Application of Genetic Algorithm to develop a new index for determination of the cuboid productivity of dimension stone quarries and finding the optimum cutting direction

Due to the lack of a criterion such as grade, it is difficult to decide on the extraction of a stone quarry. On the other hand, the goal of optimization in quarries is to produce blocks in the shape of a standard rectangular cuboid. In this research, an index called the Cubic Productivity Ratio (CPR) is defined that classifies the quarries in terms of the geometric grade of the blocks into three categories: good, moderate, and poor. In addition, by applying cutting planes and comparison of CPR values for different directions, the optimum cutting direction can also be determined. This index was implemented in the Ask Travertine quarry, Mazandaran province, Iran, and its value was calculated to be 22%, which places the quarry in a poor level in terms of block geometric quality. The optimal direction was found at N60w, indicating that in order to get the most yield, the current direction should be adjusted 35 degrees to the north. By doing that, the average volume of blocks will be at 241.63 cubic meters, the average dimensions of the cuboids will be equal to 2.93 (m) × 2.4 (m) × 2.25 (m) and the amount of marketable cuboids will be 53369.14 cubic meters, which, according to the current sale price of raw blocks, will result in revenue of about 130 billion IRR.