Further study on "an extended shortest path problem A data envelopment analysis approach"

Document Type : Short notes

Authors

1 Birjand university of technology

2 Full professor in Applied Mathematics & Operations Research, Islamic Azad University of Rasht, Iran.

Abstract

Amirteimoori proposed an approach based on data envelopment analysis (DEA) for  multi-objective path problems on networks whose arcs contain multiple positive and negative attributes [A. Amirteimoori, An extended shortest path problem: A data envelopment analysis approach, Applied Mathematics Letters 25 (2012) 1839-1843]. The approach is to define a relative efficiency for each arcs using DEA models, and then to solve a longest path problem for obtaining a path with maximum efficiency. In this note, we focus on two drawbacks of the approach and illustrate them using examples. Then, we propose remedies to eliminate them.

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References

[1] R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory, Algorithms, and Applications, PHI Englewood Cliffs NJ, 1993.
[2] A. Amirteimoori, An extended shortest path problem: A data envelopment analysis approach, Applied Math. Lett. 25 (2012), no. 11, 1839–1843.
[3] F. Ghandi, Solving multi-objective shortest path problem using data envelopment analysis, Journal of Operational Research and its Applications ( Applied Mathematics ) - Lahijan Azad University 18 (2021), no. 1, 21–38.
[4] F. Keshavarz-Kohjerdi, A. Bagheri, and A. Asgharian-Sardroud, A linear-time algorithm for the longest path problem in rectangular grid graphs, Discrete Appl. Math. 160 (2012), no. 3, 210–217.
[5] S. Kordrostami and M.J.S. Noveiri, Solving a fuzzy shortest path problem with multiple inputs and outputs by using data envelopment analysis, 2013 13th Iranian Conference on Fuzzy Systems (IFSC), IEEE, 2013, pp. 1–4.
[6] G.H. Shirdel and S. Ramezani-Tarkhorani, A DEA-based approach for finding a favorable multi-objective shortest path, Croat. Oper. Res. Rev. 9 (2018), no. 2, 149.

[7] Y. Wang, X. Li, and R. Ruiz, A fast algorithm for finding the bi-objective shortest path in complicated networks, 2018 IEEE 22nd International Conference on Computer Supported Cooperative Work in Design ((CSCWD)), IEEE, 2018, pp. 104–
109.
Communications in Combinatorics and Optimization
Volume 8, Issue 1
March 2023
Pages 253-259

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