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In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781. [1] In the 1920s A.N. Tolstoi was one of the first to study the transportation problem mathematically.
Transshipment problems form a subgroup of transportation problems, where transshipment is allowed. In transshipment, transportation may or must go through intermediate nodes, possibly changing modes of transport. The Transshipment problem has its origins in medieval times [dubious – discuss] when trading started to become a mass phenomenon ...
This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem.
Download as PDF; Printable version; In other projects ... move to sidebar hide. Transportation theory may refer to: Transportation theory (mathematics) ...
The Weber problem is a generalization of the Fermat problem since it involves both equal and unequal attractive forces (see below), while the Fermat problem only deals with equal attractive forces. It was first formulated, and solved geometrically in the triangle case, by Thomas Simpson in 1750. [4] It was later popularized by Alfred Weber in ...
The orthogonal Procrustes problem [1] is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A {\displaystyle A} and B {\displaystyle B} and asked to find an orthogonal matrix Ω {\displaystyle \Omega } which most closely maps A {\displaystyle A} to B {\displaystyle B} .
The 1-center problem can be restated as finding a star in a weighted complete graph that minimizes the maximum weight of the selected edges. The corresponding problem of minimizing the maximum weight of a path between two selected vertices, in place of a star, is called the minimax path problem .
This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows: An instance of the problem has a number of agents (i.e., cardinality parameter) and a number of job characteristics (i.e., dimensionality parameter) such as task, machine, time interval, etc. For example, an ...