A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY

Subject.The canonical task of transport logistics in the distributed system "suppliers - consumers" is considered. Goal. Development of an accurate algorithm for solving this problem according to the probabilistic criterion in the assumption of the random nature of transportation costs has...

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Main Authors: Lev Raskin, Yurii Parfeniuk, Larysa Sukhomlyn, Mykhailo Kravtsov, Leonid Surkov
Format: Article
Language:English
Published: Kharkiv National University of Radio Electronics 2021-07-01
Series:Сучасний стан наукових досліджень та технологій в промисловості
Online Access:https://itssi-journal.com/index.php/ittsi/article/view/282
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author Lev Raskin
Yurii Parfeniuk
Larysa Sukhomlyn
Mykhailo Kravtsov
Leonid Surkov
author_facet Lev Raskin
Yurii Parfeniuk
Larysa Sukhomlyn
Mykhailo Kravtsov
Leonid Surkov
author_sort Lev Raskin
collection DOAJ
description Subject.The canonical task of transport logistics in the distributed system "suppliers - consumers" is considered. Goal. Development of an accurate algorithm for solving this problem according to the probabilistic criterion in the assumption of the random nature of transportation costs has been done. Tasks. 1. Development of an exact method for solving the problem of finding a plan that minimizes the total cost of transportation in conditions when their costs are given by their distribution densities. 2. Development of a method for solving the problem when the distribution density of the cost of transportation is not known. Methods. A computational scheme for solving the problem is proposed, which is implemented by an iterative procedure for sequential improvement of the transportation plan. The convergence of this procedure is proved. In order to accelerate the convergence of the computational procedure to the exact solution, an alternative method is proposed based on the solution of a nontrivial problem of fractional nonlinear programming. The method reduces the original complex problem to solving a sequence of simpler problems. The original problem is supplemented by considering a situation that is important for practice when, in the conditions of a small sample of initial data, there is no possibility of obtaining adequate analytical descriptions for the distribution densities of the random costs of transportation. To solve the problem in this case, a minimax method is proposed for finding the best transportation plan in the most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, the modern mathematical apparatus of continuous linear programming was used. Results. A mathematical model and a method for solving the problem of transport logistics in conditions of uncertainty of the initial data are proposed. The desired plan is achieved using the solution of the fractional nonlinear programming problem. Conclusions: The problem of forming a transportation plan is considered, provided that their costs are random values. Also, a method for solving the problem of optimization of transportation for a situation where the density of distribution of random cost cannot be correctly determined is considered.
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institution Kabale University
issn 2522-9818
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language English
publishDate 2021-07-01
publisher Kharkiv National University of Radio Electronics
record_format Article
series Сучасний стан наукових досліджень та технологій в промисловості
spelling doaj-art-1305dc3c0d704ed9aa5c56d96d0ea1ea2025-08-20T03:33:15ZengKharkiv National University of Radio ElectronicsСучасний стан наукових досліджень та технологій в промисловості2522-98182524-22962021-07-012 (16)10.30837/ITSSI.2021.16.080A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTYLev Raskin0Yurii Parfeniuk1Larysa Sukhomlyn2Mykhailo Kravtsov3Leonid Surkov4National Technical University "Kharkiv Polytechnic Institute"National Technical University "Kharkiv Polytechnic Institute"Kremenchuk Mykhailo Ostrohradskyi National UniversityNational Technical University "Kharkiv Polytechnic Institute"National Technical University "Kharkiv Polytechnic Institute"Subject.The canonical task of transport logistics in the distributed system "suppliers - consumers" is considered. Goal. Development of an accurate algorithm for solving this problem according to the probabilistic criterion in the assumption of the random nature of transportation costs has been done. Tasks. 1. Development of an exact method for solving the problem of finding a plan that minimizes the total cost of transportation in conditions when their costs are given by their distribution densities. 2. Development of a method for solving the problem when the distribution density of the cost of transportation is not known. Methods. A computational scheme for solving the problem is proposed, which is implemented by an iterative procedure for sequential improvement of the transportation plan. The convergence of this procedure is proved. In order to accelerate the convergence of the computational procedure to the exact solution, an alternative method is proposed based on the solution of a nontrivial problem of fractional nonlinear programming. The method reduces the original complex problem to solving a sequence of simpler problems. The original problem is supplemented by considering a situation that is important for practice when, in the conditions of a small sample of initial data, there is no possibility of obtaining adequate analytical descriptions for the distribution densities of the random costs of transportation. To solve the problem in this case, a minimax method is proposed for finding the best transportation plan in the most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, the modern mathematical apparatus of continuous linear programming was used. Results. A mathematical model and a method for solving the problem of transport logistics in conditions of uncertainty of the initial data are proposed. The desired plan is achieved using the solution of the fractional nonlinear programming problem. Conclusions: The problem of forming a transportation plan is considered, provided that their costs are random values. Also, a method for solving the problem of optimization of transportation for a situation where the density of distribution of random cost cannot be correctly determined is considered.https://itssi-journal.com/index.php/ittsi/article/view/282
spellingShingle Lev Raskin
Yurii Parfeniuk
Larysa Sukhomlyn
Mykhailo Kravtsov
Leonid Surkov
A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
Сучасний стан наукових досліджень та технологій в промисловості
title A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
title_full A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
title_fullStr A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
title_full_unstemmed A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
title_short A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
title_sort method for solving the canonical problem of transport logistics in conditions of uncertainty
url https://itssi-journal.com/index.php/ittsi/article/view/282
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