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Path problem simplification with desired bounded lengths in acyclic networks

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Abstract

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 DBL path problem. The complexity of the algorithm is O(m), where m is the number of arcs.

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Authors and Affiliations

  1. Business Administration College, Nanchang Institute of Technology, Nanchang, 330099, China

    Zhixiong Su & Hanying Wei

  2. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Jianxun Qi

Authors
  1. Zhixiong Su
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  2. Jianxun Qi
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  3. Hanying Wei
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Correspondence to Zhixiong Su.

Additional information

Zhixiong Su is a lecturer of Business Administration College, Nanchang Institute of Technology, Nanchang, China. He holds a Ph.D in technical economic and management science from North China Electric Power University. His researches focus on operations research, network optimization, and project scheduling. His recent research has appeared in International Transaction in Operational Research, Systems Engineering - Theory & Practice, Journal of Management Sciences in China, The Scientific World Journal, and Applied Mathematics & Information Sciences. He is a member of Chinese Society of Optimization, Overall Planning and Economical Mathematics, and Operations Research Society of China.

Jianxun Qi is a professor and doctoral mentor of School of Economics and Management, North China Electric Power University. His researches focus on operations research, network planning technology, project scheduling, and global optimization. His recent research has appeared in International Transaction in Operational Research, Systems Engineering - Theory & Practice, Journal of Systems Engineering, Journal of Management Sciences in China, Chinese Journal of Management Science, The Scientific World Journal, and Journal of Industrial and Management Optimization. He is a standing director of Chinese Society of Optimization, Overall Planning and Economical Mathematics.

Hanying Wei is a lecturer of Business Administration College, Nanchang Institute of Technology, Nanchang, China. She holds a MA in technical economic and management science from North China Electric Power University. Her researches focus on technical economic, management science, and finance.

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Su, Z., Qi, J. & Wei, H. Path problem simplification with desired bounded lengths in acyclic networks. J. Syst. Sci. Syst. Eng. 24, 500–519 (2015). https://doi.org/10.1007/s11518-015-5292-y

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  • DOI: https://doi.org/10.1007/s11518-015-5292-y

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