# Production Optimization in a Grain Facility through Mixed-Integer Linear Programming +
## 2 Related Work
(2018) studied MILP formulations for the Wheat Blending Problem and proposed an hybrid Evolutionary Algorithm (EA) including an exact subordinate LP operator to solve a linear-relaxation of the problem. The method was evaluated on synthetic instances, outperforming previous results. [PERSON] et al. [PERSON] et al. (2019) introduced multiple and efficient MILP-based models for the planning and scheduling of multiproduct multistage continuous plants with sequence-dependent changeovers in a supply chain network under demand uncertainty and price elasticity of demand. The authors considered multiple key parameters and phases associated with the complete production chain of the products for the different optimization approaches studied. The global problem allows multiple plants, multiple manufactured products, multiple collection and distribution centers from which the final products are distributed to the final points of sale. A hybrid discrete/continuous model was proposed for the global problem and the Hierarchical Model Predictive Control (HMPC) method was applied to solve scenarios with uncertainty. The effectiveness of the optimization method was evaluated by comparing the obtained results on a large-scale instance with the solution delivered by a classic Cutting Plane algorithm. [PERSON] et al. [PERSON] et al. (2019) proposed a two-stage mixed-stochastic approach to deal with uncertainty in costs, demand, and supply in the wheat supply chain network. The first stage considered the selection of sites for locating silos and waste collection centers. The second stage optimized the wheat flow in the supply the network, considering uncertainty on the demand. A real case study in Iran was solved, where the proposed model was able to outperform a deterministic model. [PERSON] et al. [PERSON] et al. (2019) proposed a MILP formulation to optimize cost in a real-life food transportation problem in India. A heuristic method was applied for resolution, since authors claimed that commercial optimization software failed to compute exact solutions for large problem instances in a practical time limit. The viability of the proposed model was evaluated by solving a case study involving nine sites and eight relevant costs. For this reduced problem instance, the gap of the proposedheuristic over results computed using CPLEX were between 1.57% and 11.71%. No further comparisons with other resolution methods or real results was presented. [PERSON] et al. [PERSON] et al. (2018) proposed a MILP formulation for minimizing the total cost of the bioethanol supply chain. Accurate results were computed to satisfy the demand in a case study considering corn and barley residues in Mexico. The proposed MILP approach was robust and applicable to other similar problems. [PERSON] et al. [PERSON] et al. (2018) introduce important theoretical contributions and suitable models with the aim of understanding the double-crop production systems that make Brazil one of the world's leading and most competitive grain-producing countries. The authors propose a decision support model focused on optimal agricultural planning that pointed to multiproduct farms under risk conditions and applies this theoretical model of farm planning that uses operations research and optimization to comprehend the different productive resource allocations in farms engaged in grain production. The designed and developed model was used in the region of Sorriso, Brazil, resulting in better financial results with lower risks for grain producers in that region. As an example, the efficient frontier curves computed in the financial analysis showed that the representative farms in this region maximized their production factors. This produced a result of very high value for investors. [PERSON] et al. [PERSON] et al. (2018) analyzed and estimated the whole-farm costs of conducting on-farm trials using a modification of the classic down-time model in an LP framework, compared to previously estimated potential benefits.