Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry

Sônia Cristina Poltroniere, Silvio Alexandre Araujo, Kelly Cristina Poldi


Two important optimization problems occur in the planning and production scheduling in paper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon.These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and in- ventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed. 


Integrated problems, cutting stock problem, lot sizing problem.

Full Text:



D. Alem & R. Morabito. O problema combinado de planejamento da produção e corte de estoque sob incertezas: aplicação em fábricas de móveis de pequeno porte. Gestão & Produção, 20(1) (2013), 111–133.

L. Buschku ̈l, F. Sahling, S. Helber & H. Tempelmeier. Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectrum, 32 (2010), 231–261.

M.H. Correia, J.F. Oliveira & J.S. Ferreira. Reel and sheet cutting at a paper mill. Computers & Operations Research, 31 (2004), 1223–1243.

A. Drexl & A. Kimms. Lot sizing and scheduling – survey and extensions. European Journal of Operational Research, 99 (1997), 221–235.

A.A. Farley. Mathematical programming models for cutting-stock problems in the clothing industry. Operational Research Society, 1 (1988), 41–53.

C.T.L.S. Ghidini. Otimização de processos acoplados: programação da produção e corte de estoque. Tese de doutorado, ICMC, USP, São Carlos, SP (2008).

P.C. Gilmore & R.E. Gomory. A linear programming approach to the cutting stock problem. Operations Research, 9 (1961), 848–859.

P.C. Gilmore & R.E. Gomory. A linear programming approach to the cutting stock problem – Part II. Operations Research, 11 (1963), 863–888.

P.C. Gilmore & R.E. Gomory. Multi-stage cutting stock problems of two and more dimensions. Operations Research, 13 (1965), 94–120.

M.C.N. Gramani & P.M. França. The combined cutting stock and lot-sizing problem in industrial processes. European Journal of Operational Research, 174 (2006), 509–521.

M.C.N. Gramani, P.M. Franc ̧a & M.N. Arenales. A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem. International Journal of Production Economics, 119 (2009), 219–227.

M.C.N. Gramani, P.M. Franc ̧a & M.N. Arenales. A linear optimization approach to the combined production planning model. Journal of the Franklin Institute, 348(7) (2010), 1523–1536.

R. Jans & Z. Degraeve. Modeling industrial lot sizing problems: a review. International Journal of Production Research, 46 (2008), 1619–1643.

J. Kallrath, S. Rebennack & R. Kusche. Solving real-world cutting stock-problems in the paper industry: mathematical approaches, experience and challenges. European Journal of Operational Research, 238(1) (2014), 374–389.

B. Karimi, S.M.T. Fatemi Ghomi & J.M. Wilson. The capacitated lot sizing problem: a review of models and algorithms. OMEGA, 31 (2003), 365–378.

A.A.S. Leão. Extensões em problemas de corte: padrões compartimentados e problemas acoplados. Tese de doutorado, ICMC, USP, São Carlos, SP (2013).

K.C. Poldi & S.A. Araujo. Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem. Annals of Operations Research, 238 (2016), 497–520.

S.C. Poltroniere. “Otimização do processo de corte integrado à produção de bobinas: modelo e métodos de solução”. Tese de doutorado, ICMC, USP, Sa ̃o Carlos, SP (2006).

S.C. Poltroniere, K.C. Poldi, F.M.B. Toledo & M.N. Arenales. Coupling cutting stock-lot sizing problems in the paper industry. Annals of Operations Research, 157 (2008), 91–104.

DOI: https://doi.org/10.5540/tema.2016.017.03.0305

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia