Improvement of the Supply Chain Through Engineering and the PRP Heuristic Algorithm: Models and Case Studies

Abstract : This study presents a comprehensive literature review and technical analysis of the Production Routing Problem (PRP), focusing on integrated supply chain optimization. The research evaluates various mathematical approaches, including distributionally robust models for perishable goods and multi-scale production facilities. A core component of this work is the assessment of heuristic and matheuristic tools, such as Adaptive Large Neighborhood Search (ALNS), Genetic Algorithms (GA), and Variable Neighborhood Search (VNS), which are identified as highly efficient for solving large-scale industrial problems. Additionally, the study provides a detailed implementation roadmap, including an estimated budget ranging from $23,000 to $48,000 and a timeline of 4 to 8 months for full supply chain integration. Statistical validation through a Cost ANOVA confirms significant cost variations across different implementation phases ($p < 0.05$), highlighting the importance of strategic planning in staff training and software consultancy. The findings suggest that the integration of production, inventory, and distribution not only reduces total operational costs but also supports sustainable decision-making by balancing economic performance with environmental impact.