Optimal stock-out risk when demand is driven by several mixed-model assembly lines in the presence of emergency supply

This article focuses on the calculation of the optimal stock-out risk when resorting to emergency supplies is allowed. The studied context is a supply chain where several distant mixed-model assembly lines trigger the demand of a component used for assembly. When the cumulated lead time of a component exceeds the frozen horizon of the material requirement planning (MRP) of at least one of the assembly lines, its demand becomes stochastic. This leads to a mix between production to stock and production to order for the component of interest. The periodic replenishment policy is designed to address demand uncertainty in consistence with MRP information. To prevent stock-out propagation along the supply chain, the emergency supply is used as a last resort. The calculation of the optimal order-up-to-level and its associated optimal stock-out risk are based on a single-period trade-off between holding cost and emergency supply cost (transportation and production).