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  2. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    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.

  3. General algebraic modeling system - Wikipedia

    en.wikipedia.org/wiki/General_Algebraic_Modeling...

    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 ...

  4. Transportation theory (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Transportation_theory...

    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.

  5. Multidimensional assignment problem - Wikipedia

    en.wikipedia.org/wiki/Multidimensional...

    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 ...

  6. Combinatorial optimization - Wikipedia

    en.wikipedia.org/wiki/Combinatorial_optimization

    A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.

  7. Computational complexity theory - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    A function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem—that is, the output is not just yes or no. Notable examples include the traveling salesman problem and the integer factorization problem.

  8. Minimum-cost flow problem - Wikipedia

    en.wikipedia.org/wiki/Minimum-cost_flow_problem

    The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network.A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated.

  9. Quadratic assignment problem - Wikipedia

    en.wikipedia.org/wiki/Quadratic_assignment_problem

    The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems first introduced by Koopmans and Beckmann. [1] The problem models the following real-life problem: