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Solving a hub location-routing problem with a queue system under social responsibility by a fuzzy meta-heuristic algorithm

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Abstract

This paper presents a new multi-objective mathematical model for the hub location and routing problem under uncertainty in flows, costs, times, and number of job opportunities. This model aims at minimizing the total transportation cost consisting of routing and fixed cost and maximizing the employment and regional development as social responsibility. An M/M/c/K queue system is applied to estimate the waiting time at hub nodes and maximize the responsiveness. Also, a fuzzy queuing method is applied to model the uncertainties in this network. A powerful evolutionary meta-heuristic algorithm based on fuzzy invasive weed optimization, variable neighborhood search, and game theory is developed to solve the introduced model and obtain near-optimal Pareto solutions. Many experiments as well as a real transportation case-study show the superiority of the proposed approaches compared to the state-of-the-art algorithm.

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Acknowledgements

The authors would like to thank the Editor-in-Chief and Lead Guest Editor of the Annals of Operations Research, as well as autonomous reviewers for their helpful comments and suggestions, which greatly improved the presentation of this paper. Also, the support of the Iranian Operations Research Society is highly acknowledged by the second author, as the board member of this society.

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Authors and Affiliations

  1. School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Pardis Pourmohammadi, Reza Tavakkoli-Moghaddam & Yaser Rahimi

  2. Kent Business School, University of Kent, Canterbury, UK

    Chefi Triki

  3. Department of Engineering for Innovation, University of Salento, Lecce, Italy

    Chefi Triki

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  1. Pardis Pourmohammadi
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  2. Reza Tavakkoli-Moghaddam
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Correspondence to Reza Tavakkoli-Moghaddam or Chefi Triki.

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Appendix

Appendix

Figures 11, 12, 13, and 14 summarize the behavior of the three meta-heuristic algorithms with respect to each of the four QM, DM, SM and MID metrics. All the four figures show clearly the good performance of our GVIWO compared to both NSGA-II and MOPSO algorithms.

Fig. 11
figure 11

Comparing the three multi-objective meta-heuristic algorithms with respect to Quality Metric

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Fig. 12
figure 12

Comparing the three meta-heuristic algorithms with respect to Spacing metric

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Fig. 13
figure 13

Comparing the three meta-heuristic algorithms with respect to Diversity metric

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Fig. 14
figure 14

Comparing the three meta-heuristic algorithms with respect to Mean ideal distance

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Pourmohammadi, P., Tavakkoli-Moghaddam, R., Rahimi, Y. et al. Solving a hub location-routing problem with a queue system under social responsibility by a fuzzy meta-heuristic algorithm. Ann Oper Res 324, 1099–1128 (2023). https://doi.org/10.1007/s10479-021-04299-3

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