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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.
Specific names for the linear scheduling method have been adopted, such as: [1] Location-based scheduling (the preferred term in the book) Harmonograms; Line-of-balance; Flowline or flow line; Repetitive scheduling method; Vertical production method; Time-location matrix model; Time space scheduling method; Disturbance scheduling
This term is misleading because a single efficient point can be already obtained by solving one linear program, such as the linear program with the same feasible set and the objective function being the sum of the objectives of MOLP. [4] More recent references consider outcome set based solution concepts [5] and corresponding algorithms.
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.
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Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework.
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. This linear combination gives us an upper bound on the ...
In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm.The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints.