# Production Optimization in a Grain Facility through Mixed-Integer Linear Programming +
## 2 Related Work
From the comparison, the authors highlighted that after accounting for the whole farm costs there are still benefits to on-farm trials. Moreover, when on-farm trials cause planting and harvesting field operations to be conducted outside the optimal time, crop yields may be adversely affected. On the other hand, they affirmed that farm decision makers should take into account certain research questions that do not necessitate adversely impacting these windows until experience has been gained. In all cases, the comparative models used were based on LP to determine optimal solutions to maximize contribution margins on each considered scenario. [PERSON] et al. [PERSON] et al. (2018) introduced an LP mathematical model for assistance in the planning and management of agricultural production, as well as to assist in estimating potential gains from the use of integrated systems. They stand out as a strategic point, introducing diversification in production as a necessary condition for economic viability. The numerical results obtained support this point. A total cost reduction potential of about 30% was found when comparing the scenario with lower levels of diversification was contrasted with one of higher levels. In addition to financial gains, the authors note that the integrated systems bring benefits to the environment, more precisely with respect to to the reuse of resources. As example, the model can reuse nitrogen, phosphorus, and potassium present in animal waste. Another important conclusion is that the diversification model has a clear impact on the reduction of transaction costs. Motivated by the little recent research on optimizing seed supply chains (particularly soybeans) in Canada, [PERSON] (2018) introduced a novel MILP formulation for a soybean supply chain network. The objective function considered was to maximize the profit. The model takes into account constraints involving multiple products, growers, potential farm company facilities, potential locations of distributers, and customers. In addition, the author extends the model by adding uncertainty to certain parameters. In order to measure the effectiveness and efficiency of the optimization model, it was applied on a soybean supply chain network in Ontario where there are several soybean companies and growers in this region. The output of the optimization model is displayed by means of maps, highlighting different characteristics of importance for soybean plantations (e.g., showing the optimal soybean supply chain network for certain products). [PERSON] et al. [PERSON] et al. (2018) analyzed land use in Sumbawa District (Indonesia) to produce corn and its effect in the cutting trees as well as on environment. Production and government objectives for corn production increase annually and have an indirectly impact on clearing new land as corn planting land. Using the Simplex linear optimization method, authors focused on a cutting tree optimization model to enhance the productivity of corn and optimize the benefits of corn farmers and investors. Using the proposed method, maximum production of corn in 2019 increased to 701,984 tons of corn, the paddy field area to 44,198.5 hectares and 55,292.5 hectares of land not paddy fields. [PERSON] et al. [28] considered that the grain processing industry often excessively pursues the objective of fine processing, resulting in increasing raw material cost and low machining efficiency, etc. The authors provided an interesting methodology, applicable to food and grain production based on a food/grain optimized processing anda data analysis system which can outperform various previously designed data analysis. The designed methodology has the following functions: grain processing database is able to store and call consumer market surveys and data of grain processing enterprises, visualizing the national diet and grain processing process.