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International Journal of Production Research Volume 60, 2022 - Issue 17

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Research Article

A two-stage robust hub location problem with accelerated Benders decomposition algorithm

Reza Rahmatia Department of Industrial Engineering, Shahed University, Tehran, Iran

https://orcid.org/0000-0002-3426-1642 View further author information

Mahdi Bashirib School of Strategy and Leadership, Faculty of Business and Law, Coventry University, Coventry, UK;c Centre for Business in Society, Coventry University, Coventry, UKCorrespondence[email protected]
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Erfaneh Nikzada Department of Industrial Engineering, Shahed University, Tehran, IranView further author information

Ali Siadatd Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, HESAM Université, Metz, FranceView further author information

Pages 5235-5257 | Received 04 Apr 2020, Accepted 21 May 2021, Published online: 06 Sep 2021

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https://doi.org/10.1080/00207543.2021.1953179
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Table 1. Review of hub location problems based on robust optimisation.

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Table 2. Number of iterations and CPU time with different initial core points and Γ for AP 20-node instance.

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Table 3. Comparison of the Pareto-optimal cut Benders decomposition algorithm with classical one for AP 50-node instance.

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Figure 1. Convergence of (a) classical and (b) Pareto-optimal cut Benders decomposition algorithm for AP 20-node instance.

Table 4. Impact of uncertainty budget and α with $Ω = 1$ for AP 20-node instance.

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Table 5. Impact of uncertainty budget and α with $Ω = 2$ for AP 20-node instance.

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Table 6. Impact of uncertainty budget and α with $Ω = 1$ for AP 50-node instance.

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Table 7. Impact of uncertainty budget and α with $Ω = 1$ for CAB 25-node instance.

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Table 8. The impact of size reduction scheme for AP 50-node instances.

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Table 9. The impact of size reduction scheme for TR 81-node instance.

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Figure 2. Additional cost for wrong decisions, CAB 25-node instance.

Figure 3. Comparison between expected aggregate functions, CAB 25-node instance.

Figure 4. Network structure of (a) robust and (b) stochastic models, $α = 0.5$ , AP 10-node instance.

Table 10. Optimal hub configuration for CAB 25-node instance.

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Figure 5. Solution performance of robust and stochastic models, AP 20-node instance.

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A two-stage robust hub location problem with accelerated Benders decomposition algorithm

Table 1. Review of hub location problems based on robust optimisation.

Table 2. Number of iterations and CPU time with different initial core points and Γ for AP 20-node instance.

Table 3. Comparison of the Pareto-optimal cut Benders decomposition algorithm with classical one for AP 50-node instance.

Table 4. Impact of uncertainty budget and α with $Ω = 1$ for AP 20-node instance.

Table 5. Impact of uncertainty budget and α with $Ω = 2$ for AP 20-node instance.

Table 6. Impact of uncertainty budget and α with $Ω = 1$ for AP 50-node instance.

Table 7. Impact of uncertainty budget and α with $Ω = 1$ for CAB 25-node instance.

Table 8. The impact of size reduction scheme for AP 50-node instances.

Table 9. The impact of size reduction scheme for TR 81-node instance.

Table 10. Optimal hub configuration for CAB 25-node instance.

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A two-stage robust hub location problem with accelerated Benders decomposition algorithm

Figures & data

Table 1. Review of hub location problems based on robust optimisation.

Table 2. Number of iterations and CPU time with different initial core points and Γ for AP 20-node instance.

Table 3. Comparison of the Pareto-optimal cut Benders decomposition algorithm with classical one for AP 50-node instance.

Table 4. Impact of uncertainty budget and α with Ω=1 for AP 20-node instance.

Table 5. Impact of uncertainty budget and α with Ω=2 for AP 20-node instance.

Table 6. Impact of uncertainty budget and α with Ω=1 for AP 50-node instance.

Table 7. Impact of uncertainty budget and α with Ω=1 for CAB 25-node instance.

Table 8. The impact of size reduction scheme for AP 50-node instances.

Table 9. The impact of size reduction scheme for TR 81-node instance.

Table 10. Optimal hub configuration for CAB 25-node instance.

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Table 4. Impact of uncertainty budget and α with $Ω = 1$ for AP 20-node instance.

Table 5. Impact of uncertainty budget and α with $Ω = 2$ for AP 20-node instance.

Table 6. Impact of uncertainty budget and α with $Ω = 1$ for AP 50-node instance.

Table 7. Impact of uncertainty budget and α with $Ω = 1$ for CAB 25-node instance.