Mixed model assembly line feeding with discrete location assignments and variable station space

Nowadays, the number of parts used in assembly systems is constantly increasing due to more product models being produced in different variants. Therefore, providing all parts to an assembly line in an efficient manner is a crucial task as space is getting more and more scarce. Preparing parts by sorting them into kits or smaller bins seems to be useful to avoid overcrowded workstations at the assembly line. However, costs increase when parts have to be prepared in such ways. We formulate a new mathematical programming model to evaluate different policies for feeding, i.e., the provision of material to assembly stations. For this, it is not only decided which feeding policy is used for a part but also where exactly it is stored at the assembly stations. Furthermore, we propose a mechanism to decide on the available space per station, allowing cheaper but more space consuming policies at some stations. We prove the proposed problem to be NP-hard and propose a model-specific solving procedure using preprocessing, valid inequalities, and Branch & Cut to cope with the difficulty of the problem. Finally, the model is validated by using artificially created data based on a case study with datasets containing up to 3000 parts, reflecting real-world assembly systems. Major findings of this research are on the selection of policies and the determination of space per station. For this, factors that influence these decisions but also overall costs are investigated.