Algorithmic Approach to Study Queueing-Inventory Systems with Queue-Dependent Hybrid Replenishment Policy

Abstract

In this study, we discuss a queueing-inventory system with queue-dependent replenishment policy. Arrival of customers occurs according to a Poisson process and the service times follow an exponential distribution. When inventory level drops to zero, only the customer at the head of queue becomes impatient independently of customer number in queue. A hybrid replenishment policy is considered. For this purpose, we define the threshold value r for the number of customers in the queue. So, the queue-dependent replenishment policy is defined as follows: when the inventory level drops to s, if the number of customers is less than r, the (s, Q)-policy is applied; if the number is more or equal r, the (s, S)-policy is applied. Lead times are exponentially distributed for each policy. The system is formulated by a continuous-time Markov chain. Stability condition is established and steady-state distribution is obtained using the matrix-geometric method. Numerical studies are performed. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.