Supplier selection and determination of the lot sizing is an important component of production and logistics management for many companies. Therefore, after the select of preferred suppliers at the first should obtaine the optimize order of each of the suppliers that is the purposes and constraints of determiners. One of the most effective techniques, which can provide optimal solutions with different targets, is multi-objective programming model.Purpose of this study is to design an efficient multi-objective model of optimal to determine the lot sizing to each supplier.This work is done with designation of multi- objective model, to achieve minimizing the cost of the chain, such as the cost of purchasing, storage, transportation, etc., and also maximize the quality of materials that purchased from suppliers. Finally the model is solved by using the meta-heuristic method, multi-objective Non-dominated Sorting Genetic Algorithm II (NAGA-II), and also in order to validate the model using meta-heuristic particle swarm optimization algorithm (PSO) has been solved and results compared with the first method.