Optimal lot size for an item when holding cost is moved by depletion rate of inventory above a certain stock level

In this paper, a deterministic inventory model with depletion rate dependent holding cost is developed. The demand rate is a power function of the on-hand inventory behind to a certain stock level, at which the demand rate becomes a constant. Shortages are allowed and partially backlogged with the function of waiting time of next replenishment. It is also proved in this model that the optimal replenishment policy not only exists but also is unique. Furthermore, it is provided a simple solution procedure for finding the maximum total profit per unit time. Numerical examples have also been given to illustrate the model and real managerial fact in inventory holding for stock dependent demand.