Mathematical modeling for the three-dimensional guillotine cutting stock problem

• Grant number: 25/07868-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: June 30, 2026
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Mateus Pereira Martin
• Grantee: João Vitor Gutierres Figueroa
• Host Institution: Centro de Ciências em Gestão e Tecnologia (CCGT). Universidade Federal de São Carlos (UFSCAR). Campus de Sorocaba. Sorocaba , SP, Brazil
• Associated research grant: 22/05803-3 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings, AP.TEM

Abstract

This project addresses the three-dimensional guillotine cutting stock problem (3D-GCSP), which is highly relevant in industrial sectors such as steel block and mattress foam cutting.The 3D-GCSP consists of determining the best way to cut larger rectangular boxes (objects) to produce smaller rectangular boxes (items) as demanded, using only orthogonal guillotine cuts. The objective is to minimize the number of objects used, while respecting the technological constraint of guillotine cutting, that is, all cuts must be parallel to the faces of the object being cut, always dividing it into two smaller rectangular sub-boxes. The project proposes to adapt integer linear programming models, such as those by Furini et al. (2016) and Becker et al. (2022), originally developed for the two-dimensional version of the problem, to address the complexity of three-dimensional geometry. The proposed modeling will be validated through computational experiments, using classical instances from the literature and, when possible, real data from companies. (AU)