Jointly optimising assembly line feeding and supermarket layouts

Customised products increase the complexity of managing assembly systems efficiently, particularly when multiple part variants are required for assembly, necessitating adept handling of limited space within assembly lines. Leveraging diverse feeding policies efficiently optimises space utilisation and minimises logistical complexity in part feeding. Moreover, strategic decisions regarding the placement and sizing of preparation areas are crucial for smooth intra-logistics flows. Precise cell placement facilitates efficient transportation between preparation areas and assembly lines, reducing transportation costs, while optimal sizing minimises spatial costs. In response to these challenges, we propose a mixed-integer optimisation model that determines a feeding policy for each part and assigns parts requiring preprocessing to either regular or line-integrated cells. The collection of these cells forms the supermarket. Exploiting a callback procedure, the model ensures that navigating regular cells sharing the same delivery frequency and assembly station sequence is done by the dedicated automated guided vehicle. We enhance model efficiency using valid inequalities and symmetry-breaking constraints and validate the approach through extensive experiments on artificial instances. The results demonstrate that our cell-design optimisation approach is more cost-effective than both a simplified supermarket-based planning strategy that omits detailed cell structures and an operational simplification case restricted to line-integrated cells.