Difference Between Transportation Problem and Assignment Problem

# Difference Between Transportation Problem and Assignment Problem

Vikram Singh
Assistant Manager - Content
Updated on Jun 14, 2024 14:41 IST

The transportation problem in operational research aims to find the most economical way of transporting goods from multiple sources to multiple destinations. On the other hand, the assignment problem focuses on assigning tasks, jobs, or resources one-to-one. Both of these problems are usually solved through linear programming techniques. The transportation problem is commonly approached through simplex methods, and the assignment problem is addressed using specific algorithms like the Hungarian method. In this article, we will learn the difference between transportation problems and assignment problems with the help of examples.

Transportation Problems and Assignment Problems are types of Linear Programming Problems. Transportation Problem deals with the optimal distribution of goods or resources from multiple sources to multiple destinations. While Assignment Problem deals with allocating tasks, jobs, or resources one-to-one.

These LPP methods are used for cost minimization, resource allocation, supply chain management, workforce planning, facility location, time management, and decision-making support.

This article will briefly discuss the difference between transportation problems and assignment problems based on different parameters.

So, let’s explore the article.

Table of Content

## What is a Transportation Problem?

A transportation problem is a Linear Programming Problem that deals with identifying an optimal solution for transportation and allocating resources to various destinations and from one site to another while keeping the expenditure to a minimum.

In simple words, the main objective of the Transportation problem is to deliver (from the source to the destination) the resources at the minimum cost.

### What are the different types of transportation problems?

• Balanced: A transportation problem in which total supply equals total demand, i.e., Total Supply = Total Demand.
• Unbalanced: A transportation problem in which total supply doesn’t equal total demand, i.e., Total Supply != Total Demand.
Transportation Problem: Definition, Formulation, and Types
Transportation problems are used to find the minimum cost of transportation of goods from m source to n destination. In this article we will learn transportation problem, formulation, types and...read more
The Traveling Salesman Problem
The Traveling Salesman Problem (TSP) is a classic optimization problem in computer science and mathematics. It is a problem that has been studied for over a century and has numerous...read more
Linear Programming Problem (LPP)
Linear Programming problem or LPP is a method to find the optimum solution of set of parameters that are represented in linear form. In this article, we will discuss all...read more

### What are the different methods to solve the transportation problem?

The initial feasible solution can be found by any of the three methods:

• Northwest Corner Method (NWC)
• Least Corner Method (LCM)
• Vogel’s Approximation Method (VAM)

Once you find the initial feasible solution, use the Modified Distribution Method (MODI method) or the u-v method to find the optimal solution.

## What is an Assignment Problem?

An Assignment Problem is a special type of Transportation Problem in Operational Research that deals with assigning n origins (workers or instances) to n destinations (jobs or machines). The goal of the assignment problem is to determine the minimum cost of the assignment.

Each origin must be assigned to one and only one destination and each destination must be assigned to one and only one origin.

The solution to the assignment method can be found using the Hungarian Method.

Note: Transportation methods can be used to find the solutions to assignment problems, but assignment methods can’t be used to find the solutions to transportation problems.

## What are the Key Differences and Similarities Between Transportation and Assignment Problems?

• Transportation problems deal with the optimal distribution of goods or resources from multiple sources to multiple destinations, whereas assignment problems deal with allocating tasks, jobs, or resources one-to-one.
• Assignment Problem is a special type of transportation problem.
• Both transport and assignment problems are Linear Programming Problems.
• Both are minimization problems having an objective function and structural and non-negative constraints.
• The relationship between variables and constraints is linear.

## Conclusion

In this article, we have briefly discussed the transportation problem, the assignment problem, and the difference between both based on different parameters. Hope you will like the article.

Happy Learning!!

Difference Between Sequence and Series
Sequence is an ordered collection of elements that follows a specific pattern, whereas a series is a partial sum of sequences. In this article, we will learn the difference between...read more
Difference Between Distance and Displacement
Distance and Displacement are two important concepts in Physics as well as Mathematics. Distance is the total length of an object’s path; it is a scalar quantity. In contrast, Displacement...read more
Difference Between 2D and 3D Shapes
Looking to understand the difference between 2D and 3D shapes? This article offers a comprehensive breakdown of the fundamental differences between these two types of shapes. Whether you’re a beginner...read more
Understanding the Complexities of Zero: Rational or Irrational?
“Is zero a rational number? The great mathematical debate that divides experts. Discover the arguments for and against this mind-boggling puzzle and find out where you stand on the zero-rationality...read more
From Zero to One: Understanding the Concept of the Smallest Whole Number
If you’re reading this blog, you’re probably not just interested in the smallest whole number – you’re likely exploring the concept of whole numbers more broadly. In this article, we’ll...read more
Unlocking the Mystery of Irrational Numbers: A Guide for Beginners
An irrational number is a number that cannot be expressed as a ratio of two integers. They are infinite and non-repeating decimals that do not terminate, such as pi and...read more
Difference Between Positive and Negative Numbers
In mathematics, numbers are the basic building blocks of all mathematical concepts. In the previous articles, we have discussed rational, irrational, natural and whole numbers. All these numbers are either...read more
Difference Between Natural Numbers and Whole Numbers
When you start learning mathematics, you start with counting the numbers. In mathematics, there are different types of numbers, such as natural, whole, integers, rational, irrational, real, and complex numbers....read more
Difference Between Rational and Irrational Number
Numbers are an integral part of our lives that are used to quantify, measure, and calculate everything from the amount of time we spend on our smartphones to the distance...read more

## FAQs

What is a Transportation Problem?

A transportation problem is a Linear Programming Problem that deals with identifying an optimal solution for transportation and allocating resources to various destinations and from one site to another while keeping the expenditure to a minimum.

What is an Assignment Problem?

An Assignment Problem is a special type of Transportation Problem in Operational Research that deals with assigning n origins (workers or instances) to n destinations (jobs or machines). The goal of the assignment problem is to determine the minimum cost of the assignment.

What is the key differences and similarities between Transporation problem and assignment problem?

Transportation problem deals with the optimal distribution of goods or resources from multiple sources to multiple destinations, whereas assignment problem deals with allocating tasks, jobs, or resources one-to-one. Assignment Problem is a special type of transportation problem. Both transport and assignment problems are Linear Programming Problems. Both are minimization problems having an objective function and structural and non-negative constraints. The relationship between variable and constraints are linear.

How are transportation and assignment problems solved?

Both problems are typically solved using linear programming methods. The transportation problem often employs methods like the simplex method, while the assignment problem can use algorithms like the Hungarian method.

Can the assignment problem be considered a type of transportation problem?

Yes, the assignment problem is often seen as a special case of the transportation problem, where the objective is to optimally match elements of one set to another, such as workers to tasks.