Optimal lot-sizing policy for time-varying demand with shortages and deterioration

It has long been assumed that the shortages in inventory systems are either completely backlogged or totally lost. However, it is more reasonable to characterize that the longer the waiting time for the next replenishment is, the smaller the backlogging rate would be. In this paper, we define an appropriate partial backlogging rate to make the present model general and realistic for deteriorating items with time-varying demand and we also consider the opportunity cost due to lost sales. We show that the optimal solution minimizing the total cost is exactly the one that maximizing the profit. In addition, we verify that the optimal replenishment policy still possesses the monotonicity properties. Moreover, to generate a good estimation of the first replenishment time, we provide a simple heuristic by considering a relation between the cost components in the first cycle.