Learning Objectives – The Transportation Problems

Personalized homework help to elevate your understanding and boost your grades. Dive into a world where learning becomes easy, and complex topics transform into simple solutions.
  • 24/7 Assistance
  • Expert Tutors
  • Guaranteed Results


The transportation model is a linear program which is about the determination of the minimal cost of one commodity when being transferred from various places. Reaching up to the destinations also includes forwarding and clearing agents (C and F), facilities, and location. Planning and control. Thus the transportation model is a linear model though simplex algorithm can solve it. But the process becomes a lengthy one that will increase the chances of errors. Thus lies the significance of this for simple calculations.

Researches had been done since 1940 to solve the problem and complications of transportation. Because most of the time things get complex due to numerous locations and sources with their individual capacities and requirements. There was a common issue among every problem, and that was to minimise the transportation cost. Since then the significance of linear programming was determined. But before the discovery of linear programming simplex method was also applied but as stated above it made things more complicated and severe.


The transportation model can be defined as the determination of only one commodity that is being transported from one destination to various locations. Therefore for the determination must include the following set of information:

  1. The amount demanded in each destination
  2. The availability of the commodity in every source
  • The minimum transportation cost between the two places.

Therefore considering only one commodity transporting between the two sources, the minimum cost could only be determined if expressed in mathematical terms.

Like, let us consider:

m= number of sources (factory locations)

n= number of destinations

ai= number of commodity at the source (i = 1,2,3,….m)

bj= number of commodity at the destination ( j = 1,2,3,….n)

Cij= minimum transportation cost of the commodity between source location i and destination j

In the above, the determination of some units to be transported from one source i (ai) to destination j (bj) is clear enough to reduce the transportation cost.

Let us now consider,

Xij = the number of commodities being transported from source i to destination j.

Now we have to find Xij (non-negative value) which satisfies the following constraints:

i=1 ʃ n Xij= aifor i= 1, 2, 3…….m (availability at source i constraint)

j=1ʃ mXij= bjfor j = 1, 2, 3………..n (requirement at destination j constraint)

The total cost of transportation Z (the objective function)can be written as

Z = i=1 ʃnj=1 ʃ m XijXij

As in the above lines we see that Xijis a linear function hence it is a LPP.

Thus from the above things we conclude that the transportation cost of a particular route is proportional to the number of units transported. But things that must be kept in mind that are the source supply cannot exceed the availability of unit commodity at the source.


j=1 ʃmxij≤aj = 1, 2, 3 ….m

Similarly, requirement of the commodity at destination must be equal to or more than the demand, i.e.,

i=1 ʃ m  xij≤ bj= 1,2,3 …n

But it is seen that in reality, the supply might not be equal or more than the demand. In such situations, the transportation model must be balanced.


Links of Previous Main Topic:-

Links of Next Finance Topics:-

Download Our Solved Homework Solutions 📚

Curious about the level of quality we deliver? Navigate through our carefully curated selection of solved assignments, neatly organized by subject and level. This is a great way to get a feel for our service before you submit your own assignments.

Go ahead, download, review, and let us help you excel! 🚀

Accounting Homework

Corporate Accounting Sample

Biology Homework

Genetics Assignment Sample

Essay Writing Help

Business Plan Homework Sample

Statistics Homework

SPSS Assignment Sample

Score High with Our Experts

At MyHomeworkHelp, our experts are alumni from world-class universities and colleges. Each candidate undergoes a stringent check of their academic prowess and professional history before joining us as expert.

Hear It From Our Students

Real stories from students who’ve experienced our high-quality assistance. Discover how we’ve helped them excel!

Got Questions? We’ve Got Answers

How do I submit my homework?
Click on the "Get Help Now🚀" button at the top of our website. Fill in the required details about your assignment and our team will get back to you within 15 minutes with a free quote.
Is there a guarantee on the quality of work?
Absolutely! We ensure top-quality assistance. If you're unsatisfied with the results, we offer revisions and a money-back guarantee based on certain conditions.
How quickly can I expect my completed assignment?
Our experts work diligently to meet your deadlines. Depending on the complexity, we usually deliver assignments within the stipulated time mentioned in the quote.
Who are the experts assisting me?
Our team comprises professionals with academic expertise in various fields. Each expert is thoroughly vetted and has a track record of delivering excellence.
What if I need revisions?
Your satisfaction is our priority. If you need any revisions, contact us with the specific changes, and our experts will address them promptly.
How do you ensure the privacy of my information?
We take privacy seriously. All your data is encrypted and we follow strict confidentiality protocols. Your personal and assignment details will never be shared with third parties.