Method of sequential modification of the objective function in the assignment problem

Abstract

A new method for solving the assignment problem based on the decomposition of the orig inal problem into a number of two dimensional optimization problems is proposed. The integer val uedness and monotonicity of the iterative procedure with respect to the objective function ensures that the algorithm is finite. As a result, either a unique optimal solution of the original assignment problem or a system of constraints is obtained. In the latter case, the system of constraints can be used to obtain all optimal solutions. Examples illustrating the algorithm are discussed.

Decompositional Method for the Optimization Problem of Effective Shooting

“…A process is constructed that is monotonic in the objective function, which finally leads to the optimum solution, although successive solutions (so-called pseudosolutions) are not admissible to the original constraints. In [3][4][5] the algorithm is applied to various transport-type problems. Degeneration is a special place when it is impossible to form the initial optimum from intermediate problems.…”