Two-dimensional cutting stock problem with multiple stock sizes

In this study, we consider a two-dimensional cutting stock problem with multiple stock sizes and two-stage guillotine cuts. Our objective is to maximise the difference between total revenue earned over all cut items and total cost spent over all used panels. We propose two mathematical models, derive some optimality properties and use them to enhance the performances of the models. We develop decomposition-based heuristics that use the best of the proposed models to solve the subproblems. The results of our computational study have revealed that the models can return optimal solutions for the instances with up to 30 items in two hours and the heuristics produce near-optimal solutions for the instances with up to 50 items in five minutes. Copyright © 2024 Inderscience Enterprises Ltd.