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Study of models for a problem of irregular cutting problem applied to the steel industry

Grant number: 22/08538-9
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2022
Effective date (End): September 30, 2023
Field of knowledge:Engineering - Production Engineering - Operational Research
Principal Investigator:Marina Andretta
Grantee:Walison Adrian de Oliveira
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

Irregular cutting problems (or nesting problems) are problems that aim to determine an optimal arrangement of smaller irregular objects (items) inside larger objects (containers) in order to meet a demand. We are particularly interested in the bin packing problem, where we have several rectangular and irregular containers, each with fixed sizes, and we want to allocate all the items in these containers, without overlapping, so that the wasted area in the chosen containers is minimized.This problem can be found in steel industries that cut irregular items from rectangular slabs at the request of customers. Inspired by such an industry in the State of São Paulo, we have that a big part of the boards, after being cut, can be wasted, which means that they can be used to cut other items in future orders (which is not currently the case, in the case of this industry). Allowing the use of these already cut boards, which are currently considered scrap, enables less waste to be generated and, consequently, makes companies more sustainable. Therefore, we are interested in considering the problem in which the containers form a set of rectangular and irregular plates (the ones left over from previous cuts). A particularity of this type of cut is that the items can be freely rotated.The objective of this project is to model this problem mathematically, as a mixed integer optimization problem. When considering free rotations, we have a non-linear problem, but we can also consider simplifications of the problem, such as considering only fixed rotations (which makes it linear). Several models will be proposed and we want to verify the advantages and disadvantages of each one of them. For this, it will be necessary to study in the literature models of similar problems, which will allow the adaptation to this particular problem. We also intend to solve the proposed model using known exact methods, for instances inspired by real cases, to compare the solutions obtained for each proposed model.

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