University of Guilan Journal of Mathematical Modeling 2345-394X 13 2 2025 05 01 Balancing efficiency and shortage costs: optimal production and inventory control in a distribution network 327 339 8288 10.22124/jmm.2024.28014.2464 EN Mohammad Saffari Department of Industrial Engineering, Tafresh University, Tafresh 39518-79611, Iran Mohammad Ali Mehrpouya Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran Journal Article 2024 07 24 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. https://jmm.guilan.ac.ir/article_8288_5fcb891a9a2a0c2ac9c184769c24afeb.pdf