Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers

• Published in: Annals of operations research 2022-09, Vol.316 (2), p.785-803
• Main Authors: do Nascimento, D. N., de Araujo, S. A., Cherri, A. C.
• Format: Article
• Language: English
• Subjects: Business and Management; Combinatorics; Cutting; Economic lot size; Lot sizing; Mathematical models; Mathematical optimization; Operations research; Operations Research/Decision Theory; Production planning; S.i.: Claio 2018; Simplex method; Theory of Computation
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-020-03772-9

This paper addresses the integration of the lot-sizing problem and the one-dimensional cutting stock problem with usable leftovers (LSP-CSPUL). This integration aims to minimize the cost of cutting items from objects available in stock, allowing the bringing forward production of items that have known demands in a future planning horizon. The generation of leftovers, that will be used to cut future items, is also allowed and these leftovers are not considered waste in the current period. Inventory costs for items and leftovers are also considered. A mathematical model for the LSP-CSPUL is proposed to represent this problem and an approach, using the simplex method with column generation, is proposed to solve the linear relaxation of this model. A heuristic procedure, based on a relax-and-fix strategy, was also proposed to find integer solutions. Computational tests were performed and the results show the contributions of the proposed mathematical model, as well as, the quality of the solutions obtained using the proposed method.