In this paper, a mathematical model of multi-objective, multi-item, multi-product, and multi-period mathematical model has been developed in which several objectives; profit, total cost, and overall customer service level (OCSL) have been optimized using the Ɛ-lexicographic procedure. The potential network of supply chain may include two suppliers, one factory, and two retailers. The model considered the network design in addition to the production, inventory, and transportation planning in multi-periods. The proposed model is formulated using mixed-integer linear programming and solved by XpressIVE. The behavior of the model has been verified by solving two scenarios of different demand patterns. The results verify the ability of the developed model to assist the SC organizations to manage their networks more efficiently.