WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 21, 2022
Exact Solution of the Optimal Control Problem of Coordinating a Supplier-manufacturer Supply Chain in Advanced Geometric Concepts
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Abstract: Supply chain coordination deals with collaborative efforts of supply chain parties and making globally-optimal decisions that can improve 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 optimal solution is identified approximately through numerical estimation. Therefore, in this paper, a novel approach was presented for optimal control problem by developing a new formulation based on advanced ingredients of differential and Poisson geometry. Thus, the exact optimal solution of 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 of a single supplier and a manufacturing firm. For further illustrating 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.
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Keywords: Optimal Control Problem, Hamiltonian System, First Integral, Supply Chain Coordination, Supplier Development
Pages: 55-61
DOI: 10.37394/23202.2022.21.6