# A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers
## 6 Conclusions  
With the continuous development of the automotive industry, the mixed-flow production model is becoming more and more popular. In this paper, a decomposition-based algorithm is proposed to solve DCSPwB in automotive mixed-flow assembly, a mathematical model of DCSPwB is established, and the time cost of car sequencing is considered. Using the post-painted car body buffer, the car sequences in the paint shop are reordered to find the optimal car sequences that satisfy all hard constraints in the general assembly shop as well as properly trade-off various soft constraints, minimizing the violation of the constraint rules and the time cost of sequencing in the general assembly shop. The algorithm consists of two heuristic phases, a simple rule-based heuristic inbound phase and a PGDA-based as well as a DGA-based car outbound phase. In addition, we explore the effect of buffer capacity on DCSPwB. To evaluate the performance of the proposed algorithms, 12 test examples are provided. The results show that car sequencing methods based on different exit algorithms are all effective in reducing the violation of downstream workshop constraint rules and that the time cost of car sequencing is acceptable. PGDA tends to achieve better results, but the determination of its parameter \(M\) needs to be obtained by evaluating the quality of different solutions. The quality of the solution of DGA is not as good as that of PGDA, but its parameters are easier to obtain. Meanwhile, our research shows that in DCSPwB, the sequencing ability of the buffers is weakened as the number of cars increases, and increasing the number of lanes improves the sequencing ability of the buffers, but this improvement is tiny and even reduces the sequencing ability of the buffers when the number of lanes in the buffers reaches a certain number, and a certain number of lanes is already able to guarantee the sequencing ability of the buffers. Although the research in this paper is for a specific car sequencing problem, the solution is flexible enough to be extended to a wide range of reordering problems in reality. The general reordering rules are divided into hard and soft constraints, and modifying the weights of the different soft constraints while the determined compliance with the hard constraints can apply this method to other problems. In actuality, any problem with buffers and with resequencing nature can refer to this approach; for example, in the cross-docking distribution problem in supply chain logistics, how to plan the order of incoming and outgoing vehicles is the key to improve the efficiency of the distribution system. This is where cross-docking distribution becomes an online scheduling problem, with the warehouse serving as temporary storage with a buffers area. If different types of products unloaded are reordered within the warehouse, the scheduling difficulty of incoming and outgoing vehicles can be reduced. The object of resequencing here is different types of products, and the optimization goal can be the matching degree of products and shipping vehicles, while the effectiveness of the method can be tested on relevant types of instances in the future, such as cross-docking distribution problems in supply chain logistics. In this paper, the parameter \(M\) of PGDA is obtained by evaluating the quality of the solution on different test cases, and the possibility of determining the parameter \(M\) by  
Figure 10: Effect of number of lanes on sequencing capability. some other methods can be investigated in the future. In addition, the buffers discussed in this paper do not have return lanes, and future research can consider the problem of dynamic sequencing of buffers with return lanes. [PERSON] wrote the manuscript and collected the data. [PERSON] collected the data and contributed to the writing of the text. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.