Abstract
This paper analyzes an inventory system with Poisson demands, fixed ordering size, in which the number of items supplied in a replenishment (of one single order) is a random quantity. A modified (s, S) policy with full backlogging is adopted. The maximum number of pending orders is assumed to have a finite upper limit, to make the model more realistic. The rate of delivery of an order depends both on the supply quantiy and the number of orders pending at that instant. The main result establishes the existence of the limiting distribution of the inventory level in a matrix geometric form and derives it explicitly.
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