Разработка методических основ повышения эффективности математического инструментария решения задач производственно-транспортной логистики

Abstract

The methodological foundations of the efficiency increasing mathematical tools for solving the production and transport logistics problems are developed. The shown result, which obtained on the base of mathematical programming methods, can be used as an integral part of a simulated real system. For this purpose, a methodology for directional simulation is developed. The practical implementation of this methodology consists on using the descent direction of the analytic functions as the descent direction of the algorithmic function. For a numerical assessment of the consequences of the mismatch of the corresponding descent directions and the compensation of errors that arise in this process while determination the optimal value of the algorithmic function, a multistep procedure mechanism is proposed. The computational efficiency of the methodology of directional simulation depends on its mathematical software. It is determined that the structure of each individual model should provide the possibility of its connection to the complex of models and have the necessary free parameters for this. The diverse nature of the models often serves as the main difficulty in the problem solution. Such a barrier can be overcome if the work is based on some valid unified model variants. As a result, the models in the process of their practical implementation allow maintaining uniformity in the forms of representation of the inicial data, in the algorithms and programs used to generate the calculated information. The specified requirements are satisfied by mathematical models of transport problems with intermediate nodes. Such models allow the use of parametric decomposition schemes and lead to the problem of nonsmooth optimization. The made statement describes the methodology of guided simulation modeling, which constructively develops the idea of system optimization by moving from the problem of varying the structure of constraints to radical structural changes in the models.