Inventory pooling to deliver differentiated service

Inventory pooling is at the root of many celebrated ideas in operations management. Postponement, component commonality, and resource flexibility are some examples. Motivated by our experience in the aftermarket services industry, we propose a model of inventory pooling to meet differentiated service levels for multiple customers. Our central research question is the following: What are the minimum inventory level and optimal allocation policy when a pool of inventory is used in a single period to satisfy individual service levels for multiple customers We measure service by the probability of fulfilling a customer's entire demand immediately from stock. We characterize the optimal solution in several allocation policy classes; provide some structural results, formulas, and bounds; and also make detailed interpolicy comparisons. We show that the pooling benefit is always strictly positive, even when there are an arbitrary number of customers with perfectly positively correlated demands.