The customer waiting time in an (R, s, Q) inventory system

In practice of inventory management customer-oriented service measures play an important role. If inventory managers of stockpoints in a supply chain promise specific times of delivery that cannot be met due to a lack of stock, leadtimes at downstream stockpoints increase, causing substantial adverse effects on customer satisfaction. Hence, it is of considerable interest to understand the trade-off between safety stock and customer waiting time. In this paper, we investigate this waiting time in an (R,s,Q) inventory system under compound renewal demand. We provide an approximation for the distribution function of the customer waiting time and we determine the minimal reorder level subject to a maximum average waiting time. In a numerical study we test the performance of our approximation. Moreover, we investigate the effects of the performance of the waiting time in case the underlying demand process is indeed a compound renewal, while a discrete time model is used.