Performance analysis and optimization of hybrid manufacturing systems under a batch ordering policy

We consider a stochastic two‐stage hybrid manufacturing system for a single product where semi‐finished goods are Made‐To‐Stock (MTS) and then differentiated when demand is realized through a Make‐To‐Order (MTO) stage. Inventory for semi‐finished goods is held between the two stages. We introduce a batch ordering policy to permit economies of scale in ordering due to a cost associated with each order placed. We use the Matrix‐analytic method to evaluate system performance under this ordering policy. Afterwards, we develop an optimization model to find the optimal intermediate buffer size and the optimal replenishment order quantity for the system. We show that a base stock policy is sub‐optimal in the presence of a replenishment cost for semi‐finished goods. The savings from adopting the batch ordering policy can be high while the response time for most customer orders is not affected.