Production inventory with service time and interruptions

In all the studies on inventory systems prior to Berman et al [8], it was assumed that the serving of inventory is instantaneous. However this is not the case in many practical situations. For example in a TV showroom, a customer usually spends some time with the salesperson before buying the TV or in a computer shop, after selecting the model, one might have to wait until all the required software are installed. In Berman et al [8] it has been assumed that the amount of time taken to serve an item is constant. This leads to the analysis of a queue of demands formed in an inventory system. This study was followed by numerous studies by several researchers on many kinds of inventory models with positive service time. Krishnamoorthy and Viswanath [47] introduced the idea of positive service time in to a production inventory model by considering MAP arrivals and a correlated production process. This model being a very general one as far as the modeling parameters are considered, only a numerical study of the model was carried out there. In a very recent paper by Krishnamoorthy and Viswanath [48], assuming all the underlying distributions as exponential, a