The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm

Abstract

To determine whether a transport problem has a solution , you can use the Lagrange multiplier method . To do this, it is advisable to replace variables so that the objective function is a sum of exponentials. The peculiarity of the sum of exponents is that the principal diagonal minors of the Hessian of the sum of exponents are positive quantities , and therefore the sum of exponents has an extremum and this extremum is the minimum. Solutions of large - dimensional transport tasks are of great practical importance for optimizing transportation schedules by transport enterprises . There are several algorithms for solving this problem, but the development of other methods for solving the transport problem that would use computing power more efficiently deserves attention. The method proposed in this paper for solving the transport problem based on the use of complex numbers in the algorithm makes it simpler and more visual for practical application.