N-Policy in a Multi-server Stochastic Production Inventory System.

The paper presents the integration of the N-Policy into a multi-server stochastic production inventory system. The system comprises c identical servers, and each server activates sequentially if there is sufficient queue length and inventory; otherwise, it remains idle. Inactivity persists until the queue length reaches a predetermined manageable threshold or until there is inadequate stock. A necessary and sufficient condition for the system’s stability is established. Performance measures for the system are defined, and a relevant cost function based on these measures is formulated.