The transportation problem (Monge-Kantorovich theory) is a mathematical problem of linear programming of a special kind of search for the optimal allocation of similar objects from the battery to the receivers while minimizing the cost of the move. For ease of understanding is seen as the problem of the optimal plan of cargo transportation from point of origin to point of consumption, with minimal transportation costs.
The transportation problem is the theory of nondeterministic polynomial time computational complexity and is in the class of NP. When the total volume of proposals (goods that are available at the points of departure) is not equal to total demand for goods (freight), requested by the points of consumption, transportation problem is called unbalanced (open).
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The transportation problem (classic) is a problem of an optimal plan a homogeneous product transportation from homogeneous points of availability to homogeneous points of consumption with homogeneous vehicles (a predetermined number) with static data and Linear approach (this is the basic conditions of the problem).
For the classical transportation problem, there are two types of problems: the cost criterion (achieving a minimum cost of freight) or distances and the time criterion (maximally reduce the time spent on transportation). Under the name of the transport problem, a wide range of problems with a single mathematical model is defined, these problems are related to linear programming problems and can be solved with the optimal method. However, a special method to solve transportation problem can greatly simplify its solution, because the transportation problem was designed to minimize the cost of transportation.
In 1781, a French mathematician Gaspard Monge was the first who formalized the problem. In turn, Soviet mathematician and economist Leonid Kantorovich has made the main progress in the field during the World War II. Therefore, sometimes the problem is called the Monge-Kantorovich transportation problem.
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