The transportation problem on the transportation industry is a very interesting concept and the linear programming applications are vital in deciding the optimum transportation schedule by  minimizing the cost that is applied for the transportation of the goods.

While researching for few hours, i found loads of knowledge for this domain and went through most of the methods/models used in achieving the above.

In reality the transportation problem is applied for many cases such as,

• determine low cost location
• Optimum route to deliver the goods
• Find minimum cost production schedule
• Optimizing various Distribution systems

The main two types of the problem is known as Balanced and unbalanced transportation problems. (More on the unbalanced problems later, as it is a commonly used in reality; however, only a dummy location or a demand is added to the equation, that is all :P)

Simply put the balanced problem always have the supply equals the demand and the unbalanced the is not.

When divided the problem into to two phases;

The first is to find an initial feasible solution and the second one is to optimize it.

To find out the initial feasible solution the following methods can be used;

• North west corner rule
• least cost method
• VAM – Vogle approximity method
• Row/column minima method

For optimisation;

• Stepping stone method
• Modified distribution method (MODI)

You can find a lot of domain knowledge on this on channels like below:

Operations and transportation problems