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Transportation problem
Zymáková, Iva ; Lachout, Petr (advisor) ; Houda, Michal (referee)
As a transportation problem we usually denote one of the classical problems of the linear programming. This is just a very special case of more general problem, which is sometimes called Kantorovich transportation problem. I describe Kantorovich problem and its solution in some special cases in this work. Particularly, I describe the solution of the problem with quadratic cost and the solution of the problem with concave cost on the real line, in detail. At the end of the text, I show how the solution of the general problem could be approximated by the solutions of linear task. I solve the problem with some common distributions and with three typical cost functions { linear, strictly convex and strictly concave.
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Transportation problem
Zymáková, Iva ; Houda, Michal (referee) ; Lachout, Petr (advisor)
As a transportation problem we usually denote one of the classical problems of the linear programming. This is just a very special case of more general problem, which is sometimes called Kantorovich transportation problem. I describe Kantorovich problem and its solution in some special cases in this work. Particularly, I describe the solution of the problem with quadratic cost and the solution of the problem with concave cost on the real line, in detail. At the end of the text, I show how the solution of the general problem could be approximated by the solutions of linear task. I solve the problem with some common distributions and with three typical cost functions { linear, strictly convex and strictly concave.
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