Effect of Local Purchase on Feedback Queueing-Inventory with Reservation, Cancellation and Common Life time

Abstract

Consider a queueing system to which an inventory is attached. Customers arrive according to a Poisson process and inventory is supplied instantaneously. The inventory is replenished according to (  ) policy and lead time is exponentially distributed. After collecting inventory customers undergo a feedback. Those who want additional service join a queue, whereas other customers leave immediately after collecting inventory.  be the probability of asking for additional service (we call such customers as Feedback customers). These customers are served according to an exponential distribution. Instead of assuming customers not joining the system when inventory level is zero (as is done in several recent investigations), we introduce local purchase of the item to serve the demand during that period of time. The rate of service is slowed down when the reorder level is reached, to minimize local purchase. Just as provision for reservation is given to customers (purchase of inventory), cancellation (return of purchased item before realization of Common Life Time (CLT)) of ordered items, is also allowed. Reservation and cancellation rates are assumed to be exponential. Inventoried items are subject to decay;however, those in a cycle have a common life time (CLT). The steady state probability vector is calculated and some performance measures are discussed. The effect of local purchase is studied.