Two commodity perishable inventory system with negative and Impatient customers, postponed demands and a finite population

In this article, we consider a stochastic inventory system with two different items in stock, one is major item (first commodity) and other is gift item (second commodity), and the demands originate from a finite population of N sources. The maximum storage capacity for the i-th commodity is Si (i=1, 2) time points of demand occurrences form independent quasi random distributions. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item (first commodity) is provided as a gift for demanding a second commodity. The items are perishable in nature. If the inventory position of first commodity is zero then any arriving demand for the first commodity either enters a pool or leaves the system according to a Bernoulli trial. The system has been identified as a Markov process and the system performance measures are derived. The total expected cost rate is also considered and the results are illustrated numerically.