This paper presents an extended integrated inventory model with multi vendors that produce one item product and supply it to multi buyers. It is assumed that vendor production rates are not equal and the demands of buyers assumed to be normally distributed and independent. The model formulation was made for each buyer and vendor. Then, each cost component from the buyer and vendor is combined to form the total inventory costs. This model uses the service level as constraint. The final mathematical model consists of formulations of the total inventory costs and with certain service level
