Abstract: The company's problems can usually be modeled as a linear program consisting of a certain number of resources. If a linear programming problem in standard form has an optimal solution, then a basic admissible solution that is optimal exists. The simplex algorithm is an algorithm for solving linear optimization problems. This chapter presents two techniques for finding a basic realizable solution to initialize the simplex algorithm: the first is the Big M method, and the second is the Phase I method. The simplex algorithm moves along a sequence of vertices of the polyhedron and converges rapidly on average. Duality is an essential notion in linear programming. In mathematical programming, good performance essentially depends on the program's ability to construct useful bounds. Lagrangian duality provides a particularly fruitful framework for relaxation. Lagrangian relaxation often produces a very good relaxation value, far better than continuous relaxation.
Publication Year: 2021
Publication Date: 2021-04-15
Language: en
Type: other
Indexed In: ['crossref']
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