Modeling and solving a real-world cutting stock problem in the marble industry via mathematical programming and stochastic diffusion search approaches

Abstract In this study, one-dimensional marble plane cutting problem is studied based on the cutting equipment productivity and effective use of marble blocks. Different types of marble planes should be cut from multiple stock sized marble blocks in parallel by using a stone block-cutting machine (gang saw). Marble blocks, which have different dimensions, and quality gradations are supplied by the marble processing factory’s own marble quarries. Different quality gradations of the marble blocks and cutting equipment productivity need to be taken into account in addition to minimize the total trim loss or cost in modelling the present cutting problem. The nature of the production process in the marble industry consists of large amount of waste. Minimizing the amount of waste can be controlled indirectly by establishing an appropriate cutting plan. Therefore, minimization of the total cost of transportation and overgrading (supplying higher quality material than specified by the customer) while determining a suitable cutting plan for the marble blocks is aimed. A mixed integer linear programming (MILP) model is developed for solving the present marble plane cutting problem for small-size instances. The salient feature of the developed model is not requiring a priori enumeration of all possible cutting patterns and to permit generation of retail to reuse. For larger size problem instances a Stochastic Diffusion Search (SDS) algorithm is developed. Extensive computational studies are performed by using test instances, which are collected from a marble processing company operating at Izmir. The computational results show that the developed models and SDS algorithm are very useful in providing effective cutting plans.