Abstract

We propose a new graph model of transportation on a single-line railway section. Based on a given freight-train delivery schedule, we construct an acyclic graph with vertices denoting deliveries and arcs indicating the possibility of successive implementation of these deliveries by some locomotive. This model of the problem permits applying static graph algorithms to find an optimal locomotive assignment plan. The search for a solution of the problem without time constraints on the locomotives is reduced to finding a minimal path cover of an acyclic graph. Each path in the cover corresponds to a sequence of deliveries carried out by one locomotive. If there are temporary constraints on the locomotives (maintenance breaks), not all paths in the cover can remain valid: for some locomotives, none of the established delivery sequences can be performed from start to finish. In this case, one more solution stage is added, at which the cover is transformed in such a way that all new paths describe a sequence of deliveries that can be carried out by a given set of locomotives under given time constraints.

中文翻译：

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求解单线铁路段机车无约束和有约束优化分配问题的图法

摘要

我们提出了一种新的单线铁路段交通图模型。基于给定的货运列车交付时间表，我们构建了一个非循环图，其中顶点表示交付，弧线表示某些机车连续实施这些交付的可能性。该问题模型允许应用静态图算法来找到最佳机车分配计划。对机车没有时间限制的问题解决方案的搜索简化为寻找无环图的最小路径覆盖。封面中的每条路径对应于由一个机车执行的一系列交付。如果机车有临时限制（维护中断），则并非所有掩护路径都可以保持有效：对于某些机车，没有一个既定的交付顺序可以从头到尾执行。在这种情况下，增加了一个解决方案阶段，在该阶段，覆盖以这样一种方式转换，即所有新路径都描述了一系列交付，这些交付序列可以在给定的时间限制下由一组给定的机车执行。