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 provide the necessary products and required services to the end consumers. Each entity in this chain seeks its own benefits which 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 SC. When each entity of SC only considers its own objectives and constraints, the SC is optimized locally and this is called decentralized control mode. However, when a single decision maker determines his/her decision policy taking into account the objectives and constraints of all SC entities, it is called a centralized control mode (Simchi-Levi et al. 1999). The decision policy reached in centralized mode may not be optimal for each entity; it is however optimal for the entire SC. Furthermore, the centralized control mode can also be adopted in particular configurations. For example, vendor managed inventory (VMI) is one context where centralized control mode should be used. The replenishment policy of each facility in the SC is mainly determined in the tactical phase for subsequent periods, and decision makers should decide when and how much to order and/or produce for each entity to provide its customers with an adequate service level. In an uncertain environment, replenishment planning will be more complex where there is insufficient information on parameters related to entities in other chains. Sometimes, these entities become involved in different types of contracts to coordinate with each other. Reduces risk in a stochastic situation... middle of paper... optimal solution. Next, a simulation method is developed to compare centralized and decentralized SCs. Furthermore, to reach the near-optimal solution in the centralized model, the evolutionary strategy (ES) algorithm and imperialist competitive algorithm (ICA) are applied as meta-heuristic approaches. The rest of this paper is organized as follows: In Section 2, a literature review on inventory systems in the area of ​​SC is represented. Sections 3 and 4 have the task of defining the problem and also presenting the respective mathematical models. In Section 5 we describe a scenario generation technique to handle demand uncertainty across multiple periods. In Section 6, solution methods are developed to solve the centralized model. In Section 7 the computational results of a numerical example are presented. Finally, Section 8 contains conclusions and future research directions.