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A new economic order quantity (EOQ) model is developed for multi-item and multi-storehouse with limited funds, limited storage capacity and stochastic demand. The model is proved to be a nonlinear convex programming. For finding the optimal replenishment schedule, we design a new particle swarm optimization (PSO) algorithm that combines gradient acceleration and penalty functions. Comparing with the basic PSO and some other optimization algorithms, this improved algorithm adequately utilizes the gradient information and fitness values of objective function. Numerical results show that the improved PSO is feasible and can get better convergence efficiency and higher solution precision than the basic PSO and genetic algorithms.