# Difference Between Transportation Problem and Assignment Problem

*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**

- Transportation Problem vs Assignment Problem
- Transportation Problem
- Assignment Problem
- Key Differences and Similarities

**What is the Difference Between Transportation and Assignment Problems?**

Parameters |
Transportation Problem |
Assignment Problem |

Definition |
It deals with the optimal distribution of goods or resources from multiple sources (factories and warehouses) to multiple destinations (retail stores or customers). | It is a special type of transportation problem that assigns n origins (workers or instances) to n destinations (jobs or machines). |

Objective |
Minimize the total transportation cost | Minimize total cost or time associated with completing tasks |

Constraints |
1. Supply Constraints (The amount supplied from each source) 2. Demand Constraints (Total amount demanded at each destination). |
1. Each task is assigned to exactly one resource. 2. Each resource is assigned to exactly one task. |

Types |
Balanced and Unbalanced | Balanced and Unbalanced |

Method |
Northwest, Least Cost, Vogels Approximation, or Modi Method. Transportation methods can be used to solve assignment problems. | Hungarian MethodAssignment methods can’t be used to solve transportation problems. |

Real-World Application |
Supply Chain Optimization, Distribution Network Design, Traffic Flow Optimization | Job Scheduling Personnel, Assignment Facility Location, Machine Allocation |

**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**.

**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!!

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## 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.

**About the Author**

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio