A stochastic programming approach to the cutting stock problem with usable leftovers

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Cherri, AC (Author) Other; Cherri, LH (Author) Other; Beatriz Brito Oliveira (Author) FEUP; José Fernando Oliveira (Author) FEUP; Maria Antónia Carravilla (Author) FEUP

Journal

Title: European Journal of Operational Research

Vol. 308

Pages: 38-53

ISSN: 0377-2217

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus

Other information

Authenticus ID: P-00X-EW3

DOI: 10.1016/j.ejor.2022.11.013

Abstract (EN): In cutting processes, one of the strategies to reduce raw material waste is to generate leftovers that are large enough to return to stock for future use. The length of these leftovers is important since waste is expected to be minimal when cutting these objects in the future. However, in several situations, future demand is unknown and evaluating the best length for the leftovers is challenging. Furthermore, it may not be economically feasible to manage a stock of leftovers with multiple lengths that may not result in minimal waste when cut. In this paper, we approached the cutting stock problem with the possibility of generating leftovers as a two-stage stochastic program with recourse. We approximated the demand levels for the different items by employing a finite set of scenarios. Also, we modeled different decisions made before and after uncertainties were revealed. We proposed a mathematical model to represent this problem and developed a column generation approach to solve it. We ran computational experi-ments with randomly generated instances, considering a representative set of scenarios with a varying probability distribution. The results validated the efficiency of the proposed approach and allowed us to derive insights on the value of modeling and tackling uncertainty in this problem. Overall, the results showed that the cutting stock problem with usable leftovers benefits from a modeling approach based on sequential decision-making points and from explicitly considering uncertainty in the model and the solution method. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16