An integer linear programming model for the three-dimensional marble cutting problem

The marble blocks extracted from the quarries in the form of cubes go through a number of cutting processes in the factories. Marble slabs are produced first by cutting these blocks. Then, marble tiles are obtained from these slabs, and the cutting process is completed. The cutting plan for each block is created according to the dimensions of the products demanded by the customers. Therefore, a different cutting plan is determined for each block. While creating the cutting plan, the focus is on obtaining the maximum product from marble blocks. In this study, an integer linear programming model that creates a cutting plan is proposed to maximize the utilization rate of marble blocks. This model was used in the production process of a real marble factory. As a result of the cutting plans created with the model, customer demands were met with a waste rate of 15.73%.