【摘要】Inventory pooling is an important operational concept that has been widely used. An important open problem is to obtain the optimal inventory level for multiple customers who require different service fill rate. The main focus of this paper is to analyze the necessary and sufficient conditions on the inventory level for this class of problem. There are two main contributions: First, we derive a general expression for the bound on inventory level to meet differentiated service level for multiple customers. Second, we propose a class of allocation policies and prove that it is asymptotically optimal using Blackwell Approachability Theorem. Numerical studies show that our allocation policy can accurately deliver the correct service level to different customer using minimal level of inventory.