In the supply chain of modern manufacturing industry, the problem of lot-sizing is one of the key factors for enterprises to maximize their economic benefits. It mainly studies to determine the best production scheme for a given batch of products to minimize the sum of manufacturing costs, inventory costs and adjustment costs or to maximize profits. In recent years, swarm intelligence algorithms such as genetic algorithm and particle swarm algorithm provide a new way to solve the complex lot-sizing problem, but these algorithms are prone to fall into local optimal. In order to obtain the overall situation, this paper integrates the quantum algorithm into the classical evolutionary genetic algorithm. First, the decision variables of planned output are encoded with the unique probability amplitude and quantum bit in the quantum theory. Then, in the iterative process, the mutation rate of the gene is controlled by dynamically adjusting the quantum rotation Angle to maintain the genetic information of the optimal individual, so as to avoid falling into the trap of local optimization. The empirical case of lot-sizing problem shows that, compared with the common swarm intelligence particle swarm optimization algorithm mentioned above, the quantum evolutionary algorithm has higher accuracy and faster convergence speed, which can effectively solve the complex and multi-constrained lot-sizing problem and improve the production efficiency of enterprises.