Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers
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Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers D. N. do Nascimento1 · S. A. de Araujo2 · A. C. Cherri3 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Lot-sizing problem · Cutting stock problem · Usable leftovers · Mathematical modeling · Heuristic procedure
1 Introduction The Cutting Stock Problem (CSP) consists of cutting large objects available in stock into a set of smaller items with specified quantities and sizes by optimizing an objective function, such as minimizing the total waste or minimizing the cost of the cut objects. There are many studies of the CSP from different perspectives and their proposed solution methods in
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A. C. Cherri [email protected] D. N. do Nascimento [email protected] S. A. de Araujo [email protected]
1
Departamento de Engenharia de Produção, FEB, UNESP, Bauru, SP, Brazil
2
Departamento de Matemática, IBILCE, UNESP, São José do Rio Preto, SP, Brazil
3
Departamento de Matemática, FC, UNESP, Bauru, SP, Brazil
123
Annals of Operations Research
the literature, as we can see in Erjavec et al. (2012). In that paper, the authors proposed a method to define the optimal stock size for the expected demand of items to minimize the total cost of waste, warehousing and non-fulfilment. After tests and simulations, the authors concluded that the optimal stock size must be approximately 50% above the expected demand of items. Another example is the recent application studied in Lemos et al. (2020). Based on a real-life application of the concrete pole manufacturing, the authors considered multiple manufacturing modes integrated into the cutting stock problem. A variation of CSP that often appears in practice consists of considering the generation of usable leftovers of cut objects. If planned, these leftovers are not considered waste and they are kept in stock to meet future demand. This variation of the CSP is called the Cutting Stock Problem with Usable Leftovers
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