An integrated multi-objective mathematical model for sugarcane harvesting considering cumulative degree-days

Sugarcane is one of the main commodities in the world economy. An important step in the sugarcane supply chain is the harvest stage, requiring the support of mathematical modeling and optimization tools. Integrating the process of choosing the areas for harvesting according to the sugarcane maturation with the formation of the harvesting fronts and associating them with machine relocation costs is challenging. This paper contributes with a novel integer mathematical model that considers these concerns using three conflicting objectives. The first is that the sugarcane should be harvested as close as possible to its maturity, considering the sugarcane should be harvested as close as possible to its maturity by considering a combined measure of temperature and time since planting. The second aims to minimize the number of harvest fronts. The third objective is to minimize the costs involved with the relocation of the harvesters that cut the cane. Different strategies for obtaining Pareto-optimal solutions were proposed using exact methods, including MIP start and a decomposition technique. In the worst case, solutions with tolerable integrality gaps were obtained (inferior to 3%) in less than 1.5 h. Computational tests in real case studies were conducted in the sugarcane industry in two countries, indicating strong trade-offs in the determined solutions. In the Brazilian case, harvesting as close to maturation as possible, for example, causes an increase of 158% in the number of harvest fronts and 47% in the transportation costs, considering the minimum values for these objectives. Other trade-offs were seen and discussed when one of the other objectives was prioritized. These different compromise solutions help the decision-makers choose the most appropriate harvesting schedule according to their preferences.