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重复性建设项目中确定关键路线的方法研究

ISSN号：1007-3221
期刊名称：运筹与管理
时间：2015
页码：34-40
分类：O153.1[理学—数学;理学—基础数学] TP311.1[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术]
作者机构：[1]Business Administration College, Nanchang Institute of Technology, Nanchang, 330099, China, [2]School of Economics and Management, North China Electric Power University, Beij'ing, 102206, China
相关基金：The authors would like to acknowledge the Natural Science Foundation of China （No. 71171079 and 71271081）, the Natural Science Foundation of Jiangxi Provincial Department of Science and Technology in China （No. 20151BAB211015）, and the Jiangxi Research Center of Soft Science for Water Security ＆ Sustainable Development for financially supporting this work. The authors are also grateful to the anonymous referee for a careful review of the details of this paper and the helpful suggestions that led to its improvement.
相关项目：最长（短）路上的奇异现象研究

关键词：路径问题, 有限长度, 循环网络, 多项式算法, 有界, 等效简化, 路径长度, 算法复杂度, Operations research, path problem with desired bounded lengths, equivalent simplification,path length model, acyclic network

中文摘要：

路径决心是运筹学的一个基本问题。当前的答案主要集中于最短、最长的路径。我们考虑一个更多的概括问题；明确地，我们与需要的围住的长度(DBL 路径问题) 考虑路径问题。这个问题有广泛的应用；然而，这个问题难得多，特别为大规模问题。解决这个问题的一条有效途径是相等的简化。我们集中于在非循环的网络简化这个问题并且创造简化在各种各样的路径长度之间的关系的一个路径长度模型。基于这个模型，我们设计多项式算法计算最短，最长秒最突然，并且第二穿越任何弧的最长的路径。而且，我们为 DBL 路径问题的相等的简化设计一个多项式算法。算法的复杂性是 O (m) ，在 m 是弧的数字的地方。

英文摘要：

Path determination is a fundamental problem of operations research. Current solutions mainly focus on the shortest and longest paths. We consider a more generalized problem; specifically, we consider the path problem with desired bounded lengths （DBL path problem）. This problem has extensive applications; however, this problem is much harder, especially for large-scale problems. An effective approach to this problem is equivalent simplification. We focus on simplifying the problem in acyclic networks and creating a path length model that simplifies relationships between various path lengths. Based on this model, we design polynomial algorithms to compute the shortest, longest, second shortest, and second longest paths that traverse any arc. Furthermore, we design a polynomial algorithm for the equivalent simplification of the is O（m）, where m is the number of arcs. DBL path problem. The complexity of the algorithm

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