Modelling of an $M/M/2$ production inventory system with multiple vacation
Authors :
P. Beena 1 and K. P. Jose 2 *
Author Address :
1 Department of Mathematics, Government Sanskrit College Pattambi, Kerala, India.
2 P. G. & Research Department of Mathematics, St.Peter’s College, Kolenchery -682311 Kerala, India.
*Corresponding author.
Abstract :
The paper analyzes an M/M/2 multiple vacations production inventory system with two heterogeneous servers. Server 2 avails multiple vacation, whereas the other one continues static even when the system is vacant. At a time one unit of order arrive from customers randomly. We model the system according to (s,~S) policy and the products are manufactured one at a time. The arrival of demands is according to a Poisson process. The duration of the vacation time of server 2 is exponentially distributed. Once the stock position goes down to s, the manufacturing procedure is started and it ceases at the point when the stock position is at the largest extent S. The time gap between the replenishment of two successive items is also distributed exponentially with rate $\beta$ . Matrix Geometric Method is employed to derive the steady state solution. Several measures of performance in the steady state are derived. An appropriate cost function is constructed and numerical experiments are conducted to obtain the optimum value of the cost function for parameter values.
Keywords :
Heterogeneous server, Matrix Geometric Method, Multiple vacation, Cost analysis.
DOI :
Article Info :
Received : November 24, 2019; Accepted : February 10, 2020.
