Can the Desired Service Level be Achieved When the Demand and Lost Sales are Unobserved?

In this paper we consider an inventory management problem in the retail industry with unobserved lost sales. The retailer does not know the demand for a particular product but she has access to Point-Of-Sale (POS) data. The retailer uses a fixed review period, order-up-to level system to control the inventory. The objective of the retailer is to achieve a pre-specified service level. We define the service level as the fraction of demand satisfied from inventory. However, due to the unobserved lost sales nature of the problem, the retailer cannot exactly measure the current service level. We propose a POS data-based mechanism for periodic updating of the order-up-to level. We show that the periodic updating approach yields the desired service level without using any inventory information. Once the periodic updating scheme converges, it also gives the actual demand distribution.