Stochastic modelling of M/M/2 production inventory systems with vacation scheduling for servers and production unit

Abstract

The article analyzes an M/M/2 multiple vacation production inventory system, where a production facility consists of two heterogeneous servers with multiple vacations. The inventory is restocked according to (s,S) policy. The production facility takes a vacation once the inventory level reaches S, and after completing the vacation, if the inventory level exceeds s, the production facility goes on another random vacation with the same distribution rate. The matrix geometric method is used to estimate the steady state distribution of the obtained Markov chain. Various performance measures and cost analysis are done along with numerical results.