Optimal policy for an inventory system with power demand, backlogged shortages and production rate proportional to demand rate

This article analyzes an inventory system for items with time-varying demand. The way by which demand occurs during the inventory cycle follows a power demand pattern. The production of items allows to add stock in the inventory during a replenishment period. The production rate is proportional to demand rate. Shortages are allowed and completely backlogged. Holding cost, shortage cost and order cost are the costs considered in the inventory model. The aim consists of the minimization of the total cost per inventory cycle. An efficient approach is developed to obtain the optimal scheduling period and the optimal reorder point. In addition, the economic lot size and the minimum cost of the inventory management is determined. Some numerical examples are presented for illustrating the proposed inventory model.