An inventory system with Markov dependent reordering levels (Q916555)

The authors study an inventory system of the (s,S) type when the demands occur for one unit at a time in such a way that the time intervals between successive demand epochs form a family of independent and identically distributed random variables with a common distribution function G(.). The recorder levels are assumed to vary according to a Markov chain over the state space \(\{\) 0,1,2,....,s\(\}\) with \(s\leq S-1\). The replenishment is assumed to be instantaneous (unfortunately the authors do not state this explicitly). The inventory level process is studied and the limit distribution of the inventory level as \(t\to \infty\) obtained. The total expected cost per unit is taken as the objective function and using the convex nature of the function, constraints are obtained. A numerical example is provided when \(s=2\).