They are often encountered in supply chain, logistics, and distribution network optimization. 

In a balanced transportation problem, the total supply of goods equals the total demand. This balance simplifies the problem because each supply source can be fully utilized to meet the demand without any excess or shortage. 

Unbalanced transportation problems occur when the total supply does not equal the total demand. Solving unbalanced cases requires adjusting the problem to a balanced form or using heuristic methods to obtain an initial solution that can then be optimized. These methods help find solutions that minimize transportation costs while adhering to the constraints of supply and demand.