compare assignment problem with transportation problem

Difference between transportation and assignment problems?

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.

If you’re unable to see the whole table kindly convert the mobile view to the desktop view

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.

Checkout  Home page  for more informative content and Follow us on  facebook  for more 

Related Posts

3d printing design revolution or intellectual property nightmare

Introduction to 3D printing In this article, we will closely look at the intellectual property rights for 3D printing  and […]

HVAC Engineer Salary, Roles, Responsibilities, Qualification

Who is an HVAC Engineer? An HVAC engineer is one who manages heating, ventilation, and air conditioning Plan designed and […]

Copyright © 2003 by Robert Fourer, David M. Gay and Brian W. Kernighan

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

Navigation menu

Balanced and Unbalanced Transportation Problems

The two categories of transportation problems are balanced and unbalanced transportation problems . As we all know, a transportation problem is a type of Linear Programming Problem (LPP) in which items are carried from a set of sources to a set of destinations based on the supply and demand of the sources and destinations, with the goal of minimizing the total transportation cost. It is also known as the Hitchcock problem.

Introduction to Balanced and Unbalanced Transportation Problems

Balanced transportation problem.

The problem is considered to be a balanced transportation problem when both supplies and demands are equal.

Unbalanced Transportation Problem

Unbalanced transportation problem is defined as a situation in which supply and demand are not equal. A dummy row or a dummy column is added to this type of problem, depending on the necessity, to make it a balanced problem. The problem can then be addressed in the same way as the balanced problem.

Methods of Solving Transportation Problems

There are three ways for determining the initial basic feasible solution. They are

1. NorthWest Corner Cell Method.

2. Vogel’s Approximation Method (VAM).

3. Least Call Cell Method.

The following is the basic framework of the balanced transportation problem:

The destinations D1, D2, D3, and D4 in the above table are where the products/goods will be transported from various sources O1, O2, O3, and O4. The supply from the source Oi is represented by S i . The demand for the destination Dj is d j . If a product is delivered from source Si to destination Dj, then the cost is called C ij .

Let us now explore the process of solving the balanced transportation problem using one of the ways known as the NorthWest Corner Method in this article.

Solving Balanced Transportation problem by Northwest Corner Method

Consider this scenario:

With three sources (O1, O2, and O3) and four destinations (D1, D2, D3, and D4), what is the best way to solve this problem? The supply for the sources O1, O2, and O3 are 300, 400, and 500, respectively. Demands for the destination D1, D2, D3, and D4 are 250, 350, 400, and 200, respectively.

The starting point for the North West Corner technique is (O1, D1), which is the table’s northwest corner. The cost of transportation is calculated for each value in the cell. As indicated in the diagram, compare the demand for column D1 with the supply from source O1 and assign a minimum of two to the cell (O1, D1).

Column D1’s demand has been met, hence the entire column will be canceled. The supply from the source O1 is still 300 – 250 = 50.

Analyze the northwest corner, i.e. (O1, D2), of the remaining table, excluding column D1, and assign the lowest among the supply for the appropriate column and rows. Because the supply from O1 is 50 and the demand for D2 is 350, allocate 50 to the cell (O1, D2).

Now, row O1 is canceled because the supply from row O1 has been completed. Hence, the demand for Column D2 has become 350 – 50 = 50.

The northwest corner cell in the remaining table is (O2, D2). The shortest supply from source O2 (400) and the demand for column D2 (300) is 300, thus putting 300 in the cell (O2, D2). Because the demand for column D2 has been met, the column can be deleted, and the remaining supply from source O2 is 400 – 300 = 100.

Again, find the northwest corner of the table, i.e. (O2, D3), and compare the O2 supply (i.e. 100) to the D2 demand (i.e. 400) and assign the smaller (i.e. 100) to the cell (O2, D2). Row O2 has been canceled because the supply from O2 has been completed. Column D3 has a leftover demand of 400 – 100 = 300.

Continuing in the same manner, the final cell values will be:

It should be observed that the demand for the relevant columns and rows is equal in the last remaining cell, which was cell (O3, D4). In this situation, the supply from O3 was 200, and the demand for D4 was 200, therefore this cell was assigned to it. Nothing was left for any row or column at the end.

To achieve the basic solution, multiply the allotted value by the respective cell value (i.e. the cost) and add them all together.

I.e., (250 × 3) + (50 × 1) + (300 × 6) + (100 × 5) + (300 × 3) + (200 × 2) = 4400.

Solving Unbalanced Transportation Problem

An unbalanced transportation problem is provided below. Because the sum of all the supplies, O1, O2, O3, and O4, does not equal the sum of all the demands, D1, D2, D3, D4, and D5, the situation is unbalanced.

The idea of a dummy row or dummy column will be applied in this type of scenario. Because the supply is more than the demand in this situation, a fake demand column will be inserted, with a demand of (total supply – total demand), i.e. 117 – 95 = 22, as seen in the image below. A fake supply row would have been introduced if demand was greater than supply.

Now this problem has been changed to a balanced transportation problem, and it can be addressed using any of the ways listed below to solve a balanced transportation problem, such as the northwest corner method mentioned earlier.

Frequently Asked Questions on Balanced and Unbalanced Transportation Problems

What is meant by balanced and unbalanced transportation problems.

The problem is referred to as a balanced transportation problem when both supplies and demands are equal. Unbalanced transportation is defined as a situation where supply and demand are not equal.

What is called a transportation problem?

The transportation problem is a type of Linear Programming Problem in which commodities are carried from a set of sources to a set of destinations while taking into account the supply and demand of the sources and destinations, respectively, in order to reduce the total cost of transportation.

What are the different methods to solve transportation problems?

The following are three approaches to solve the transportation issue:

• NorthWest Corner Cell Method.
• Least Call Cell Method.
• Vogel’s Approximation Method (VAM).

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Implementation and Comparison of Four Algorithms on Transportation Problem

• Conference paper
• First Online: 17 June 2022
• Cite this conference paper

• Eghbal Hosseini 22 ,
• Line Reinhardt 22 ,
• Kayhan Zrar Ghafoor 23 &
• Danda B. Rawat 24  

Part of the book series: Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering ((LNICST,volume 442))

Included in the following conference series:

• International Summit Smart City 360°

1032 Accesses

The transportation problem is a very applicable and relevant logistic problem. In this paper, to test meta-heuristics on the transportation problem and also improve initial feasible solutions in few number of iterations, four recent and effective meta-heuristic algorithms are used to solve transportation problems. Laying Chicken Algorithm (LCA), Volcano Eruption Algorithm (VEA), COVID-19 Optimizer Algorithm (CVA), and Multiverse Algorithm (MVA) are implemented to solve different sizes of the transportation problem. Computational results show that CVA is the most efficient optimizer for large size cases and LCA is the best algorithm for the others. Finally, convergence of algorithms will be discussed and rate of convergence will be compared. The advantage of these heuristics are that they can be easily adapted to more challenging versions of the transportation problem which are not solveable by the Simplex method.

• Transportation problems
• Meta-heuristic algorithm

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Aizemberg, L., Kramer, H.H., Pessoa, A.A., Uchoa, E.: Formulations for a problem of petroleum transportation. Eur. J. Oper. Res. 237 (1), 82–90 (2014). https://doi.org/10.1016/j.ejor.2014.01.036

Article   MathSciNet   MATH   Google Scholar  

Amaliah, B., Fatichah, C., Suryani, E.: A new heuristic method of finding the initial basic feasible solution to solve the transportation problem. J. King Saud Univ. Comput. Inf. Sci. 22 (2020)

Google Scholar  

Cosma, O., Pop, P.C., Dănciulescu, D.: A novel matheuristic approach for a two-stage transportation problem with fixed costs associated to the routes. Comput. Oper. Res. 118 , 104906 (2020). https://doi.org/10.1016/j.cor.2020.104906

Hosseini, E.: Laying chicken algorithm: a new meta-heuristic approach to solve continuous programming problems. J. Appl. Comput. Math. 6 (1), 1–8 (2017)

Article   Google Scholar  

Hosseini, E., Sadiq, A.S., Ghafoor, K.Z., Rawat, D.B., Saif, M., Yang, X.: Volcano eruption algorithm for solving optimization problems. Neural Comput. Appl. 33 (7), 2321–37 (2021)

Hosseini, E., Ghafoor, K.Z., Sadiq, A.S., Guizani, M., Emrouznejad, A.: Covid-19 optimizer algorithm, modeling and controlling of coronavirus distribution process. IEEE J. Biomed. Health Inf. 24 (10), 2765–2775 (2020)

Hosseini, E., Ghafoor, K.Z., Emrouznejad, A., Sadiq, A.S., Rawat, D.B.: Novel metaheuristic based on multiverse theory for optimization problems in emerging systems. Appl. Intell. 11 , 1–8 (2020)

Juman, Z.A., Hoque, M.A.: An efficient heuristic to obtain a better initial feasible solution to the transportation problem. Appl. Soft Comput. 1 (34), 813–26 (2015)

Juman, Z.A.M.S., Hoque, M.A., Buhari, M.I.: A sensitivity analysis and an implementation of the Wellknown Vogel’s approximation method for solving unbalanced transportation problem. Malays. J. Sci. 32 (1), 66–72 (2013)

Ramadan, S.Z., Ramadan, I.Z.: Hybrid two-stage algorithm for solving transportation problem. Mod. Appl. Sci. 6 (4), 12 (2012)

Soriano, A., Vidal, T., Gansterer, M., Doerner, K.: The vehicle routing problem with arrival time diversification on a multigraph. Eur. J. Oper. Res. 286 (2), 564–575 (2020)

Article   MathSciNet   Google Scholar  

Download references

Author information

Authors and affiliations.

Department of People and Technology, Roskilde University, Roskilde, Denmark

Eghbal Hosseini & Line Reinhardt

Department of Software Engineering, Salahaddin University-Erbil, Erbil, 44002, Kurdistan Region, Iraq

Kayhan Zrar Ghafoor

Department of Electrical Engineering and Computer Science, Howard University, Washington, DC, USA

Danda B. Rawat

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Kayhan Zrar Ghafoor .

Editor information

Editors and affiliations.

Instituto Politécnico de Viana do Castelo, Viana do Castelo, Portugal

Auckland University of Technology, Auckland, New Zealand

Sérgio Ivan Lopes

SRM Institute of Science and Technology, Chennai, India

Nishu Gupta

Howard University, Washington, DC, USA

Stoke-on-Trent, Birmingham, UK

Politecnico di Milano, Milan, Italy

Hamid Reza Karimi 

Rights and permissions

Reprints and permissions

Copyright information

© 2022 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper.

Hosseini, E., Reinhardt, L., Ghafoor, K.Z., Rawat, D.B. (2022). Implementation and Comparison of Four Algorithms on Transportation Problem. In: Paiva, S., et al. Science and Technologies for Smart Cities. SmartCity 360 2021. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-031-06371-8_28

Download citation

DOI : https://doi.org/10.1007/978-3-031-06371-8_28

Published : 17 June 2022

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-06370-1

Online ISBN : 978-3-031-06371-8

eBook Packages : Computer Science Computer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research