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The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, [9] but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems.
Generalized assignment problem; Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling; Knapsack problem, quadratic knapsack problem, and several variants [2] [3]: MP9
Pages in category "Linear programming" The following 58 pages are in this category, out of 58 total. ... Linear-fractional programming; LP-type problem; M.
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
This was an open problem until 2007, when an efficient algorithm based on dynamic programming was published. [ 14 ] The minimum number of knife changes problem (for the one-dimensional problem): this is concerned with sequencing and permuting the patterns so as to minimise the number of times the slitting knives have to be moved.
Basic solution (linear programming) — solution at vertex of feasible region; Fourier–Motzkin elimination; Hilbert basis (linear programming) — set of integer vectors in a convex cone which generate all integer vectors in the cone; LP-type problem; Linear inequality; Vertex enumeration problem — list all vertices of the feasible set
Integer linear programming: solve linear programming problems where some or all the unknowns are restricted to integer values Branch and cut; Cutting-plane method; Karmarkar's algorithm: The first reasonably efficient algorithm that solves the linear programming problem in polynomial time.