An economic lot-size model with partial backlogging hinging on waiting time and shortage period

We study a continuous review inventory control system over a infinite-horizon with deterministic demand where shortage is partially backlogged. The backlogging is characterized using an approach in which the collective behavior of customers hinges on the waiting time and on the shortage period. We assume that the fraction of the customers who are not willing to wait is proportional to the ratio between the waiting time and the length of the shortage cycle. Taking into account the above assumption we determine the optimal inventory policy. Several models studied by other authors result to be particular cases of the considered model.