On the cutting stock problem under stochastic demand |
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Authors: | Jr" target="_blank">Douglas José AlemJr Jr" target="_blank">Pedro Augusto MunariJr Marcos Nereu Arenales Paulo Augusto Valente Ferreira |
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Institution: | 1.Department of Applied Mathematic and Statistic,University of S?o Paulo,S?o Carlos,Brazil;2.School of Electrical and Computer Engineering,University of Campinas,Campinas,Brazil |
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Abstract: | This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated
as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to
be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items
due to the decisions made in the first stage. The problem’s objective is to minimize the total expected cost incurred in both
stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for
solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known
measures of uncertainty effects in stochastic programming: the value of stochastic solution—VSS—and the expected value of perfect information—EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches,
even under small variations in the parameters of the problem. |
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Keywords: | |
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