Efficient policies for an inventory system with power demand pattern and mixture of backorders and lost sales

In this paper we study an inventory model where shortages are allowed. We consider that the demand follows a power pattern. During the shortage period a fraction of the demand is backlogged and the remainder are considered lost sales. The objective consists of determining the lot size and the order level such that the total inventory cost per unit time is minimized. We present a general procedure to obtain the optimal inventory policy and the minimum associated cost.