# DEVELOPMENT OF METHODS FOR SUPPLY MANAGEMENT IN TRANSPORTATION NETWORKS UNDER CONDITIONS OF UNCERTAINTY OF TRANSPORTATION COST VALUES

• Lev Raskin National Technical University «Kharkiv Polytechnic Institute»
• Oksana Sira
• Yurii Parfeniuk National Technical University «Kharkiv Polytechnic Institute»
• Kseniia Bazilevych National Aerospace University "Kharkiv Aviation Institute"
Keywords: transport linear programming problem, random transportation costs, exact solution algorithm, worst distribution density, minimax solution

### Abstract

The problem of transport management in a distributed logistics system "suppliers – consumers" is considered. Under the assumption of a random nature of transportation costs, an exact algorithm for solving this problem by a probabilistic criterion has been developed. This algorithm is implemented by an iterative procedure for sequential improvement of the transportation plan. The rate of convergence of a computational procedure to an exact solution depends significantly on the dimension of the problem and is unacceptably low in real problems. In this regard, an alternative method is proposed, based on reducing the original problem to solving a nontrivial problem of fractional-nonlinear programming. A method for solving this problem has been developed and substantiated. The corresponding computational algorithm reduces the fractional-nonlinear model to the quadratic one. The resulting problem is solved by known methods. Further, 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. In this case, the available volume of statistical material is sufficient only to estimate the first two moments of unknown distribution densities. For this marginal case, a minimax method for finding the transportation plan is proposed. The first step is to solve the problem of determining the worst distribution density with the given values of the first two moments. In the second step, the transportation plan is found, which is the best in this most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, let’s use the modern mathematical apparatus of continuous linear programming

### Author Biographies

Lev Raskin, National Technical University «Kharkiv Polytechnic Institute»

Department of Distributed Information Systems and Cloud Technologies

Oksana Sira

Doctor of Technical Sciences, Professor

Department of Distributed Information Systems and Cloud Technologies

Yurii Parfeniuk, National Technical University «Kharkiv Polytechnic Institute»

Department of Distributed Information Systems and Cloud Technologies

Kseniia Bazilevych, National Aerospace University "Kharkiv Aviation Institute"

Department of Mathematical Modeling and Artificial Intelligence

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Published
2021-03-29
How to Cite
Raskin, L., Sira, O., Parfeniuk, Y., & Bazilevych, K. (2021). DEVELOPMENT OF METHODS FOR SUPPLY MANAGEMENT IN TRANSPORTATION NETWORKS UNDER CONDITIONS OF UNCERTAINTY OF TRANSPORTATION COST VALUES. EUREKA: Physics and Engineering, (2), 108-123. https://doi.org/10.21303/2461-4262.2021.001691
Issue
Section
Mathematics