EOQ-based inventory management in single-machine multi-item systems

The present paper proposes an approach for including the finite capacity constraint in the EOQ model (and, in more general terms, in inventory systems) to study the context of single-machine multi-item systems. In particular, the proposed approach regulates the processing of different items by a shared resource according to a control model based on an ordering policy that combines the Economic Order Quantity with a policy based on minimum and maximum inventory levels (min–max policy). To achieve such a challenging result, the present work exploits the analogy between “switched arrival systems” (a particular class of hybrid systems) and min-max inventory systems. The development and parameterization of the abovementioned control model, therefore, refers to switched arrival systems control theory and mixed-integer linear programming. The present work also contributes to the integration of static tools (i.e., the EOQ model) and control tools, approaching these areas. The paper concludes with a real case application that illustrates the proposed approach and allows for a future research path to be drawn.