MILP for the inventory and routing problem for replenishment the car assembly line

The inbound logistics for feeding the workstation inside the factory represents a critical issue in the car manufacturing industry. Nowadays, this issue is even more critical than in the past since more types of cars are being produced in the assembly lines. Consequently, as workstations have to install many types of components, they also need to have an inventory of different types of components in a usually compact space. The replenishment of inventory is a critical issue since a lack of it could cause line stoppage or reprocessing. On the other hand, an excess of inventory could increase the holding cost or even block the replenishment paths. The decision of the replenishment routes cannot be made without taking into consideration the inventory needed in each station during the production time, which will depend on the production, sequence plan sent by the central office. This problem deals with medium-sized instances and it is solved using online solvers. The contribution of this paper is a MILP model for the replenishment and inventory of the components in a car assembly line.