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Ali, S.M., Fathollahi-Fard, A.M., Ahnaf, R. and Wong, K.Y. (2023). A multi-objective closed-loop supply chain under uncertainty: An efficient Lagrangian relaxation reformulation using a neighborhood-based algorithm, Journal of Cleaner Production 423: 138702, DOI: 10.1016/j.jclepro.2023.138702. Search in Google Scholar

Araújo, C.V.D., de Souza, C.C. and Usberti, F.L. (2024). Lagrangian relaxation for maximum service in multicast routing with QoS constraints, International Transactions in Operational Research 31(1): 140–166, DOI: 10.1111/itor.13200. Search in Google Scholar

Beasley, J.E. (1990). OR-Library, http://people.brunel.ac.uk/~mastjjb/jeb/info.html. Search in Google Scholar

Bilge, Ü., Kurtulan, M. and Kıraç, F. (2007). A tabu search algorithm for the single machine total weighted tardiness problem, European Journal of Operational Research 176(3): 1423–1435, DOI: 10.1016/j.ejor.2005.10.030. Search in Google Scholar

Bragin, M.A., Luh, P.B., Yan, J.H., Yu, N. and Stern, G.A. (2015). Convergence of the surrogate Lagrangian relaxation method, Journal of Optimization Theory and Applications 164(1): 173–201, DOI: 10.1007/s10957-014-0561-3. Search in Google Scholar

Butt, A.A. and Collins, R.T. (2013). Multi-target tracking by Lagrangian relaxation to min-cost network flow, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Portland, USA, pp. 1846–1853, DOI: 10.1109/CVPR.2013.241. Search in Google Scholar

Chen, H. and Luh, P.B. (2003). An alternative framework to Lagrangian relaxation approach for job shop scheduling, European Journal of Operational Research 149(3): 499–512, DOI: 10.1109/CDC.1999.832909. Search in Google Scholar

Congram, R.K., Potts, C.N. and van de Velde, S.L. (2002). An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem, INFORMS Journal on Computing 14(1): 52–67, DOI: 10.1287/ijoc.14.1.52.7712. Search in Google Scholar

Crauwels, H., Potts, C.N. and Van Wassenhove, L.N. (1998). Local search heuristics for the single machine total weighted tardiness scheduling problem, INFORMS Journal on Computing 10(3): 341–350, DOI: 10.1287/ijoc.10.3.341. Search in Google Scholar

Cui, H. and Luo, X. (2017). An improved Lagrangian relaxation approach to scheduling steelmaking-continuous casting process, Computers & Chemical Engineering 106: 133–146, DOI: 10.1016/j.compchemeng.2017.05.026. Search in Google Scholar

Everett, H. (1963). Generalized Lagrange multiplier method for solving problems of optimum allocation of resources, Operations Research 11(3): 399–417, DOI: 10.1287/opre.11.3.399. Search in Google Scholar

Fisher, M.L. (1976). A dual algorithm for the one-machine scheduling problem, Mathematical Programming 11(1): 229–251, DOI: 10.1007/BF01580393. Search in Google Scholar

Fisher, M.L. (2004). The Lagrangian relaxation method for solving integer programming problems, Management Science 50(12_supp): 1861–1871, DOI: 10.1287/mnsc.1040.0263. Search in Google Scholar

Fu, Y.-M. and Diabat, A. (2015). A Lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem, Applied Mathematical Modelling 39(3–4): 1194–1201, DOI: 10.1016/j.apm.2014.07.006. Search in Google Scholar

Gaudioso, M., Gorgone, E., Labbé, M. and Rodríguez-Chía, A.M. (2017). Lagrangian relaxation for SVM feature selection, Computers & Operations Research 87: 137–145, DOI: 10.1016/j.cor.2017.06.001. Search in Google Scholar

Gocgun, Y. and Ghate, A. (2012). Lagrangian relaxation and constraint generation for allocation and advanced scheduling, Computers & Operations Research 39(10): 2323–2336, DOI: 10.1016/j.cor.2011.11.017. Search in Google Scholar

Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnoy Kan, A.H.G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics 5: 287–326, DOI: 10.1016/S0167-5060(08)70356-X. Search in Google Scholar

Hajibabaei, M. and Behnamian, J. (2023). Fuzzy cleaner production in assembly flexible job-shop scheduling with machine breakdown and batch transportation: Lagrangian relaxation, Journal of Combinatorial Optimization 45(5): 112, DOI: 10.1007/s10878-023-01046-1. Search in Google Scholar

Held, M., Wolfe, P. and Crowder, H.P. (1974). Validation of subgradient optimization, Mathematical Programming 6(1): 62–88, DOI: 10.1007/BF01580223. Search in Google Scholar

Huang, D., Wang, Y., Jia, S., Liu, Z. and Wang, S. (2023). A lagrangian relaxation approach for the electric bus charging scheduling optimisation problem, Transportmetrica A: Transport Science 19(2): 2023690, DOI: 10.1080/23249935.2021.2023690. Search in Google Scholar

Idzikowski, R. (2023). LagrangianRelaxation, Code and experimental results, https://github.com/ridzikowski/LagrangianRelaxation. Search in Google Scholar

Koulamas, C. (2010). The single-machine total tardiness scheduling problem: Review and extensions, European Journal of Operational Research 202(1): 1–7, DOI: 10.1016/j.ejor.2009.04.007. Search in Google Scholar

Lawler, E.L. (1977). A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness, Annals of Discrete Mathematics 1: 331–342, DOI: 10.1016/S0167-5060(08)70742-8. Search in Google Scholar

Lenstra, J.K., Kan, A.R. and Brucker, P. (1977). Complexity of machine scheduling problems, Annals of Discrete Mathematics 1: 343–362, DOI: 10.1016/S0167-5060(08)70743-X. Search in Google Scholar

Liu, X., Wang, W., Chen, X., Sterna, M. and Blazewicz, J. (2023). Exact approaches to late work scheduling on unrelated machines, International Journal of Applied Mathematics and Computer Science 33(2): 285–295, DOI: 10.34768/amcs-2023-0021. Search in Google Scholar

Matsuo, H., Juck Suh, C. and Sullivan, R.S. (1989). A controlled search simulated annealing method for the single machine weighted tardiness problem, Annals of Operations Research 21(1): 85–108, DOI: 10.1007/BF02022094. Search in Google Scholar

Nishi, T., Hiranaka, Y. and Inuiguchi, M. (2010). Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness, Computers & Operations Research 37(1): 189–198, DOI: 10.1016/j.cor.2009.04.008. Search in Google Scholar

Nowak, M.P. and Römisch, W. (2000). Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty, Annals of Operations Research 100(1–4): 251–272, DOI: 10.1023/A:1019248506301. Search in Google Scholar

Potts, C.N. and Van Wassenhove, L.N. (1985). A branch and bound algorithm for the total weighted tardiness problem, Operations Research 33(2): 363–377, DOI: 10.1287/opre.33.2.363. Search in Google Scholar

Potts, C. and Van Wassenhove, L.N. (1991). Single machine tardiness sequencing heuristics, IIE Transactions 23(4): 346–354, DOI: 10.1080/07408179108963868. Search in Google Scholar

Simanchev, R.Y. and Urazova, I. (2023). Integer models for the total weighted tardiness problem on a single machine, International Conference on Mathematical Optimization Theory and Operations Research, Ekaterinburg, Russia, pp. 176–187, DOI: 10.1007/978-3-031-43257-6_14. Search in Google Scholar

Song, M., Cheng, L. and Lu, B. (2024). Solving the multi-compartment vehicle routing problem by an augmented Lagrangian relaxation method, Expert Systems with Applications A 237: 121511, DOI: 10.1016/j.eswa.2023.121511. Search in Google Scholar

Song, M., Lu, B., Cheng, L. and Sun, C. (2023). Lagrangian relaxation-based decomposition approaches for the capacitated arc routing problem in the state-space-time network, Transportation Letters 15(10): 1317–1336, DOI: 10.1080/19427867.2022.2148368. Search in Google Scholar

Speckenmeyer, P., Hilmer, C., Rauchecker, G. and Schryen, G. (2023). Parallel branch-and-price algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times, SSRN: 4537436, (preprint). Search in Google Scholar

Zakharova, Y. (2023). Hybrid evolutionary algorithm with optimized operators for total weighted tardiness problem, International Conference on Mathematical Optimization Theory and Operations Research, Ekaterinburg, Russia, pp. 224–238, DOI: 10.1007/978-3-031-35305-5_15. Search in Google Scholar

Zhang, C., Gao, Y., Yang, L., Gao, Z. and Qi, J. (2020). Joint optimization of train scheduling and maintenance planning in a railway network: A heuristic algorithm using Lagrangian relaxation, Transportation Research B: Methodological 134: 64–92, DOI: 10.1016/j.trb.2020.02.008. Search in Google Scholar

Zhao, Q. and Yuan, J. (2023). Single-machine primary-secondary scheduling with total tardiness being the primary criterion, Journal of Scheduling 27(3): 1–10, DOI: 10.1007/s10951-023-00793-7. Search in Google Scholar

Zhou, Y. and Lee, G.M. (2017). A Lagrangian relaxation-based solution method for a green vehicle routing problem to minimize greenhouse gas emissions, Sustainability 9(5): 776, DOI: 10.3390/su9050776. Search in Google Scholar

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