The multi-manned joint assembly line balancing and feeding problem

The Joint Assembly Line Balancing and Feeding Problem (JALBFP) assigns a line feeding mode to each component (Assembly Line Feeding Problem) and each task to a workplace of a station (Assembly Line Balancing Problem). Current literature offers numerous optimisation models that solve these problems sequentially. However, only few optimisation models, provide a joint solution. To solve the JALBFP for a multi-manned assembly line, we propose a Mixed Integer Linear Programming (MILP) model and a heuristic that relies on the Adaptive Large Neighborhood Search (ALNS) framework by considering multiple workplaces per station and three different feeding policies: line stocking, travelling kitting and sequencing. The objective function minimises the cost of the whole assembly system which considers supermarket, transportation, assembly operations, and investment costs. Although the JALBFP requires higher computation times, it leads to a higher total cost reduction compared to the sequential approach. Through a numerical study, we validate the heuristic approach and find that the average deviation to the MILP model is around 1%. We also compare the solution of the JALBFP with that of the sequential approach and find an average total cost reduction of 10.1% and a maximum total cost reduction of 43.8%.

联合装配线平衡与物料配送问题（Joint Assembly Line Balancing and Feeding Problem, JALBFP）涵盖两类子问题：为各零部件分配线边配送模式（对应装配线物料配送问题（Assembly Line Feeding Problem）），以及将每道工序指派至工位的作业台（对应装配线平衡问题（Assembly Line Balancing Problem））。现有文献已提出诸多针对两类问题的序贯求解优化模型，但仅少数模型可实现联合求解。为求解多作业台装配线的JALBFP，本文提出混合整数线性规划（Mixed Integer Linear Programming, MILP）模型，以及一种基于自适应大邻域搜索（Adaptive Large Neighborhood Search, ALNS）框架的启发式算法，该算法兼顾单工位多作业台场景与三类配送策略：线边备货、巡回拣配与排序配送。本文的目标函数为最小化整个装配系统的总成本，该成本涵盖物料超市成本、运输成本、装配作业成本与投资成本。尽管联合求解方法的计算耗时更长，但相较序贯求解方法，其可实现更高的总成本降幅。通过数值实验，本文验证了所提启发式算法的有效性，发现其与MILP模型的平均偏差约为1%。同时，本文将联合求解方法的结果与序贯求解方法的结果进行对比，发现平均总成本降幅可达10.1%，最大总成本降幅可达43.8%。