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Purpose: This study addresses the production optimization of a cellular manufacturing system (CMS) in magnetic production enterprises. Magnetic products and raw materials are more critical to transport than general products because the attraction or repulsion between magnetic poles can easily cause traffic jams. This study needs to address a method to promote the scheduling efficiency of the problem. Design/methodology/approach: To address this problem, this study formulated a mixed-integer linear programming (MILP) model to describe the problem and proposed an auction and negotiation-based approach with a local search to solve it. Auction- and negotiation-based approaches can obtain feasible and high-quality solutions. A local search operator was proposed to optimize the feasible solutions using an improved conjunctive graph model. Findings: Verification tests were performed on a series of numerical examples. The results demonstrated that the proposed auction and negotiation-based approach with a local search operator is better than existing solution methods for the problem identified. Statistical analysis of the experiment results using the Statistical Package for the Social Sciences (SPSS) software demonstrated that the proposed approach is efficient, stable and suitable for solving large-scale numerical instances. Originality/value: An improved auction and negotiation-based approach was proposed; The conjunctive graph model was also improved to describe the problem of CMS with traffic jam constraint and build the local search operator; The authors' proposed approach can get better solution than the existing algorithms by testing benchmark instances and real-world instances from enterprises. [ABSTRACT FROM AUTHOR]