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%