Balancing stocks and backlogs with stochastic lead times. A special case (Q1085039)

The paper gives compact, finite horizon and asymptotic results concerning an inventory system, that allows backlogging, with constant demand and costs but stochastic lead times, not necessarily i.i.d., under two special conditions. The special conditions are: (1) no crossovers of orders; (2) there are both shortage and stock build-up between any two consecutive orders. It is shown that the minimal total expected cost, namely, of holding inventory, shortages and replenishments, as well as the optimal replenishment times depend, among other parameters, only on the lead time variances as representatives of the stochastic component of the model. The results are direct extensions of the deterministic EOQ model and lend themselves to tractable sensitivity analysis. Further possible developments are discussed.