On the cutting stock problem under stochastic demand

Douglas Alem, Pedro Munari, Marcos Arenales, Paulo Augusto Valente

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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.
Original languageEnglish
Pages (from-to)169-186
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - 2010


  • cutting stock problems
  • stochastic programming
  • linear optimization
  • column generation


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