An inventory model with server interruptions and retrials

In the previous chapter we assumed that replenishment is instantaneous and no shortage is permitted (shortage cost infinity).In this chapter we assume that replenishment of inventory does not materialize immediately as placement of order ,rather takes a random amount of time for order materialization .Thus we have now a finite shortage cost situation. Another salient feature of this chapter is that the QBD we develop here is level dependent. The reason behind this is the state dependent retrial rate of orbital customers. LDQBD's are much more complex than LIQBD's since we do not get a repeating pattern for the entries of the infinitesimal generator of the process. However we make it level independent through a process called truncation. The first study on inventory models with positive lead time, with unsatisfied customers thus created going to an orbit to try again for inventory from there, was by Artalejo et. al [6]. Whereas their approach is algorithmic, Ushakumari [68] produces analytical solution to the same model. Following these, a number of papers on inventory models with retrial of unsatisfied customels emerged. One may refer to Krishnamoorthy and Islam [30,31] Two other papers where an inventory model with retrial of demands is considered " The results of this chapter was presented as a paper at the8 " ' lntemational Workshop on