A bottleneck routing problem with a system of priority tasks

A. G. Chentsov
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Abstract

We consider a minimax routing problem related to visiting megacities under precedence conditions and cost functions with task list dependence. It is supposed that some megacity system requiring visiting above all is selected. For solving, an approach with decomposition into a set of two minimax routing problems is proposed. A two-step widely understood dynamic programming procedure realizing an optimal composition solution is constructed. The above-mentioned optimality is established by theoretical methods. Application of the results obtained is possible under investigation of multi-stage processes connected with regular allocation of resources. Another variant of application concerns the particular case of one-element megacities (i.e., cities) and may be related to the issues of aviation logistics under organization of flights using one tool (airplane or helicopter) under system of tasks on the realization of passing cargo transportation with prioritization of visits realized above all.
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优先级任务系统的瓶颈路由问题
考虑了一类具有任务列表依赖的代价函数和优先条件下访问特大城市的极大极小路由问题。假设选择了一些最需要参观的超大城市系统。为了求解这一问题,提出了一种分解为两个极大极小路由问题的方法。构造了一个可实现最优组合解的两步动态规划过程。通过理论方法建立了上述最优性。在与资源的定期分配有关的多阶段过程的研究中,可以应用所获得的结果。应用的另一种变体涉及单元素特大城市(即城市)的特殊情况,可能与使用一种工具(飞机或直升机)组织航班的任务系统下的航空物流问题有关,该任务系统实现了通过货物运输的优先级,首先实现了访问。
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