Sustainable Phosphorus Fertilizer Supply Chain Management to Improve Crop Yield and P Use Efficiency Using an Ensemble Heuristic-Metaheuristic Optimization Algorithm

Phosphorus (P) is the most important substance in inorganic fertilizers used in the agriculture industry. In this study, a multi-product and multi-objective model is presented considering economic and environmental concerns to design a renewable and sustainable P-fertilizer supply chain management (PFSCM) strategy. To handle the complexities of the model, an ensemble heuristic-metaheuristic algorithm utilizing the heuristic information available in the model, the whale optimization algorithm, and a variable neighborhood search (named H-WOA-VNS) is proposed. First, a problem-dependent heuristic is designed to generate a set of near-optimal feasible solutions. These solutions are fed into a population-based whale optimization algorithm which benefits from exploration and exploitation strategies. Finally, the single-solution variable neighborhood search is applied to further improve the quality of the solution using local search operators. The objective function of the algorithm is formulated as a weighted average function to minimize total economic cost while increasing crop yield and P use efficiency. The experimental results for a real case study of the P-fertilizer supply chain confirm the effectiveness of the proposed method in improving the crop yield and P use efficiency by 33% and 27.8%, respectively. The results demonstrate that the proposed H-WOA-VNS algorithm outperforms the Heuristic, WOA, and VNS models in reducing the total objective function value of the PFSCM model by 9.8%, 2.9%, and 4%, respectively.