‎Optimal Control Problem: A Case Study on Production Planning in the Reverse Logistics System

Document Type : Research Article

Authors

• Mohammad Eshaghnezhad ¹
• Amin Mansoori ²
• Sohrab Effati ²

¹ Department of Applied Mathematics, Faculty of Basic Sciences, Shahid Sattari University of Aeronautical Science and Technology, Tehran, Iran.

² Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

10.22067/jstinp.2023.81194.1037

Abstract

Finished products and manufacturing plants are some elements of the production system in the supply chain, and there are other manufacturing plants. They produce work in process and finished products and hold them in warehouses. So, they need to plan and control production and inventories. Isolated planning and control by different manufacturers increase inventories in them, and then they must plan and control integratory. This paper presents an iterative approach for solving the optimal control problem with bounded control variables. The projection function constructs ‎the iterative method to approximate the control law. Employing the approximation of control law, the approximation of state and the co-state variables are obtained. For this purpose, we apply the Hamiltonian of the optimal control problem. From the Hamiltonian, the approximation of control law and then the approximation of state law is obtained. A simple example is given to compare the results with another published paper. Also, a case study on production planning in a three-stock reverse logistics system with deteriorating items is derived to show the method's performance.

Keywords

• Optimal control problem‎
• ‎Projection method‎
• Production planning system‎‎
• Reverse logistics system

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