Developing a new formulation and exact solution approach for continuous time optimal control model: application to coordinating a supplier-manufacturer supply chain

Document Type : Research Paper


Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran



Supply chain coordination deals with collaborative efforts of supply chain parties and making globally-optimal decisions that can improve the overall performance and efficiency of the entire supply chain. In many situations, the problem of supply chain coordination requires formulation of a continuous time optimal control model, in which the optimal solution is identified approximately through numerical estimation. Therefore, in this paper, a novel approach was presented for optimal control problems by developing a new formulation based on advanced ingredients of differential and Poisson geometry. Thus, the exact optimal solution of the control problem can be obtained using an analytical methodology that converts the Hamilton-Jacobi-Bellman partial differential equation (PDE) into a reduced Hamiltonian system. The proposed approach was applied to the problem of coordinating supplier development programs in a two-echelon supply chain comprising a single supplier and a manufacturing firm. To further illustrate the applicability and efficiency of the proposed methodology, a numerical example was also provided. The proposed approach offers unique advantages and can be applied to find the exact solution of optimal control models in various optimization problems. The developed method provides further insights into analytical methods for solving supply chain coordination problems and is supported by advanced geometric concepts and structured instructions.