balancing efficiency and shortage costs: optimal production and inventory control in a distribution network

This article explores the integration of control theory techniques into production and inventory management systems within distribution networks. we examine a distribution network model where each node encompasses production and inventory segments, aiming to enhance overall benefit by adjusting key decision variables like production rate and total release. the proposed model formulates an optimal control problem which emphasizes the nonlinear nature of shortage costs and their impact on decision-making, especially concerning high-cost escalations due to shortages. the study proposes numerical solutions using the legendre pseudospectral method, demonstrating its effectiveness in solving complex optimal control problems with multiple variables.