This paper proposes a Cloud-centric platform offering efficient inventory management as a service for supply chain stakeholders. The offered service will enable all stakeholders in a supply chain to minimize both their ordering costs and their shortage costs, while managing their inventories. The proposed cloud-based platform stores all the data, relating to a given product item, released by the involved stakeholders throughout its life cycle; from its manufacture up to its retail, passing through its distribution, storage, etc. The objective of the offered service is to provide stakeholders, in a supply chain, with efficient replenishment schemes derived collaboratively on the basis of real-time information flow, including retail information. A stakeholder calls the proposed service in order to compute a real-time optimal "inventory threshold", with regard to a given product category, to be considered in its replenishment policy. By optimal we mean that it minimizes the stock disruption likelihood, while minimizing the allocated resources in term of storage space and inventory cash value. The computation of the optimal parameters is based on a probabilistic model. Analytical results illustrate the efficiency of the inventory optimization service offered by our proposed cloud-centric platform.