Models and methods to support a new type of inventory performance measure: The expected shortages when a stockout occurs

When analyzing a reorder point, order quantity (r,Q) inventory systems, one important question that often gets very little, if any, attention is: When a stockout occurs, how large is it? This paper is directed at researchers and practicing inventory planners with two objectives. First, we provide several models and algorithms to compute the Expected Shortages When a Stockout Occurs (ESWSO) for a variety of stochastic environments. We show that when ESWSO is used in conjunction with the traditional fill rate measures it greatly enhances a planner's ability to plan for shortages. Second, we develop two cost-minimizing inventory models – one addressing the backorder and the other the shortage scenario – to show how the ESWSO can be seamlessly integrated into an inventory–cost framework to specify lot sizes and safety stocks.