In this research a multi-item economic production quantity (EPQ) model with a single machine is investigated. It is assumed that the production capacity of the machine is limited, with no shortages allowed. The model formulated in this study has been developed such that the objective function is to minimize the total inventory cost where the optimal order and production quantities for each item are the decision variables. In this research a hybrid algorithm hereby called GPSO-LS is proposed to find a near-optimal solution. The proposed algorithm is based on genetic algorithm and particle swarm optimization. In this context, the Taguchi method is used to tune the parameters of the algorithm. Lower and upper bounds for the optimal value of the objective function have been developed in order to measure the quality of the solutions provided by GPSO-LS. Numerical results obtained show the effectiveness of the proposed GPSO-LS and the features of the presented model. A main finding of this study is that increasing the production rate and/or decreasing the demand rate of items reduces the total inventory cost. This finding supports managers in making decisions such as investment in increasing production capacity, resorting to external sources, or incurring lost sales cost.