Investigation of a production inventory model with two servers having multiple vacations

Abstract

In this paper, a production inventory system with two servers involving multiple vacations is considered. Customers’ demand is in accordance with the Poisson process. The time for production and addition of each item to the inventory is exponentially distributed. The reloading of the inventory is done as per the (s, S) policy. When no customer waits for service in the system or no inventory is available to satisfy their demands or both, multiple vacations are taken by the servers. The period taken by servers 1 and 2 for their vacation is also exponentially distributed. The system works with the assumption that both the servers are heterogeneous. It is also presumed that their service rates are exponentially distributed with parameters µ1 and µ2. The minimum service rates of both the servers are taken as µ and such a case is also considered with two homogeneous servers. The final algorithmic solution to the problem is obtained by Matrix Analytic Method (MAM). We could also derive some significant measures of performance of the model in the steady state. Finally, we could also construct and analyze cost function numerically.