Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems
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Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems Gislaine Mara Melega1
· Silvio Alexandre de Araujo2
· Reinaldo Morabito1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we address a two-stage integrated lot-sizing, scheduling and cutting stock problem with sequence-dependent setup times and setup costs. In production stage one, a cutting machine is used to cut large objects into smaller pieces, in which cutting patterns are generated and used to cut the pieces, and should be sequenced in order to obtain a complete cutting plan for the problem. The cut pieces, from production stage one, are used to assemble final products in production stage two, where the final products are scheduled in order to meet the client’s demands. To solve the two-stage integrated problem, we present solution methods based on a price-and-branch approach, in which a column generation procedure is proposed to generate columns and the integer problem is solved by decomposition solution approaches. A computational study is conducted using randomly generated data and an analysis showing the impact of the solution approaches in the two-stage integrated problem is presented. In addition, the performance and benefits of the integrated approach are compared to an empirical simulation of the common practice (sequential approach). Keywords Cutting stock and scheduling problems · Lot-sizing and scheduling problems · Sequence-dependent setups · Price-and-branch approaches
1 Introduction The number of mathematical models that addresses integrated/combined/coupled/ simultaneous problems, as they have been called in the literature, has significantly increased in recent years (Copil et al. 2017; Melega et al. 2018). The idea of an integrated problem is to simultaneously consider the decisions related to the problems involved, so as to capture the interdependency among the decisions in order to obtain a better global solution, i.e., the integrated approach aims to reduce the total costs (or increase the profit), when compared to solving the problem that is not integrated but rather only externally coordinated by some
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Gislaine Mara Melega [email protected]
1
Departamento de Engenharia de Produção, Universidade Federal de São Carlos, Rodovia Washington Luís - Km 235, São Carlos, SP 13565-905, Brazil
2
Instituto de Biociências, Letras e Ciências Exatas, Departamento de Matemática, Universidade Estadual Paulista, São José do Rio Preto, SP 15054-000, Brazil
123
Annals of Operations Research
mechanism to be devised. The tendency of coupling approaches is often tailored to specific industrial applications, such as in beverage, foundry, animal food, glass, furniture and paper industries. In this paper, we are interested in a comprehensive integration between three well-known problems in the literature, the production lot-sizing problem, the production scheduling problem and the cutting stock problem. The vast body of literature on the inte
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