Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

E G Birgin, R D Lobato and R Morabito
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E G Birgin: University of São Paulo, São Paulo, Brazil
R D Lobato: University of São Paulo, São Paulo, Brazil
R Morabito: Federal University of São Carlos, São Carlos, Brazil

Journal of the Operational Research Society, 2012, vol. 63, issue 2, 183-200

Abstract: In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method.

Date: 2012
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