The Players (Vendors, Retailers, Distributors, Etc.) In a Supply Chain May Belong to Different Corporate Entities and Be More Interested In Minimizing Their Own Cost Rather Than That of the Chain As a Whole. This Kind of Single-Sided Optimal Strategy Is Not Suitable For Today’S Global Competitive Environment. In Real Life, There Are Many Examples In Which a Manufacturer (Here As Vendor) Has Own Set of Direct Outlets (Here As Buyers) to Route the Produced Item to End Customers. a Production Model For Deteriorating Items With the Fuzzy Costs Has Been Developed Taking into Account the Views of Both the Vendor and the Multi-Buyers.