Closed-form (R,S) inventory policies for perishable inventory systems with supply chain disruptions

Hospital pharmacy managers make inventory decisions for thousands of different perishable drugs. Commonly, these managers do not have the resources to implement advanced mathematical models. Closed-form solutions are attractive because they provide the inventory policy quickly and are easy to implement. However, when deriving these solutions, one must consider that pharmaceutical supply chains experience disruptions. We first derive closed-form solutions for a non-perishable lost-sales (R,S) periodic review inventory system with supply chain disruptions. We then extend the solutions to incorporate perishability and apply the solutions to a hospital pharmacy inventory system. We find that (i) it is important to account for perishability and supply chain disruptions simultaneously as only accounting for supply chain disruptions increases both drug shortages [possible 65% increase] and waste [possible waste equivalent to 50% of the daily demand], (ii) it is critical to consider the duration of and time between supply chain disruptions, (iii) the expected number of shortages is insensitive to changes in the standard deviation when demand is normally distributed, but for short expiration lifetimes, the expected number wasted increases linearly as the standard deviation of demand increases, and (iv) not accurately depicting the supply chain disruption process can triple the number of shortages.