Development hybrid OA-RG with multi-row time-aggregated cover cuts for solving MINLP in coffee plantation maintenance

The object of this research is the NP-hard combinatorial optimization problem in the allocation of limited resources for the maintenance of smallholder coffee plantations. In this study, a hybrid method of outer Approximation (OA) and reduced gradient (RG), enhanced by multi-row time-aggregated cover cuts (MTACC) is proposed to address the computational time efficiency problem in mixed-integer nonlinear programming (MINLP)-based combinatorial optimization problems. The testing was conducted using plantation land data from the Rahmat Kinara Coffee Farmers Association, which includes 538 land blocks with a total area of 825.5 hectares. Based on the numerical results obtained, it shows a reduction in the number of iterations by up to 38.83% and an increase in the speed of convergence time by up to 12.84%. The nw feature in MTACC specifically controls the length of the time window to form multi-row covering slices that are suitable for the characteristics of the constraints, which affects the master and RG subproblems in overcoming the computational load. The evaluation results for testing parameters nw = 7 and nw = 14 show an increased contribution to convergence time of up to 10.1% by reducing the average master MILP time by 6.16%. Evaluation of the area under curve (AUC) metric confirms that MTACC is more stable in controlling optimality gaps across global iterations based on AUC (abs) assessment, which decreased by 21.6%; AUC per iteration decreased by 19.9%, and normalized AUC also decreased by 18.6%. The results obtained can be effectively applied in small to large-scale coffee plantations, especially in decision support systems on low-power computing devices for production sustainability