The optimal inventory model with many orders and permissible shortage

It is a problem for many retailers how to control inventory so that the average inventory profit is maximum or the average inventory cost is minimum, which is concerned more and more enterprises and scholars. At present, the theme of inventory management about several orders and permissible shortage is a popular. These papers are generally used the stationary policy. The economic ordering quantity in inventory management is a well-known stationary ordering policy. In this thesis, an inventory model with many orders and permissible shortage is established. Then, an approach based on Lagrange Multiplier Method is used to prove that the stationary ordering policy is the optimal ordering policy, and attain the optimal ordering number and quantity. At last, the numerical examples are given to verify the validity of the model.