A Production Inventory System with N-Policy and Enhanced Production Rate

This paper investigates the role of N-policy in an (s, S) production inventory system with positive service times. Customer arrivals follow a Poisson Process, while service times and production rates are exponentially distributed. The service mechanism operates under an N-policy, and to enhance production efficiency, the production rate increases when the number of customers exceeds N − 1 and the inventory level falls below min{N, s}. The system is analyzed using the Matrix Geometric method, and a necessary and sufficient condition for system stability is established. Key performance measures are derived, and a suitable cost function is developed to evaluate system efficiency.