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Master's Dissertation
DOI
10.11606/D.55.2007.tde-07052007-142853
Document
Author
Full name
Douglas José Alem Junior
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2007
Supervisor
Committee
Arenales, Marcos Nereu (President)
Ferreira, Paulo Augusto Valente
Hoto, Robinson Samuel Vieira
Title in Portuguese
O problema de corte de estoque com demanda estocástica
Keywords in Portuguese
Método Simplex com geração de colunas
Otimização combinatória
Problema de corte de estoque
Programação estocástica
Abstract in Portuguese
O presente trabalho desenvolve uma extensão do problema de corte de estoque unidimensional no caso em que a demanda pelos vários tipos de itens não é exatamente conhecida. Para considerar a aleatoriedade, foi proposto um modelo de programação estocástica de dois estágios com recurso. As varáveis de primeiro estágio são os números de barras cortadas por padrão de corte, e as variáveis de segundo estágio, os números de itens produzidos em escassez e em escassez. O objetivo do modelo é minimizar o custo total esperado. Para resolver a relaxação linear do modelo, foram propostos um método exato baseado no método Simplex com geração de colunas e uma estratégia heurística, que considera o valor esperado da demanda na resolução do problema de corte de estoque. As duas estratégias foram comparadas, assim como a possibilidade de resolver o problema de corte ignorando as incertezas. Finalmente, observou-se que é mais interessante determinar o valor ótimo do modelo recurso quando o problema sofre mais influência da aleatoriedade
Title in English
The cutting stock problem under stochastic demand
Keywords in English
Column generation
Combinatorial optimization
Stochastic programming
The cutting stock problem
Abstract in English
This paper presents an integer linear optimization model of large scale for the one-dimensional cutting stock problem in the case which a demand is considered a random variable. To take this randomness into account, the problem was formulated as a two-stage stochastic linear program with recourse. The first stage decision variables are given by the number of bars that has to be cut according to each pattern, and the second stage decision variables by the number of holding items or backordering items production. The model objective is minimizes the total expected cost. We propose two methods to solve the model linear relaxation, one of them it is a Simplex-based method with column generation. The second method is a heuristic strategy that adopted the expected value of demand. We compare both strategies and the possibly of ignoring uncertainties on model. Finally, we observe that is much more interesting to determine the optimal recourse model solution when we have problems that are more afected by randomness
 
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DissertaFinal.pdf (1.11 Mbytes)
Publishing Date
2007-05-07
 
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