## Who Discovered transportation problem?

The problem was formalized by the French mathematician Gaspard Monge in 1781. In the 1920s A.N. Tolstoi was one of the first to study the transportation problem mathematically.

**Why is optimal transport important?**

Optimal transport gives a framework for comparing measures µ and ν in a Lagrangian framework. Essentially one pays a cost for transporting one measure to another. To illustrate this consider the first measure µ as a pile of sand and the second measure ν as a hole we wish to fill up.

**What is optimal transport in machine learning?**

Optimal transport (OT) lifts ideas from classical geometry to probability distributions, providing a means for geometric computation on uncertain data.

### How is Modi method calculated?

The work of the loop is over and the new solution looks as shown below. Check the total number of allocated cells is equal to (m + n – 1). Again find u values and v values using the formula ui + vj = Cij where Cij is the cost value only for allocated cell. Assign u1 = 0 then we get v2 = 1.

**What are the types of transportation problem?**

There are two different types of transportation problems based on the initial given information: Balanced Transportation Problems: cases where the total supply is equal to the total demand. Unbalanced Transportation Problems: cases where the total supply is not equal to the total demand.

**What is U and V in Modi method?**

The modified distribution method, is also known as MODI method or (u – v) method provides a minimum cost solution to the transportation problems. MODI method is an improvement over stepping stone method.

## Why Modi method is applied?

MODI METHOD The MODI (modified distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over other methods for solving transportation problems.