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

Document Type : Research Article

Authors

1 Department of Industrial Engineering, Tafresh University, Tafresh 39518-79611, Iran

2 Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran

Abstract

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.

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Journal of Mathematical Modeling
Volume 13, Issue 2
May 2025
Pages 327-339

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