
Exact Solution of the Optimal Control Problem of Coordinating a Supplier-manufacturer Supply Chain in Advanced Geometric Concepts
Author(s) -
Atefeh HasanZadeh
Publication year - 2022
Publication title -
wseas transactions on systems
Language(s) - English
Resource type - Journals
eISSN - 2224-2678
pISSN - 1109-2777
DOI - 10.37394/23202.2022.21.6
Subject(s) - supply chain , optimal control , mathematical optimization , computer science , hamiltonian (control theory) , control (management) , partial differential equation , mathematics , mathematical analysis , artificial intelligence , political science , law
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.