A Bi-Objective Two-Level Capacitated Facility Location Model with Primary–Backup Assignments under Depot Disruptions
Article Sidebar
Main Article Content
Abstract
Supply chain disruptions affect the economic and delivery performance of distribution networks. This study develops a bi-objective two-level capacitated facility location model under depot disruptions, assigning customers to primary and backup depots through the same satellite to ensure service continuity. The model minimizes expected system cost and delivery time under capacity restrictions. The initial nonlinear formulation is reformulated as an equivalent mixed-integer linear programming model, and a normalized weighted-sum approach examines the objective trade-off. Experiments on 20–70-node instances reveal a clear cost–delivery-time trade-off. Both single-objective models reach proven optimality for up to 35 nodes, while larger instances exhibit increasing solution times and optimality gaps. The results demonstrate the value of balancing economic and delivery performance in disruption aware distribution network design.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Avella P, Boccia M. A cutting plane algorithm for the capacitated facility location problem. Comput Optim Appl. 2009;43:39-65. DOI: https://doi.org/10.1007/s10589-007-9125-x
Ho SC. An iterated tabu search heuristic for the single-source capacitated facility location problem. Appl Soft Comput. 2015;27:169-78. DOI: https://doi.org/10.1016/j.asoc.2014.11.004
Rahmaniani R, Ghaderi A. An algorithm with different exploration mechanisms: experimental results to capacitated facility location/network design problem. Expert Syst Appl. 2015;42(7):3790-800. DOI: https://doi.org/10.1016/j.eswa.2014.12.051
Aardal K, Labbé M, Leung J, Queyranne M. On the two-level uncapacitated facility location problem. INFORMS J Comput. 1996;8(3):289-301. DOI: https://doi.org/10.1287/ijoc.8.3.289
Tragantalerngsak S, Holt J, Rönnqvist M. Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem. Eur J Oper Res.1997;102(3):611-25. DOI: https://doi.org/10.1016/S0377-2217(96)00227-5
Tragantalerngsak S, Holt J, Rönnqvist M. An exact method for the two-echelon, single-source, capacitated facility location problem. Eur J Oper Res. 2000;123(3):473-89. DOI: https://doi.org/10.1016/S0377-2217(99)00105-8
Drezner Z. Heuristic solution methods for two location problems with unreliable facilities. J Oper Res Soc. 1987;38(6):509-14. DOI: https://doi.org/10.1057/jors.1987.88
Snyder LV, Daskin MS. Reliability models for facility location: the expected failure cost case. Transp Sci. 2005;39(3):400-16. DOI: https://doi.org/10.1287/trsc.1040.0107
Snyder LV. Facility location under uncertainty: a review. IIE Trans. 2006;38(7):547-64. DOI: https://doi.org/10.1080/07408170500216480
Cui T, Ouyang Y, Shen ZJM. Reliable facility location design under the risk of disruptions. Oper Res. 2010;58(4):998-1011. DOI: https://doi.org/10.1287/opre.1090.0801
Li Q, Zeng B, Savachkin A. Reliable facility location design under disruptions. Comput Oper Res. 2013;40(4):901-9. DOI: https://doi.org/10.1016/j.cor.2012.11.012
Afify B, Soeanu A, Awasthi A. Separation linearization approach for the capacitated facility location problem under disruption. Expert Syst Appl. 2021;169:114187. DOI: https://doi.org/10.1016/j.eswa.2020.114187
Lu X, Cheng C. Locating facilities with resiliency to capacity failures and correlated demand uncertainty. Transp Res Part E Logist Transp Rev. 2021;153:102444. DOI: https://doi.org/10.1016/j.tre.2021.102444
Koca E. Two-stage stochastic facility location problem with disruptions and restricted shortages. Comput Ind Eng. 2023;183:109484. DOI: https://doi.org/10.1016/j.cie.2023.109484
Hu H, Tang J. Robust facility location considering protection and backup under facility disruptions with decision dependent uncertainty. Eur J Oper Res. 2025;325(3):474-86. DOI: https://doi.org/10.1016/j.ejor.2025.03.027
Aldrighetti R, Battini D, Ivanov D, Zennaro I. Costs of resilience and disruptions in supply chain network design models: a review and future research directions. Int J Prod Econ. 2021;235:108103. DOI: https://doi.org/10.1016/j.ijpe.2021.108103
Fugaro S, Sgalambro A. Multi-objective facility location problems: systematic literature review and research agenda. Comput Ind Eng. 2026;216:111994. DOI: https://doi.org/10.1016/j.cie.2026.111994
Medal HR, Pohl EA, Rossetti MD. A multi-objective integrated facility location-hardening model: analyzing the pre- and post-disruption tradeoff. Eur J Oper Res. 2014;237(1):257-70. DOI: https://doi.org/10.1016/j.ejor.2014.01.040
Titkanna T, Kongkaew W, Sirivongpaisal N. Hybrid cuckoo search algorithm for location allocation optimization in insurgency-prone agricultural supply chains. Eng Optim. 2026. DOI: https://doi.org/10.1080/0305215X.2026.2672121
Ramshani M, Ostrowski J, Zhang K, Li X. Two-level uncapacitated facility location problem with disruptions. Comput Ind Eng. 2019;137:106089. DOI: https://doi.org/10.1016/j.cie.2019.106089
Harnnarong D, Boonperm A. Two-level capacitated facility location problem under disruption and fortification. Asia Pac J Sci Technol. 2024;29(2):APST-29-02-03.
Marler RT, Arora JS. Survey of multiobjective optimization methods for engineering. Struct Multidiscip Optim. 2004;26(6):369-95. DOI: https://doi.org/10.1007/s00158-003-0368-6