The present work aims to strengthen the core competitiveness of industrial enterprises in the supply chain environment, and enhance the efficiency of inventory management and the utilization rate of inventory resources. First, an analysis is performed on the supply and demand relationship between suppliers and manufacturers in the supply chain environment and the production mode of intelligent plant based on cloud manufacturing. It is found that the efficient management of spare parts inventory can effectively reduce costs and improve service levels. On this basis, different prediction methods are proposed for different data types of spare parts demand, which are all verified. Finally, the inventory management system based on cloud-edge collaborative computing is constructed, and the genetic algorithm is selected as a comparison to validate the performance of the system reported here. The experimental results indicate that prediction method based on weighted summation of eigenvalues and fitting proposed here has the smallest error and the best fitting effect in the demand prediction of machine spare parts, and the minimum error after fitting is only 2.2%. Besides, the spare parts demand prediction method can well complete the prediction in the face of three different types of time series of spare parts demand data, and the relative error of prediction is maintained at about 10%. This prediction system can meet the basic requirements of spare parts demand prediction and achieve higher prediction accuracy than the periodic prediction method. Moreover, the inventory management system based on cloud-edge collaborative computing has shorter processing time, higher efficiency, better stability, and better overall performance than genetic algorithm. The research results provide reference and ideas for the application of edge computing in inventory management, which have certain reference significance and application value.