Analysis of Queueing-Inventory System that Delivers an Item for Pre-Booked Orders

This paper considers the delivers an item for pre-booked orders in queueing-inventory system. This system considers the maximum capacity of stock to be S units with two waiting platforms and two dedicated servers. The demands arrive according to the Poisson process and enter into the plafform 1 (PL 1) of size M, including one at the service point. The server 1 (SR 1) is used to pick up orders from the client in PL 1, and the assumption is that orders will be picked even if the stock level is zero. Following order selection, the client joins the platform 2 (PL 2), it has a virtual waiting area of size N.Subsequently, server 2 (SR 2) fabrication the selected orders one by one and distributes them to the PL 2 client. Both service durations are distributed exponentially. The arriving clients are lost if the PL 1 is full. An external supplier replenishes the stock, which is carried out according to the (s, Q) reordering policy. The exponential distribution determines the lead time for reordering. Several numerical results for different parameters are given to clarify the system’s key performance indicators. In addition, an investigation is conducted into the required numerical interpretations to improve the suggested model.