difference between the transportation and assignment problems is that

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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?

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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?

• Assignment Problem is a special type of transportation problem.
• Both are minimization problems having an objective function and structural and non-negative constraints.
• The relationship between variables and constraints is linear.

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!!

Related Reads

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.

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Difference between transportation and assignment problems?

• 3 mins read

lets understand the Difference between transportation and assignment problems?

Transportation problems and assignment problems are two types of linear programming problems that arise in different applications.

The main difference between transportation and assignment problems is in the nature of the decision variables and the constraints.

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Additional Different between Transportation and Assignment Problems are as follows : 

Decision Variables:

In a transportation problem, the decision variables represent the flow of goods from sources to destinations. Each variable represents the quantity of goods transported from a source to a destination.

In contrast, in an assignment problem, the decision variables represent the assignment of agents to tasks. Each variable represents whether an agent is assigned to a particular task or not.

Constraints:

In a transportation problem, the constraints ensure that the supply from each source matches the demand at each destination and that the total flow of goods does not exceed the capacity of each source and destination.

In contrast, in an assignment problem, the constraints ensure that each task is assigned to exactly one agent and that each agent is assigned to at most one task.

Objective function:

The objective function in a transportation problem typically involves minimizing the total cost of transportation or maximizing the total profit of transportation.

In an assignment problem, the objective function typically involves minimizing the total cost or maximizing the total benefit of assigning agents to tasks.

In summary,

The transportation problem is concerned with finding the optimal way to transport goods from sources to destinations,

while the assignment problem is concerned with finding the optimal way to assign agents to tasks.

Both problems are important in operations research and have numerous practical applications.

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Operations Research/Transportation and Assignment Problem

The Transportation and Assignment problems deal with assigning sources and jobs to destinations and machines. We will discuss the transportation problem first.

Suppose a company has m factories where it manufactures its product and n outlets from where the product is sold. Transporting the product from a factory to an outlet costs some money which depends on several factors and varies for each choice of factory and outlet. The total amount of the product a particular factory makes is fixed and so is the total amount a particular outlet can store. The problem is to decide how much of the product should be supplied from each factory to each outlet so that the total cost is minimum.

Let us consider an example.

Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D and E. The capacities of the three plants during the next quarter are 1000, 1500 and 1200 cars. The quarterly demands of the two distribution centers are 2300 and 1400 cars. The transportation costs (which depend on the mileage, transport company etc) between the plants and the distribution centers is as follows:

Which plant should supply how many cars to which outlet so that the total cost is minimum?

The problem can be formulated as a LP model:

The whole model is:

subject to,

The problem can now be solved using the simplex method. A convenient procedure is discussed in the next section.

• Book:Operations Research