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  2. Cutting stock problem - Wikipedia

    en.wikipedia.org/wiki/Cutting_stock_problem

    Mathematical formulation and solution approaches [ edit ] The standard formulation for the cutting-stock problem (but not the only one) starts with a list of m orders, each requiring q j {\displaystyle q_{j}} pieces, where j = 1 , … , m {\displaystyle j=1,\ldots ,m} .

  3. LP-type problem - Wikipedia

    en.wikipedia.org/wiki/LP-type_problem

    In this formulation, the set S is the set of all vertices in both polytopes, and the function value f(A) is the negation of the smallest distance between the convex hulls of the two subsets A of vertices in the two polytopes. The combinatorial dimension of the problem is d + 1 if the two polytopes are disjoint, or d + 2 if they have a nonempty ...

  4. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

  5. Cutting-plane method - Wikipedia

    en.wikipedia.org/wiki/Cutting-plane_method

    Cutting planes were proposed by Ralph Gomory in the 1950s as a method for solving integer programming and mixed-integer programming problems. However, most experts, including Gomory himself, considered them to be impractical due to numerical instability, as well as ineffective because many rounds of cuts were needed to make progress towards the solution.

  6. Design optimization - Wikipedia

    en.wikipedia.org/wiki/Design_optimization

    Design optimization is an engineering design methodology using a mathematical formulation of a design problem to support selection of the optimal design among many alternatives. Design optimization involves the following stages: [ 1 ] [ 2 ]

  7. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    Suppose we have the linear program: Maximize c T x subject to Ax ≤ b, x ≥ 0.. We would like to construct an upper bound on the solution. So we create a linear combination of the constraints, with positive coefficients, such that the coefficients of x in the constraints are at least c T.

  8. Benders decomposition - Wikipedia

    en.wikipedia.org/wiki/Benders_decomposition

    Benders decomposition (or Benders' decomposition) is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure. This block structure often occurs in applications such as stochastic programming as the uncertainty is usually represented with scenarios.

  9. Algebraic modeling language - Wikipedia

    en.wikipedia.org/wiki/Algebraic_modeling_language

    The algebraic formulation of a model does not contain any hints how to process it. An AML does not solve those problems directly; instead, it calls appropriate external algorithms to obtain a solution. These algorithms are called solvers and can handle certain kind of mathematical problems like: linear problems; integer problems