Much of the research in perishable items inventory management has focused on the first-in-first-out issue process. However, motivated by the technical characteristics of the blood unit issue process, we model an order-up-to-level policy under periodic review setting with random issue of items from inventory. We provide empirical evidence in support of the random issuing assumption using real data on serial numbers of blood units issued from a blood bank. For general demand distribution we derive exact expressions for per period expected shortage, expected wastage and expected cost as functions of the policy parameters R (order-up-to-level) and T (review period). Since the exact model becomes computationally burdensome with increase in the number of periods of life of the perishable item an approximate model for the random issuing process is developed. The accuracy of the approximation is affirmed using simulation analysis. A gradient search-based heuristic is provided to identify the optimum policy parameters for the approximate model. A real life application of the model is demonstrated in determining the optimum frequency and order-up-to-level for blood collection at a blood bank.