A new method for solving the problem on the organization of wagon flows under condition of energy efficiency of transportation
DOI:
https://doi.org/10.15587/1729-4061.2017.111940Keywords:
knapsack problem, set function, vector optimization, organization of wagon flows, energy efficiency of transportationAbstract
The paper considers solving a problem of rational organization of wagon flows in a polygon of selected technological railroad stations using a technique for solving a knapsack problem employing set functions. Based on the results of present work, the authors developed a method for solving a knapsack-type problem that makes it possible to adapt the algorithm of solving a vector optimization problem to the rational system of organizing wagon flows in trains without using differentiation operations and to solve a basic optimization problem employing the Lagrange multipliers. The applicability of the Lagrange method was proved for the problems on a conditional extremum in terms of set functions. Its special feature is the rejection of Boolean variables. We confirmed correctness of the mathematical notation of solution to a knapsack-type problem and proved adequacy of the proposed algorithm, as well as adapted it for adjusting a plan of freight trains formation in order to improve energy efficiency of transportation. By reducing the complexity of the problem, it has become possible to reduce computer processor time needed for calculation, and employ this algorithm when designing an automated work place (AWP) for an engineer responsible for planning the formation of trains. It should be specially noted that a reduction of the time needed to solve a problem makes it possible to timely adjust the plan of freight trains formation, to eliminate a lot of irrational variants when handling wagons at technical stations.
The proposed algorithm helps identify variants to direct train flows to the most promising destinations at minimal energy cost for transportation. Limitations of the proposed approach include a closed cycle of routes of the loaded wagons and part of these routes traveled unloaded until the next loading. In some cases, there is a need to change a weight of the train composition, associated with fractures of weight, and, therefore, a change in the balance between wagon flows and train flows.
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Copyright (c) 2017 Oleksandr Papakhov, Natalya Logvinova, Olesya Kharchenko, Andriy Milyanych, Victor Sichenko
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