Three Dimensional Cutting Problem: An Integer Programming Approach

Cutting problem is one of the major problems faced in marble factories. Huge marble blocks coming from marble quarries are first cut into planes according to their depths. Then these planes are sized according to the length and width of the demanded products. In this study, cutting problem of a marble factory is handled. The two problems, which are cutting marble blocks into planes and sizing these planes, are integrated together. An integer programming model is built for the integrated problem. The objective of the model is to minimize total waste of marble while finding the cutting design of the marble block and marble planes. The model is used to solve the cutting problem of a real life marble processing factory. It is shown that the mathematical model decreases wasted amount of marble considerably compared to the industry average.