Optimization and Allocation Model of Idle Resources in Shared Supply Chain Based on Differential Game Theory and Optimal Control Theory

In China’s current economic growth, facing traditional development limits, the 19th National Congress proposed efficient resource utilization. The sharing economy, leveraging modern tech like the Internet, big data, and cloud computing, connects idle resources with sharing platforms, enhancing resource circulation and use. Emerging forms like "shared supply chains" reconfigure surplus and idle resources, aiming to improve utilization and reduce waste. This article focuses on idle resource matching dynamics in supply chains under sharing platforms, studying centralized and decentralized decision-making scenarios. It uses the Hamilton Jacobi Bellman (HJB) equation to find optimal matching, sharing trajectories, and profits in single supply-demand systems. For multiple parties, it aims to maximize profits, with the sharing ratio as the control variable. The article expands sharing economy research, aids enterprise decision-making, and aligns with national economic trends. It promotes resource integration, reduces costs, enhances competitiveness, and achieves win-win situations. Future research can explore matching effort, idle resource quantity impact, and system stability in uncertain supply-demand situations.