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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.
Transportation costs are independent of the shipped amount; The transshipment problem is a unique Linear Programming Problem (LLP) in that it considers the assumption that all sources and sinks can both receive and distribute shipments at the same time (function in both directions) [1]
There is a close connection between linear programs, eigenequations, John von Neumann's general equilibrium model, and structural equilibrium models (see dual linear program for details). [ 1 ] [ 2 ] [ 3 ] Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing.
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
A transportation problem from George Dantzig is used to provide a sample GAMS model. [6] This model is part of the model library which contains many more complete GAMS models. This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories. Dantzig, G B, Chapter 3.3. In Linear Programming and ...
Frank Lauren Hitchcock (March 6, 1875 – May 31, 1957) was an American mathematician and physicist known for his formulation of the transportation problem in 1941. Academic life [ edit ]
Minimize the global transportation cost based on the global distance travelled as well as the fixed costs associated with the used vehicles and drivers; Minimize the number of vehicles needed to serve all customers; Least variation in travel time and vehicle load; Minimize penalties for low quality service; Maximize a collected profit/score.
In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a vertex of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS.