Summary: For a finite planning horizon, there has been a considerable body of research papers in the area of operations management that dealt with four different inventory shortage models in the last two decades. In this paper, we establish the models to reflect the fact that the longer the waiting time, the smaller the backlogging rate. We then use maximizing profit as the objective to make an appropriate comparison among those four alternatives. The theoretical results reveal that Model 4 provides the highest profit only if the profit margin is sufficiently low. Otherwise, in general, Model 3 has the highest profit among them.