A stochastic inventory model with lead time and lot size interaction

Most deterministic and stochastic inventory models assume that the lead time is a given parameter, and determine the optimal operating policy on the basis of this unrealistic assumption. In this paper, we incorporate a common inter-relationship between lot size and lead time in the stochastic continuous review inventory control (Q,r) model. We present an efficient iterative procedure that determines the optimal or near-optimal lot size and reorder point that minimize the total annual inventory cost for the extended (Q,r) model. We further propose another analytical procedure that generates the lot size and safety stock simultaneously. We also show that our model will result in smaller production lot size and shorter lead time than an earlier model reported in the literature.