Multivariate chance-constrained method applied in multi-objective optimization problems of manufacturing processes

TORRES, Alexandre Fonseca

dc.creator	TORRES, Alexandre Fonseca
dc.date.issued	2020-12-07
dc.identifier.uri	https://repositorio.unifei.edu.br/jspui/handle/123456789/2401
dc.description.sponsorship	Agência 1	pt_BR
dc.language	eng	en
dc.publisher	Universidade Federal de Itajubá	pt_BR
dc.rights	Acesso Aberto	pt_BR
dc.subject	Chance-constrained	en
dc.subject	Multivariate method	en
dc.subject	Optimization problems of manufacturing processes	en
dc.title	Multivariate chance-constrained method applied in multi-objective optimization problems of manufacturing processes	en
dc.type	Tese	pt_BR
dc.date.available	2021-04-15
dc.date.available	2021-04-15T13:27:30Z
dc.date.accessioned	2021-04-15T13:27:30Z
dc.creator.Lattes	http://lattes.cnpq.br/0960950329289507	pt_BR
dc.contributor.advisor1	BALESTRASSI, Pedro Paulo
dc.contributor.advisor1Lattes	http://lattes.cnpq.br/8999535447828760	pt_BR
dc.contributor.advisor-co1	COSTA, Antonio Fernando Branco
dc.contributor.advisor-co1Lattes	http://lattes.cnpq.br/6100382011052492	pt_BR
dc.description.resumo	In the multi-objective optimization problems of manufacturing processes, the responses of interest are often significantly correlated. In addition to the multivariate nature of the problems, product demands, productive capacities, cycle times, the costs of labor, machines, and tools are just some of the many random variables involved in the optimization model. In particular, when using Design of Experiments (DoE) techniques and regression methods, the estimated coefficients for the empirical models - such as response surface models - are also stochastic. However, it has been observed that most of the articles published in this research area are limited to represent the stochastic variables in a deterministic way. Within this context, the present study aimed to propose the use of stochastic programming techniques combined with multivariate statistical methods including some process capability indices widely used in the industry, such as the 𝐶𝑝𝑘 capacity index and the Parts Per Million (𝑃𝑃𝑀) index. The use of the methods combined used resulted in the proposal of the Multivariate Chance-Constrained Programming (MCCP). To test the applicability of the MCCP method, a multi-objective optimization problem of the AISI 52100 hardened steel turning process was selected as a case study given its widespread use and relevance to the industry nowadays. As a starting point for this study, a set of experimental results obtained from a central composite design was used. The decision variables were the cutting speed (𝑉𝑐), the feed rate (𝑓) and the depth of cut (𝑎𝑝). The responses of interest selected for this work were the total machining cost per part (𝐾𝑝), the material removal rate (𝑀𝑅𝑅), the tool life (𝑇), the average roughness (𝑅𝑎) and the total roughness (𝑅𝑡). After analyzing the data and building the mathematical models for the responses of interest, three approaches were carried out. In the first approach, the 𝐶𝑝𝑘 index included the calculation of the variance of the response surface model of 𝑅𝑎. In the second approach, the probability that 𝐾𝑝 is less than or equal to a predefined value was modelled as a stochastic objective function. Finally, the third approach described the application of the proposed MCCP method. In this approach, the 𝑃𝑃𝑀 index was calculated using a normal bivariate distribution for both 𝑅 𝑎 and 𝑅𝑡. The main results of this research were: a) the demonstration and validation of an equation used to calculate the variance of a continuous, derivable and dependent function of stochastic variables; b) the analysis of the impact of seven stochastic industrial variables (setup time, lot size, machine and labor costs, insert changing time, tool holder price, tool holder life and insert price) on the cost of the process; c) finding that maximizing tool life may reduce cost in some cases – for example when using Wiper tools – but the change of the cutting conditions alone does not necessarily reduce the cost of the process, as in what occurred in the case study analyzed.	en
dc.publisher.country	Brasil	pt_BR
dc.publisher.department	IEPG - Instituto de Engenharia de Produção e Gestão	pt_BR
dc.publisher.program	Programa de Pós-Graduação: Doutorado - Engenharia de Produção	pt_BR
dc.publisher.initials	UNIFEI	pt_BR
dc.subject.cnpq	CNPQ::ENGENHARIAS::ENGENHARIA DE PRODUÇÃO	pt_BR
dc.relation.references	TORRES, Alexandre Fonseca. Multivariate chance-constrained method applied in multi-objective optimization problems of manufacturing processes. 2020. 105 f. Tese (Doutorado em Engenharia de Produção) – Universidade Federal de Itajubá, Itajubá, 2020.	pt_BR