# Production Optimization in a Grain Facility through Mixed-Integer Linear Programming +
## 8 Conclusions and Future Work  
This article addressed a relevant problem for production in the agriculture field. In this context, efficient and accurate models are needed for resource management, in order to minimize operation costs and enhance competitiveness. A MILP optimization model based on discrete time windows was proposed for a capacitated multi-product multi-line production scheduling problem. The model incorporates relevant constraints in the context of grain production, considering both treated and inoculated products. A theoretical analysis of the NP-completeness of the optimization problem was developed. In turn, a bounds-based scheme was proposed to accelerate the convergence to the optimal solution of the optimization problem. The proposed MILP model was implemented in AMPL and solved using CPLEX. The model was evaluated on a real-life case study, considering real data from the 2020 soybean harvest of the top Uruguayan grain producer and exporter. Many real-life situations were \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{_Scenario_} & \multicolumn{2}{c}{_Time_} & \multicolumn{2}{c}{_Objective_} \\ \cline{2-5}  & **Average** & **Best** & **Average** & **Best** \\ \hline HoursBound & \(-139\%\) & \(0\%\) & \(0.040\%\) & \(0.000\%\) \\ ShiftBound & \(22\%\) & \(99\%\) & \(-0.949\%\) & \(0.000\%\) \\ AllBounds & \(14\%\) & \(99\%\) & \(1.914\%\) & \(1.807\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Improvements of bound schemes over the NoBounds scenario. taken into account, including multiple products, multiple production lines, limited shelf life, storage facilities, operator shifts, and cleaning of the machinery. The main results of the experimental evaluation indicated that the computed solutions achieved an efficient storage capacity, significantly reducing the number of cleaning stops for machinery and the number of operator shifts required. The plan computed by the proposed model achieved significant cost reductions (more than 10%, USD 20,000) over the ad hoc planning heuristic applied by the company. Furthermore, the computed plans also improving storage occupancy and costs of machinery cleaning supplies. The proposed bounds-based scheme was useful to speed up the resolution of the optimization problem in two scenarios: in a factor of 1.28\(\times\) using the ShiftsBound type and in a factor of 1.17\(\times\) using the AllBounds type. Conversely, execution times were worse using the HoursBound type (a factor of 0.41\(\times\)). The proposed bound scheme was useful to accelerate the resolution of the considered optimization problem. The approach based on embedding bounds in the optimization problem is suitable to be applied in any problem where the objective function is an aggregation of monotone increasing functions. In that case, the proposed method is directly applicable as we did in our research, even if the functions are not linear. Overall, the approach is also a useful idea that can be applied to other optimization problems. In this regard, the validation of the proposed model should be extended by considering new problem instances and different grain production problems, subject to the availability of data, by working with other companies in the agri-food sector. The main lines of future work are related to improve the optimization model, and expand the case studies to properly reflect the current reality of grain production companies. The optimization model can be improved by including additional realistic features in the optimization model, such as silo farms for raw grains, shared to store the processed grains and uncertainty on demands. Regarding the discretization step considered to determine production, a problem model to plan days will certainly allow for more accurate production planning, further optimization of machinery cleanings, operator shift costs, and improved storage management. The proposed model should be adapted to take into consideration these new features and related new constraints.