Optimal control policies for dynamic inventory systems with service level dependent demand

Empirical studies have shown that stockouts may adversely affect future demand. However, much of the literature on inventory optimization has ignored this effect. In this paper, we investigate the effect of stockouts on a firm's operational policy and total discounted profit. We show that compared with classic periodic review inventory models with no stockout effect, the optimal inventory control policies for inventory systems with stockout-dependent demand have different but interesting structures. Specifically, the optimal perceived stock-out service levels exhibit a mean-reverting pattern. These results shed lights on operational decisions and customer services to effectively manage inventory systems. Numerical studies show that neglecting stockout-dependent demand can lead to significant drop in the firm's performance when compared with the optimum. This paper deepens our understanding on inventory systems when customer demand is discouraged by stockouts, and it helps inventory managers develop effective inventory control mechanisms that incorporate stockout effect. © 2023 Elsevier B.V.