Queueing Inventory with an Additional Mode of Production

Abstract

We consider a queueing inventory system in which customer arrives according to a Poisson process with rate λ and inventory items being served with negligible service time. When the inventory level drops to a defined threshold s, production of items begins, continuing until the inventory reaches the maximum capacity S. The time required for normal production of an item is exponential with parameter β. When the inventory level further drops to another specified level r, the production rate increases to θβ, where θ>1. The system reverts to the normal production mode when the inventory level reaches r + 1. The system is studied in detail, and stationary probabilities are computed, along with various performance measures. A numerical illustration is provided. Sensitivity analysis is conducted to analyze the effect of various parameters on the system performance.