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  2. Nearest neighbour algorithm - Wikipedia

    en.wikipedia.org/wiki/Nearest_neighbour_algorithm

    In the worst case, the algorithm results in a tour that is much longer than the optimal tour. To be precise, for every constant r there is an instance of the traveling salesman problem such that the length of the tour computed by the nearest neighbour algorithm is greater than r times the length of the optimal tour. Moreover, for each number of ...

  3. Held–Karp algorithm - Wikipedia

    en.wikipedia.org/wiki/Held–Karp_algorithm

    The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman [1] and by Held and Karp [2] to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to ...

  4. Vehicle routing problem - Wikipedia

    en.wikipedia.org/wiki/Vehicle_routing_problem

    There are many methods to solve vehicle routing problems manually. For example, optimum routing is a big efficiency issue for forklifts in large warehouses. Some of the manual methods to decide upon the most efficient route are: Largest gap, S-shape, Aisle-by-aisle, Combined and Combined +.

  5. Travelling salesman problem - Wikipedia

    en.wikipedia.org/wiki/Travelling_salesman_problem

    Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle in a weighted graph with the minimal weight of the weightiest edge. A real-world example is avoiding narrow streets with big buses. [15] The problem is of considerable practical importance, apart from evident transportation and logistics areas.

  6. Route assignment - Wikipedia

    en.wikipedia.org/wiki/Route_assignment

    Because problems are large, an algorithm is needed to solve the assignment problem, and the Frank-Wolfe algorithm (with various modern modifications since first published) is used. Start with an all or nothing assignment, and then follow the rule developed by Frank-Wolfe to iterate toward the minimum value of the objective function.

  7. 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.

  8. 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.

  9. Network simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Network_simplex_algorithm

    For a long time, the existence of a provably efficient network simplex algorithm was one of the major open problems in complexity theory, even though efficient-in-practice versions were available. In 1995 Orlin provided the first polynomial algorithm with runtime of O ( V 2 E log ⁡ ( V C ) ) {\displaystyle O(V^{2}E\log(VC))} where C ...