Annals of Operations Research

, Volume 233, Issue 1, pp 335–364

A retrial inventory system with single and modified multiple vacation for server


DOI: 10.1007/s10479-013-1417-1

Cite this article as:
Padmavathi, I., Sivakumar, B. & Arivarignan, G. Ann Oper Res (2015) 233: 335. doi:10.1007/s10479-013-1417-1


This paper considers a continuous review stochastic (s,S) inventory system with Poisson demand and exponentially distributed delivery time. The demands that occur during the stock out period or during the server vacation period enter into an orbit of infinite size. These orbiting demands retry to get satisfied by sending out signals so that the time durations are exponentially distributed. We consider two models which differ in the way that server go for vacation. The joint probability distribution of the inventory level, the number of demands in the orbit and the server status is obtained in the steady state case. Various system performance measures in the steady state is derived and the long-run total expected cost rate is calculated. Several numerical examples, which provide insight into the behaviour of the cost function, are presented.


Modified multiple vacation policy Single vacation policy Retrial inventory Matrix—Geometric method 



a column vector of appropriate dimension containing all ones.

\({\bf 0}\)

a zero matrix of appropriate dimension.

\({\bf 0}_{(i,j)}\)

a zero matrix with i rows and j columns.


Identity matrix of order n


Heaviside function


Kronecker delta




\(=\left (\begin{array}{c} 1 \\ 0 \\ \vdots\\ 0 \end{array} \right )_{(s+1, 1)}\)


Transpose of es+1(1)

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of MathematicsMadurai Kamaraj UniversityMaduraiINDIA