A stochastic periodic review inventory model with back-order discounts and ordering cost dependent on lead time for the mixtures of distributions

A mixture inventory system analyzed in this paper explores the problem that the lead time and ordering cost reductions are inter-dependent in a periodic review inventory model with back-order price discounts for protection interval demand with the mixture of normal distributions. The objectives of this paper are twofold. First, we want to correct and improve the recently studied model by optimizing the review period, back-order price discount, target level and lead time simultaneously to achieve significant savings in the total related cost and higher service level. Second, we consider that the demands of the different customers are not identical in the protection interval to accommodate more practical features of the real inventory systems. For the proposed model, a computational algorithm with the help of the software Mathematica 7 is furnished to derive the optimal solution. Finally, we provide numerical examples to illustrate the results.