On the cutting stock problem under stochastic demand

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 stag...

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Bibliographic Details
Published in:Annals of operations research 2010-09, Vol.179 (1), p.169-186
Main Authors: Alem, Douglas José,  Munari, Pedro Augusto, Arenales, Marcos Nereu, Ferreira, Paulo Augusto Valente
Format: Article
Language:English
Subjects:
Business and Management
Combinatorics
Costs
Cutting
Cutting stock problem
Demand
Expected values
Fines & penalties
Linear programming
Marketing
Operations research
Operations Research/Decision Theory
Optimization
Probability
Programming
Pulp & paper industry
Random variables
Raw materials
Stochastic models
Stochasticity
Stocks
Studies
Theory of Computation
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-008-0454-7