Sustainable water footprint management in agriculture: a review of linear programming-based models and future directions

The sustainable management of water resources in agriculture is a global imperative as climate change, population growth, and competing demands increasingly strain freshwater systems. This review systematically analyzes 58 peer-reviewed studies that utilize linear programming (LP) and its advanced variants to optimize agricultural water use, with a specific emphasis on improving water footprint (WF) efficiency. Applications are categorized into three core domains: crop allocation and land use, irrigation scheduling, and economic optimization. The findings reveal that although LP continues to dominate, alternative models such as mixed-integer programming (MILP), weighted and fuzzy goal programming (WGP, FGP), and fractional programming, are gaining traction for their ability to address real-world complexities and multiobjective decision environments. However, critical gaps remain, particularly in the integration of WF indicators, climate variability, and socioeconomic dynamics. This review not only maps the existing optimization landscape but also proposes a forward-looking research agenda. Key directions include the development of hybrid models, the explicit incorporation of WF metrics into objective functions, and the integration of decision-support systems for policy and farm-level planning. Water footprint-aware optimization is thus positioned not merely as a technical instrument but as a transformative tool for advancing agricultural sustainability, enhancing resilience, equity, and ecological stewardship in water-scarce regions and beyond.