An analytical approach to optimizing sustainable farm operations through linear reformulation

Abstract

The organic food sector has been steadily gaining prominence and expanding its global market share, driving an increasing demand for advanced optimization techniques to enhance the efficiency of sustainable production systems. This paper addresses machinery routing and activity scheduling in a large-scale organic farm case study by developing two mathematical programming decision support models and testing their efficiency. An initial mixed-integer linear programming (MILP) model, inspired by the Traveling Salesman Problem (TSP), was first proposed to optimize farm operations. However, it revealed computational limitations, making the model intractable when scaled to real operational farm demands. To improve efficiency, a linear programming (LP) model based on the previous MILP model was developed to reduce computational complexity and provide flexibility for future integrations. The model performance and scalability were evaluated using resolution time from five different solvers (two commercial and three open-source) across four progressive planning scenarios with scheduling horizons ranging from 7 to 60 days. Results showed that the LP model demonstrates satisfactory efficiency for real-scale farm optimization, achieving timely resolution across all combinations of solvers and planning schedules. Commercial solvers consistently demonstrated the best performance across planning scenarios, while open-source solvers CBC and HiGHS also showed satisfactory solving. Evolving the model proposed from a purely operational tool to a strategic one in the future could align farm logistics with the interconnected goals of the surrounding local food system and community, contributing to Sustainable Development Goals (SDGs) 2 and 12.