developing a mathematical model for vendor managed inventory considering deterioration and amelioration items in a three-level supply chain

todays, improving the competitiveness of companies and rapidly responding to diverse customers’ demands requires efficient management of the supply chain. integration is one of the effective indices in a supply chain, and vendor managed inventory (vmi) is one of the innovative approaches in this field. in this paper, an integrated model based on a vmi system for deteriorating and ameliorating items in a three-level supply chain is developed. to coordinate retailers and producers in the supply chain, the common replenishment cycle is used which is a technique of a vmi system. the assumptions of this model consist of a deterministic demand rate for each retailer, certain production and deterioration rates. furthermore, in this paper the amelioration of items is mentioned that follow the weibull distribution. first, a mixed-integer nonlinear mathematical model is presented. then to validate the proposed model, a numerical example is given. to solve the model, a genetic algorithm method is presented.