Optimal Conserve Inventory from One Outturn Gizmos to Two Intake Gizmos When Inter-Arrival Breakdown is a Random Variable

In inventory control theory the one of the important model is to estimate the conserve inventory when the stations are in series. In this model a system with two nodes are suggested. In the first phase it is assumed that there is only machine A
1
and the second phase as two machines say
$B_{2}^{1}$
and
$B_{2}^{11}$
. The machines in the second stage may have same or different process types. During the breakdown time of the machine in the first stage a reserve inventory is maintained to ensure uninterrupted production in the next stage. This conserve inventory is needed as otherwise; the machines in the second stage may become idle which will impact not only the profits but also bring loss due to non-functioning of machines. Mathematical models has been derived for obtaining conserve inventory by treating repair time and inter arrival time as random variables