# Production Optimization in a Grain Facility through Mixed-Integer Linear Programming +
## 2 Related Work  
Several articles in the literature have proposed linear programming (LP) or MILP models for solving different optimization problems related to grain production, logistics, and/or chain supply problems. Early works in the area applied linear and mixed-integer programming models for problems related to harvesting methods and machinery selection. [PERSON] et al. [10] applied MILP for mixed cropping systems, computing an optimal spacing for planting navy beans. [PERSON] et al. [11] proposed a mathematical model for multi-stage optimization in agri-food supply chain. A real case study in Algeria was solved. The proposed model significantly outperformed a planning heuristic. A subsequent article by the same authors [12] applied the Agent Unified Modeling Language (AUML) protocol specification to build an effective system for production and transportation. The proposed model was effective to compute accurate values of the optimized functions. [PERSON] et al. [13] introduced a very important survey (until that date) contained a review of optimization methods for short-term scheduling of batch processes. The authors introduced general optimization constraints that in particular can be perfectly instantiated, for example, for the efficient and effective production of a soybean production plant, among other grains. Allowing the minimization of waiting times, optimizing the use of machines online, the hours of the operators, and other parameters that have a strong impact on the productivity of the plant. In addition, they provide a list of available academic and commercial software, and tackle the issue of rescheduling capabilities of the various optimization approaches, and include extensions that go beyond short-term batch scheduling. [PERSON] [PERSON] and [PERSON] (2014) proposed a multi-period MILP model for minimizing costs of blending and shipping on the wheat supply chain. A real-life case study demonstrated the approach as effective. An hybrid deterministic/non-deterministic model was proposed by [PERSON] et al. [PERSON] et al. (2015) for minimizing the building cost of a distribution network farm. Results reported for the supply chain of barley in Mexico showed that the model computed accurate solutions. The analysis and optimization of production lines of a processing plant has an superlative economic value as well as a strategic impact for the industrial market, allowing an increase in quality and quantity of production in less time, producing more with less cost. Based on this premise, [PERSON] et al. [PERSON] et al. (2016) used the Method of Problem Analysis and Solving (MAPS), an efficient set of statistical tools that provides a methodology and an improvement in process quality, with the goal of optimizing the production line in a wheat mill, transforming unproductive into productive hours. Using data collection at stops, at random times, there was an average operations/day value of 60.5% and a best result of 83%, taken as an objective to be accomplished. The authors found that the problem of excessive stops focused on four major causes, representing 87% of all cases. Through the combination of different mathematical strategies as well as knowledge of industrial practice, it was possible to efficiently attack and solve these four problematic cases of stops. As a global result, they found that increasing the number of productive hours in 22.5%, monthly income grew to superlative levels when compared to the corresponding cost of investing in more hours of feasible dedication of the workers. [PERSON] et al. [PERSON] et al. (2017) applied a multi-period MIP model for the optimization of production scheduling of fruit beverages. A case study in Brazil was used for validation of the proposed approach. Results demonstrated the applicability of the proposed approach under realistic assumptions. [PERSON] et al. [PERSON] et al.