A supply chain (SC) is a network of organizations containing suppliers, manufacturers, distributors, wholesalers, and retailers. Each of these components plays its specific role in operations and production to deliver the required products and services to the end consumers. Each entity in this chain seeks its own benefits that can be achieved with or without collaboration with other entities in the chain. Depending on how decisions are made, there are two main types of CS. When each SC entity only considers its own objectives and constraints, the SC is locally optimized and this is called a decentralized control mode. However, when a single decision maker determines his decision policy taking into account the objectives and constraints of all SC entities, we speak of a centralized control mode (Simchi-Levi et al. 1999). The decision policy carried out in centralized mode may not be optimal for each entity; however, it is optimal for the entire SC. In addition, centralized control mode can also be adopted in special configurations. For example, Vendor Managed Inventory (VMI) is a context in which centralized control mode should be used. The replenishment policy of each SC establishment is mainly determined at the tactical stage for the upcoming periods and decision makers have to decide when and when. what quantity to order and/or produce for each entity in order to provide its customers with an appropriate level of service. In an uncertain environment, replenishment planning will be more complex when there is insufficient information on parameters related to other entities in the chain. Sometimes these entities are involved in different types of contracts to coordinate with each other. This reduces the risk in a stochastic situation...... middle of paper ...... imal solution. Then, a simulation method is developed to compare centralized and decentralized SCs. Furthermore, to achieve the near-optimal solution in the centralized model, the Evolution Strategy (ES) algorithm and the Imperialist Competition Algorithm (ICA) as meta-heuristic approaches are applied. The remainder of this article is organized as follows: In section 2, a literature review on inventory systems in the field of SC is represented. Sections 3 and 4 are responsible for defining the problem and also presenting the respective mathematical models. In Section 5, a scenario generation technique is described to deal with demand uncertainty over multiple periods. In Section 6, solution methods are developed to solve the centralized model. In Section 7, the calculation results of a numerical example are presented. Finally, Section 8 contains conclusions and future research directions.