Abstract In recent years, Supply Chain Management (SCM) has been the main focus in various industries in order to improve efficiencies and reduce costs. In today's supply chain, the determination of sale for a specific customer and in a specific period of time is highly considered, especially when dealing with perishable products such as blood, food, etc. These products must be consumed before perishing. This paper represents a model to determines the optimal level of sales for perishable products in a two-echelon supply chain by using the policy of Vendor Managed Inventory (VMI). The proposed model in this paper is formulated based on one vendor and multiple buyers. It aims to optimize the sales profit by using exact and meta-heuristics methods including GA, PSO and CPSO. The results show that applying VMI on two-echelon supply chain for perishable products is an effective approach to optimize the profitability of the proposed network. Key word Supply chain management, Perishing products, Vendor managed inventory, Two-echelon supply chain Introduction: Perishable products have led enterprises to consider various factors to manage the supply chain especially due to their soon expiry date. Moreover, the costs of these products are very high. In addition, many expenses are incurred before the product reaches to the final consumer, including costs relating to manufacturing, warehousing and transportation. However, these perishable products will not be usable after the expiry period. Some perishable products have a fixed known expiry date, usually written on the product label, but some others have random lifetimes, and within time consumers are less likely to buy the products whose expiry dates are closer, and therefore the negative impact on the demand of these products is began due to the time that they spend on the shelf (INTRODUCTION-3). Also, the freshness of perishable products has an impact on their prices during simultaneous selling (INTRODUCTION-4). So the process of modeling perishable products is very complex (INTRODUCTION-2). The system of Vendor Managed Inventory (VIM) is a mechanism where the purchase orders are created by supplier based on order information exchanged by a customer/retailer (INTRODUCTION-5). Although the Vendor Managed Inventory (VIM) has been employed in many papers, because the impact on the cost efficiency of supply chain network, but there is little consideration of how this model has evolved as the implementation matures and progresses (INTRODUCTION-6). In supply chain networks, the VMI system is different from traditional supply chains, each participant in the chain is aware of the needs of customer which helps vendors and retailers to collaborate in an effective way and therefore make the optimal profit. The supply chain includes the interactions of different companies that seek greater market share and decreased costs (INTRODUCTION-8). However, to decrease the risk of disruption that faced by warehouses, support services and markup pricing strategy are examined (INTRODUCTION-10). In order to determine the optimal parameters of the proposed VMI system, exact or meta-heuristic methods can be used. However, the optimal solution to such these problems can be impractical using traditional algorithms, especially for larger problems. Three meta-heuristic methods have been proposed, including co-evolutionary particle Swarm Optimization(CPSO), Particle Swarm Optimization (PSO) and Genetic Algorithm(GA). In this paper, exact or meta-heuristic methods are used to determine the optimal parameters of the proposed VIM system including PSO, CPSO, and GA. While the calculating the optimum order quantities for retailers as the total inventory and transportation cost are reduced by using an algorithm that based on particle swarm optimization PSO to find a near solution, and algorithm GA is used to verify the solution obtained by PSO (INTRODUCTION-9). The rest of the sections of this paper are organized as follows. In section 2, the literature review on different studies is covered. The main subject of these studies covers the application of different inventory models using VIM policy for perishable products. In section 3, some assumptions for modeling the considered problem. In section 4, the mathematical modeling of the two-echelon supply chain system and also the constraints of the problem are presented using the VIM policy. The results are presented in section 5. Finally, the conclusion is presented in section 6. 3.Litreature review: savvy supply chain managers focus on involved all links in managing the flow of products, information and services from their suppliers to their customers, and they pursue tangible results focused on revenue growth, cost and asset utilization (1-L-I-supply chain management). However, the intense pressure comes from government regulatory acts to implement and to become the industries environmental sustainable (ES), and this situation put the manufacturing industries for green practices from raw materials to finished products under pressure (3-L-I government regulation). As the success of green-supply chain management G-SCM system may also depend on appropriate used-product collection strategies (2-L-max profit). Also, the adopting investment strategy lead to reduce emissions, save energy, create value for customers and thus increase the productivity for the manufacturing and service companies (4-L-I-benefits). It is inevitable in green supply chain management GSCM to reduce the harmful impact on the environment (4-L-Ithreates and limitions). In the study conducted by.Razmi, Jafar, Reza Hosseini Rad, and Mohamad Sadegh Sangari on the twoechelon supply chain under the system of VMI. They applied a mathematical modeling to find the optimal value for the cost of inventory in the supply chain.Then, they compared the solution with the traditional methods (2nd new pragraph 6- VIM).Other studies have been conducted on two-echelon supply chain network including 9Taleizadeh, Ata Allah, et al/Taleizadeh, Ata Allah, Shayan Tavakoli, Ioannis Konstantaras, and Masoud Rabbani)paper (2nd new pragraph 7-VIM). Bakeshlu, Ehsan Afshar, et al./Bakeshlu, Ehsan Afshar, Javad Sadeghi, Tahereh Poorbagheri, and Mahziar Taghizadeh. devolped a model for one retailer and one vendor in the VIM system. They used demand rate to minimize the total cost in their VMI supply chain network(2nd new pragraph 8-VIM). Finally,the model is solved using genetic algorithm.An a multi-item economic order quantity model devolped by Nia, Ali Roozbeh, Mohammad Hemmati Far, and Seyed Taghi Akhavan Niaki. They proposed a non-linear programming model to find the optimal solution by application of genetic algorithm (pragraph 9-VIM). In recent years, several inventory models for perishable products have been analysied by researchers. Asghari, Tooba, Soroush Aghamohamadi-Bosjin, and Masoud Rabbani reviewed different inventory models for perishable items. They stated that few studies have investigated the models of profit maximization with demand-choice flexibility ,and the expansion in innovation of pricing policies in various industries has also been recently observed.(3nd new paragraph 10-VIM).Lütke entrup, Gunther,Van Beek, Grunow, and Seiler devolved Mixed-integer linear programming (MILP) models with taking the shelf-life issues in the considerations in production of youghert (3nd new paragraph 11-VIM). According to Myers, a model is designed to maximize the retailer's total profit under uncertainty of customer demand (3nd new paragraph 12-VIM). However, the policy of VMI is rarely considered in the deteriorating items case, as the collaboration between the EOQ model and VIM system of a two-level supply chain is considerd (single supplier-single retailer) based on constant deterioration and demand (3nd new paragraph 13-VIM). Many papers focus on developing a new system of VMI for the supply chain network, as they use VMI to optimize the profit, cost, or overall benefit by focusing on the various goods, especially perishable products with various approaches to find the optimal solution of the proposed network.(1111111111111)(Pramudyo, Cahyono Sigit, and Huynh Trung Luong. "One vendor-one retailer in vendor managed inventory problem with stochastic demand." International Journal of Industrial and Systems Engineering 27.1 (2017): 90-106.) The success of the VMI of the buyer is affected by the quality of the relationship between the buyer and the supplier, and the mentioned system leads to improve supply chain control, higher levels of customer service and cost reduction (4nd new paragragh 14-the purpose of VIM). Companies are less able to compete effectively in isolation from their suppliers and other entities in the supply chain, so they seek to develop links to be more effectively to extend across traditional corporate boundaries. (4nd new paragraph 15-the lack of clarity in supply chain management). Also, the role of information technology plays in supply chains by integrating different functions into their overall process through flow coordination, information integration and inter-organizational collaboration (4nd new paragraph 16-the uncertainty). Most papers address the perishable products that assume a one-level supply chain network. This is evident in many studies such as: new para(one-1),new para (one-2) Furthermore, there are a limited number of studies that look at the two-echelon supply network for perishable products, like studies of new para (final) In addition, few of these studies have taken VMI into account to optimize the total profit of the sales model (new para(two-1)). Copeing in markets where the customers have well-established preferences, i.e. they demand high-quality products, fresh ,but it is almost impossible to guarantee a timely and adequate supply of products under uncertainty regarding the size, quality and timing of catches is high (5nd paragraph 17-the flucation). In the study present that using VMI in a two-echelon supply chain network, a bi-objective non-linear optimization model to maximize the profit of inventory and to minimize the carbon emissions of transportation is developed (6 nd paragraph 18-the two supply chain management).While the Mixed Integer Non-Linear Programming (MINLP) model is formulated to maximize the profit and minimize the total cost of four-echelon citrus supply chain (7nd paragraph 19-fourth supply chain). On the other hand, focusing on one echelon of the supply chain is a one of the limitation of the this study (7nd paragraph 20one supply chain management). In order to address the research gap, this paper has developed the aim of maximizing the total profit of the two-echelon supply chain network for perishable products. Besides, utilizing the VIM system in the entire supply chain management helped to obtain the appropriate information of the customer and adjust the sale to achieve the optimum profit. Also we can get the best solution when dealing. In addition, we can determine the better solution when dealing with multiple customers by applying the exact method with three effective meta-heuristics method. Accordingly, this paper studies these issues and develops a model for the perishable products to reduce or eliminate the effects of deviations in traditional networks, and works on the policy of VMI in a two-level supply chain network to maximize sales profits.