are as follows:

  • Enumeration method. The list of all the people and jobs is prepared first in this method. After that, the assignment is made based on time, distance, and capabilities.
  • Simplex method. In this method, first, the identification of the linear program takes place. After that, using slack variables, you solve the program.
  • Transportation method. Not used very often due to its complexities, but transportation methods can also be used to assign different people to various jobs.
  • Hungarian method. It is an algorithm-based method for solving assignment problems.


To sum up, an assignment problem is a particular type of linear programming. The main objective of the problem of assignment is to minimize the cost and maximize the profits. Balanced and unbalanced assignment problems are two types of it. So, learn about them by reading the information provided above.

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