A multi-level inventory system with a make-to-order supplier

We study a supply network comprising a factory, a central warehouse using a discrete-time reorder point-reorder quantity policy and multiple regional distribution centres applying discrete-time base-stock policies under consideration of a fill rate constraint. The warehouse is supplied from the factory, which has a limited capacity and which follows a make-to-order strategy. The complete system is analysed by decomposition into three layers that are linked through layer-specific random replenishment lead times. An overall optimisation model including as decision variables the processing time in the factory and the parameters of the inventory policies applied in the warehouse and the distribution centres is formulated and solved.