An integer programming approach for the three-dimensional cutting planning problem of marble processing industry

摘要

The three-dimensional cutting problem is one of the major problems faced in the 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, the cutting problem of a marble processing factory is handled. Two different integer programming (IP) approaches are developed. In the first one, an IP model is built for each of the two cutting problems, which are cutting marble blocks into planes and sizing these planes. In the second approach, these two IP models are integrated together to handle the two different cutting operations together. The objective of both models is to minimize total spoilage of marble while finding the cutting designs of the marble blocks and marble planes. A number of real life problems are solved using both approaches. Computational results are compared statistically. Results showed that both approaches decrease the wasted amount of marble compared to the industry’s average.