Nonlinear stochastic inventory model with single deteriorating item

The problem of inventory is concerned. Considering that people have two reactions: patient and impatient. In a period of stockout of stores, the lost of customers is assumed to be a normal stochastic variable. A nonlinear stochastic inventory model with single deteriorating item is set up. The model is more appropriate to practice. A numerical example is given. By using Matlab, the optimal control strategy is solved, and then the approximately optimal ordering quantity and the approximately optimal length of time of stockout period are obtained.