Abstract
The article suggests an approach of solving the problem of warehouse and transport infrastructure optimization in a region. The task is to determine the optimal capacity and location of the support network of warehouses in the region, as well as power, composition and location of motor fleets. Optimization is carried out using mathematical models of a regional warehouse network and a network of motor fleets. These models are presented as mathematical programming problems with separable functions. The process of finding the optimal solution of problems is complicated due to high dimensionality, non-linearity of functions, and the fact that a part of variables are constrained to integer, and some variables can take values only from a discrete set. Given the mentioned above complications search for an exact solution was rejected. The article suggests an approximate approach to solving problems. This approach employs effective computational schemes for solving multidimensional optimization problems. We use the continuous relaxation of the original problem to obtain its approximate solution. An approximately optimal solution of continuous relaxation is taken as an approximate solution of the original problem. The suggested solution method implies linearization of the obtained continuous relaxation and use of the separable programming scheme and the scheme of branches and bounds. We describe the use of the simplex method for solving the linearized continuous relaxation of the original problem and the specific moments of the branches and bounds method implementation. The paper shows the finiteness of the algorithm and recommends how to accelerate process of finding a solution.
Highlights
Economy in Industry is complicated due to high dimensionality, non-linearity of functions, and the fact that a part of variables are constrained to integer, and some variables can take values only from a discrete set
The paper proposes an approximate approach to solving problems. This approach is directed on usage of effective computational schemes for solving multidimensional optimization problems which have high dimensionality
It is proposed to carry out transition to continuous relaxation of the original problem in order to obtain its approximate solution
Summary
К проблеме оптимизации региональной складской и автотранспортной инфраструктуры. Докт. техн. наук, проф. Предлагается подход к решению проблемы оптимизации складской и транспортной инфраструктуры региона. С целью оптимизации рассматриваются математические модели региональной складской сети и сети автотранспортных парков. Перечисленные особенности задач обусловливают отказ от поиска точного решения. Для приближенного решения задачи выполняется переход к ее непрерывной релаксации, которая предполагает отказ от требований целочисленности (дискретности) переменных. В качестве приближенного решения исходной задачи принимается приближенно оптимальное решение ее непрерывной релаксации. Предлагаемый метод решения подразумевает линеаризацию полученной непрерывной релаксации и использование схем сепарабельного программирования и ветвей, и границ. В статье оговорены особенности использования симплекс-метода при решении линеаризованной непрерывной релаксации исходной задачи, указаны специфические моменты реализации метода ветвей и границ. Ю. К проблеме оптимизации региональной складской и автотранспортной инфраструктуры / И.
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