Comparison of two periodic review models for stochastic and price-sensitive demand environment

In this paper, we study two periodic review inventory models which primarily differ in terms of how backordering cost is charged: time-independent backordering (TIB) model where the backordering cost is charged per unit backordered and is independent of the length of time for which backorders persist; and the time-dependent backordering (TDB) model where the backordering cost is charged based on the number of backorders as well as the length of time for which they are on the books (i.e., it is charged per unit per unit time). Our objective is to investigate the impact of these two different backordering cost structures on the optimal decisions of a firm in a stochastic and price-sensitive demand environment. In order to do so, we first develop a general framework, where both such costs exist, in a profit maximizing context. Subsequently, we analyze two special cases of this general framework with either one of the costs--that is, TIB and TDB models--and derive some analytical results regarding the values and behavior of the optimal decisions for both of them. We then concentrate on comparing the two models through extensive numerical experiments. Our investigation demonstrates that the TIB model generally results in longer review periods and lower retail prices. As far as the base stock level is concerned, we show that it can be higher in either setting; however, the safety stock is considerably lower for the TIB model. Lastly, indeed if a firm's backordering cost is indeed time-dependent, then use of the TIB model for making decisions results in significant profit penalty under most market/operating conditions (specifically for innovative products), except when demand uncertainty and/or the backordering cost are quite low (i.e., for mature, commodity products).