A queuing system with inventory and competing suppliers

A single-server queuing system is considered where service consumes one unit of inventory which is maintained by two suppliers with different price and replenishment lead times. During inventory stockout, new customers refuse to enter the system (lost sales) but the existing ones remain in queue until inventory becomes available again (backlogged demand). We analytically derive the joint distribution of queue length and on-hand inventory in steady state and determine supplier-specific ordering policies that maximise the average system profit. A special case of the system with multiple servers is addressed. A numerical study reveals dynamics of the optimal ordering policy with respect to price and replenishment lead-times. [Received: 15 April 2018; Revised: 21 November 2018; Accepted: 18 December 2018]