In this paper, a mathematical model for a multi-item multi-period capacitated lot-sizing problem in an integrated supply chain network composed of multiple suppliers, plants and distribution centers is developed. The combinations of several functions such as purchasing, production, storage, backordering and transportation are considered. The objective is to simultaneously determine the optimal raw material order quantity, production and inventory levels, and the transportation amount, so that the demand can be satisfied with the lowest possible cost. Transfer decisions between plants are made when demand at a plant can be fulfilled by other production sites to cope with the under-capacity and stock-out problems of that plant. Since the proposed model is NP-hard, a genetic algorithm is used to solve the model. To validate the results, particle swarm optimization and imperialist competitive algorithm are applied to solve the model as well. The results show that genetic algorithm offers better solution compared to other algorithms.