Multi-objective sustainable closed-loop agricultural supply chain optimization under uncertainty respecting water circularity: olive products

Abstract Driven by economic fluctuation and environmental concerns, the agricultural sector urgently requires integrated closed-loop supply chain (CLSC) models that balance profitability with sustainability. Current literature often overlooks simultaneous economic and environmental objectives, particularly concerning water circularity and reverse logistics in the olive industry. This study addresses this gap by proposing a novel bi-objective mixed integer linear programming model designed to minimize both the total supply chain cost (encompassing procurement, facility setup, operation, storage, and transportation) and total water consumption. Uncertainty regarding product yield, influenced by factors like climate and soil, is systematically incorporated using the possibilistic programming approach. The comprehensive network explicitly models forward flows, reverse logistics, package recovery, and rich wastewater utilization. This complex mathematical problem is solved using four rigorously tuned multi-objective metaheuristics (NSGA-II, NRGA, MOVNS, and MOSA). Applied to a real-world olive network case study, the model demonstrated major reductions in logistics costs, waste production, and water use. A critical finding reveals that the most impactful leverage point for water and cost efficiency lies upstream in cultivation practices (e.g., irrigation management and pest control), rather than downstream industrial recovery, providing actionable guidance for sustainable supply chain management. This research delivers a unified decision framework for water-aware CLSCs under uncertainty.