Location problem method applied to sugar and ethanol mills location optimization

Brazil is the world's largest producer of sugarcane and has a great potential for sugar and ethanol production. Sao Paulo is its main producer state and produced more than 367,450 million tons of sugarcane in 2012/2013 harvest season. In this study, operations research techniques are applied to obtain optimum locations for establishing new and/or to expand sugar and ethanol mills in the state of Sao Paulo. Data were obtained from the CANASAT project, which annually maps the sugarcane cultivated areas in Sao Paulo, using remote sensing and geospatial processing techniques. Since sugarcane is processed at mills near the cane fields, it has been used data from 2012/2013 harvest season to identify the largest cultivation areas in the state. The p-median problem was formulated as a binary linear programming problem and two methods were applied for approaching the solutions: MATLAB©Â optimization package (standard branch-and-bound) and a heuristic greedy algorithm. As a result, one noticed that the difference between the two methods ranges from 1.6% to 12% in the distance sum. Regarding to CPU time, MATLAB© standard branch-and-bound is 157 times slower in the best case and up to 43,446 times in the worst. It were also compared two different approaches for computing the distance among the predefined locations, Euclidean straight-line and shortest-path drive distances. When shortest-path drive distance is used rather than the Euclidean distance, facilities locations change. However, by the Pearson's correlation coefficient (r=0.99036; R2=0.98075), it was found that the drive distance is strongly correlated to the Euclidean distance and the dispersion is homogeneous for short distances. This result indicates that for studies on mills optimum location, one could rely on Euclidean distances since mills must be located near the cane fields.