Linear Programming

• Published in: Optimization in Engineering Sciences pp. 1 - 22
• Main Authors: Borne, Pierre, Filip, Florin Gheorghe, Stefanoiu, Dan, Popescu, Dumitru
• Format: Book Chapter
• Language: English
• Published: United States John Wiley & Sons, Incorporated 2012; John Wiley & Sons, Inc
• Subjects: Automatic control engineering; Lagrange method; linear programming; optimization; resource allocation; simplex algorithm
• ISBN: 9781848214323; 1848214324
• DOI: 10.1002/9781118577899.ch1

The purpose of linear programming is to optimize a linear function J (x) = f T x of a set of variables grouped in vector x∈ R n in the presence of linear constraints. A procedure, which enables us to solve the problem of finding a point x∈ R n of the polyhedron that minimizes or maximizes J function, is understand by using linear programming. The chapter describes the Lagrange method and the simplex algorithm. The algorithm allows finding the minimum in a finite number of iterations and, moreover, by only using elementary computations. The approach is based on the idea search for the minimum among the vertices of the polyhedron defined by the constraints. Finally, the chapter talks about the application of linear programming to the optimization of resource allocation for achieving the objectives of a company subjected to management restrictions and environmental constraints.