Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost

Silva, Eduardo M. and Melega, Gislaine M. and Akartunali, Kerem and de Araujo, Silvio A. (2023) Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost. European Journal of Operational Research, 304 (2). pp. 443-460. ISSN 0377-2217 (https://doi.org/10.1016/j.ejor.2022.04.023)

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Abstract

In this paper, we study the one-dimensional multi-period cutting stock problem with setup costs on cutting patterns. We present pattern-based and pseudo-polynomial formulations for the problem. Reformulations are also proposed to improve the lower bounds. We then present a thorough theoretical analysis to establish the strength of the various proposed formulations in comparison to each other. Finally, a computational analysis is conducted to complement the theoretical analysis and provide further insights with respect to the complexity and strength of the formulations.

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