Optimization of Distribution Risk of Hazardous Materials in the Production Routing Problem for Rail Supply Chain

Abstract

The production routing problem (PRP) typically arises from the integration of lot-sizing and vehicle routing challenges. Prior research has demonstrated that this integration can significantly reduce operational costs. This paper investigates the PRP with a primary focus on minimizing risks associated with the production and distribution of hazardous materials (hazmat) via rail networks. As sustainability concerns regarding social and environmental impacts grow, addressing the threats hazmat poses to human health and ecosystems becomes critical. Risk serves as the key metric for assessing the dangers inherent in handling these materials. The problem is formulated as a mixed-integer nonlinear programming (MINLP) model. The risk function is nonlinear, influenced by train load, exposed population density, and material-specific characteristics. Due to the computational complexity of solving nonlinear models directly, a genetic algorithm (GA) is employed to solve the model efficiently. Eight benchmark instances were tested to evaluate the model and compare the performance of a direct nonlinear solver against the proposed genetic algorithm. Results indicate that the genetic algorithm yields superior solutions within equivalent computational timeframes. Sensitivity analysis further examines how alterations in production and storage capacities influence overall risk levels. This study introduces a novel production routing framework specifically for hazardous materials, aligned with sustainability goals. It utilizes a nonlinear risk model solved via a genetic algorithm, bridging the gap between production planning and risk-aware distribution in rail supply chains.