Stochastic inventory model with finite production rate and partial backorders

One of the most widespread stochastic inventory models is the classical stochastic continuous review inventory control (Q, R) model. However, there are some restrictive assumptions in deriving this model. One of these assumptions is that the production rate is infinite which has motivated many researchers to develop (Q, R) models with finite production rate. In these models, the randomness of demand is indirectly introduced in the models by assuming that the safety stock is equal to a safety factor multiplied by the standard deviation of lead time demand. In this paper, the classical stochastic continuous review inventory control (Q, R) model is generalised for the case when the production rate is finite and unmet demand is partially backordered. Unlike the models presented in the literature, the probabilistic nature of the demand is reflected directly in the formulation of the proposed model. Furthermore, the optimal lot size and reorder point are determined for this model. Two types of items are investigated; fast‐moving and slow‐moving items. Also, the effect of the production rate on the optimal solution is studied through numerical examples. The results show that the production rate impacts the inventory and production decisions significantly.