Exploring Queueing Inventory Systems: A New Perspective on Managing Stock and Service Efficiency: Have you ever wondered how businesses manage their inventory while ensuring customers don’t have to wait too long for service? This balance between stocking products and serving customers efficiently is a crucial challenge in operations management. 

Prof. R. Sivasamy published an article (13 June, 2025), "On a Queueing Inventory System with Lost Sales, PH Vacation, and Random Order Size (s, S) Policy," in the ‘Arabian Journal of Mathematics’ explores this fascinating intersection of queueing theory and inventory management. The article is now available for viewing, downloading, and citation at [Springer](https://link.springer.com/article/10.1007/s40065-025-00529-9). 

This study introduces a Queueing Inventory System (QIS) that accounts for lost sales, vacation periods, and random order sizes—offering valuable insights into optimizing stock levels while maintaining service efficiency. 

A QIS is a mathematical model that helps businesses determine how to manage inventory while serving customers efficiently. It combines two essential components:  1. Queueing Theory – The study of waiting lines, helping businesses minimize customer wait times, 2. Inventory Management– The process of stocking and replenishing goods to meet demand.  By integrating these two concepts, businesses can reduce stock shortages, minimize customer wait times, and optimize operational costs. 

This research introduces a (s, S) inventory policy, where: ‘s’ represents the minimum stock level that triggers a new order, ‘S’ is the maximum stock level after replenishment. Additionally, the study incorporates ‘Phase-type (PH)’ vacations, meaning the service provider takes breaks when stock is depleted, affecting customer flow and inventory dynamics. 

Efficient inventory management is crucial for businesses, especially those dealing with fluctuating demand. Imagine a grocery store running out of essential items—customers may leave, resulting in lost sales. Similarly, if a store over-orders, it may face storage costs and waste. 

To make a balance between random demands and costs, this study provides a mathematical framework to help businesses: 1. Predict stock shortages and adjust order sizes accordingly, 2. Minimize lost sales by optimizing inventory levels and 3. Balance service efficiency with stock availability. 

Real-World Applications:

1. Retail & E-Commerce: Online retailers and supermarkets can use queueing inventory models to ensure they have enough stock while avoiding excessive inventory costs.
2. Healthcare & Pharmacies: Hospitals and pharmacies rely on inventory systems to manage medical supplies efficiently, ensuring patients receive timely care.
3. Manufacturing & Logistics: Factories and warehouses use queueing inventory models to streamline production and distribution, reducing delays and excess stock.