Effectiveness of N-Policy in Managing a Multi-server Stochastic Inventory System with Service Time: A Comprehensive Analysis

Stochastic models for inventory management are powerful tools that help to optimize inventory decisions and reduce inventory risk. This paper presents an N-policy in a multi-server continuous review (s, S) stochastic inventory system with service time. The system comprises c homogeneous parallel servers, activated based on predetermined queue length thresholds. Inter-arrival time, service time, and lead time are assumed to follow exponential distributions. The study establishes a necessary and sufficient condition for system stability. The Matrix-Geometric method is used to study the characteristics of this model. The performance measures of the system are found, and an appropriate cost function associated with it is developed. The performance evaluation and optimization issues are also discussed and presented both numerically and graphically. Through rigorous numerical calculations, the optimal (s,S) pair is determined for specific parameters. This comprehensive analysis enhances our understanding of stochastic models in inventory management, offering valuable insights into system dynamics and facilitating informed decision-making for efficient inventory control and risk reduction.