Multi-objective economic-resource-production optimization of sustainable organic mixed farming systems with nutrient recycling

Abstract

Abstract This paper addresses the optimal design of mixed crop-livestock farming systems for resource efficiency, economic profitability, and environmental sustainability. The trade-offs among profit, water productivity, and organic matter accumulation are considered. We propose a novel optimization model that accounts for economics, crop cultivation, livestock production, water requirement, soil organic matter, and nitrogen cycling, among other important elements of organic farming systems. The resulting problem is a multi-objective mixed-integer nonlinear fractional programming (MINLFP) problem, which consists of fractional objective function and nonconvex nonlinear constraints. After reformulating the nonconvex constraints into convex ones, we propose a tailored global optimization algorithm to solve the resulting MINLFP problem. We further present a case study on a 100 ha organic mixed crop-livestock farm with 19 types of crops, 22 types of crop products, 3 type of livestock, and 2 types of animal products to illustrate the applicability of the proposed model and solution methods. Computational results suggest that it is more profitable to produce more high value cash crops and milk; it is more water efficient to grow cash crops than fodder; and it generates more soil organic matter accumulation by growing more crops with larger amount of root stubble and enlarging the heard size.