In this paper, a new period-based approach is proposed for modeling a capacitated inventory system, operating under an (S,T) policy with backlog. The system experiences stochastic discrete demand and lead time. By using the proposed method, a mathematical model is developed. The model can accurately estimate the inventory system measures of performance: the expected inventory on-hands and over-storage amount. Through a simulation experiment, the new model is compared with two other models, which are developed by using a widely used mean-based approach. The comparison is conducted based on a case study data set. The results demonstrate that the period-based model is superior to the mean-based models with respect to capturing the behaviors of the inventory system. Therefore, better inventory policy parameters can be obtained by employing the new model.

In this paper, a period review inventory model with controllable lead time has been considered where shortages are partially backlogged. The backorder rate is dependent on the backorder discount and the length of the protection interval, which is sum of the review period and the lead time. Two cases have been discussed for protection interval demand which are (a) Demand distribution is known (Normal Distribution) (b) Demand distribution is unknown (Minimax distribution). Further, algorithms have been developed which jointly optimize the backorder discount, the review period and the lead time for each case. Numerical examples are also presented to illustrate the results.