The assembly line feeding problem: An extended formulation with multiple line feeding policies and a case study

As the number of car models in the automotive industry increases, automotive manufacturers are increasingly implementing multi-model assembly lines. These require more part numbers at the assembly line, which results in a shortage of space at the line. Manufacturers use a broad range of line feeding policies to achieve feasible solutions and lower costs. This increases the complexity of assigning line feeding policies to part numbers. To address this problem, we extend existing mixed-integer programming formulations from the literature by modeling nine different line feeding policies as well as different line feeding policies per part family and considering variable walking distances not only at the assembly line but also in the supermarket. Moreover, we extend our formulation by allowing flexible line side spacing. The mathematical model is applied in a case study at a large German automotive company. While models from the literature have been able to reduce total costs by only 0.49%, our proposed model reduces total costs by 3.36% compared to manual planning. By allowing flexible line side spacing, a reduction of 7.54% is possible. An extension of the base model to a rounding of operators without flexible line side spacing allows us to reduce the needed operators by 6.88% compared to manual planning.