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Motivated by the practical supply chain management of the automobile industry, we study the car sequencing problem (CSP) that minimizes the conflicts occur when sequentially manufacturing cars on an assembly line. The CSP is a well-established problem, subject to the paint batching constraints to decrease the energy consumption for color changeovers and production rate constraints in the assembly shop to ensure a smooth usage of car options. However, the existing solution algorithms to this problem do not take into account the block batches, which desires a consecutive production batch of cars requiring a certain option. This requirement often occurs when specialized labor time window is short in the customized car production scenario, and renders additional complexities to the traditional car sequencing problem. In this paper, we present a novel model to deal with these constraints and simultaneously generate the sequencing and replenishment decisions. Besides, we develop two math-heuristic algorithms to solve the proposed large-scale CSP. The presented heuristics are on the basis of relax-and-fix procedures, fix-and-optimize procedures and adaptive variable neighborhood search. To solve the large-sized instances (commercial solvers, i.e., Cplex, cannot obtain a feasible result within 1 h), we design and implement a reinforced parameter tuning mechanism to dynamically select the parameter values, so as to speed up the search process. The proposed models and heuristics are tested on representative instances generated from the benchmark in the literature (CSPLib), as well as large-sized instances generated from real-world cases. We report on extensive computational experiments and provide basic managerial insights into the planning process. [ABSTRACT FROM AUTHOR]

B Correction to: J Wireless Com Network (2022) 2022:26 b https://doi.org/10.1186/s13638-022-02113-7 Following publication of the original article [[1]], the authors flagged that Wenchao Wei had been erroneously affiliated with affiliation 3 instead of affiliation 2. Reference 1 Yu Y, Lu X, Zhao T, Cheng M, Liu L, Wei W. Heuristic approaches for the car sequencing problems with block batches. [Extracted from the article]