Originally developed by Kantorovich to optimize plywood production, FTP, name this problem, efficiently solved using the simplex method, which calls for the optimization of a linear objective function given linear constraints.
One early method for this procedure was Fourier-Motzkin elimination, and the Hirsch conjecture provides an upper bound on the runtime of one method. Another method involves introducing slack variables and then manipulating the tableau through repeated pivoting. Karmarkar's algorithm and other interior point methods are among the fastest solutions, and the ellipsoid algorithm was the first polynomial time algorithm for it. The cutting-plane method can be used to solve the integer variety, which is NP-hard but which can sometimes be approximated by examining the dual. Originally developed by Kantorovich to optimize plywood production, FTP, name this problem, efficiently solved using the simplex method, which calls for the optimization of a linear objective function given linear constraints.
One early method for this procedure was Fourier-Motzkin elimination, and the Hirsch conjecture provides an upper bound on the runtime of one method.
linear programming