In this paper, a mathematical model for multi-product inventory management in a three-tier supply chain consisting of multi-supplier, a manufacturer, and several retailers is presented. The model determines different factors such as the optimum ordering of the raw materials and the optimal level of the production items with the optimal order of the products by retailers at each level of the chain, with the objective of minimizing inventory management costs in the supply chain. An algorithm is presented to determine the solution of the problem and the implementation of the proposed method is demonstrated using some numerical example.