A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Abstract Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness.

[1]  Marcos Nereu Arenales,et al.  PROBLEMA DE DIMENSIONAMENTO DE LOTES MONOESTÁGIO COM RESTRIÇÃO DE CAPACIDADE: MODELAGEM, MÉTODO DE RESOLUÇÃO E RESULTADOS COMPUTACIONAIS , 2000 .

[2]  Marcos Nereu Arenales,et al.  Abordagens para otimização integrada dos problemas de geração e seqüenciamento de padrões de corte: caso unidimensional , 2005 .

[3]  Franklina Maria Bragion Toledo,et al.  A coupling cutting stock-lot sizing problem in the paper industry , 2007, Ann. Oper. Res..

[4]  P. Camerini,et al.  On improving relaxation methods by modified gradient techniques , 1975 .

[5]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[6]  James R. Evans.  An efficient implementation of the Wagner-Whitin algorithm for dynamic lot-sizing , 1985 .

[7]  William W. Trigeiro,et al.  Capacitated lot sizing with setup times , 1989 .

[8]  R. Gomory,et al.  Multistage Cutting Stock Problems of Two and More Dimensions , 1965 .

[9]  Linda Hendry,et al.  A Cutting Stock and Scheduling Problem in the Copper Industry , 1996 .

[10]  Reinaldo Morabito,et al.  Optimizing the cutting of stock plates in a furniture company , 2000 .

[11]  Alf Kimms,et al.  Lot sizing and scheduling -- Survey and extensions , 1997 .

[12]  Paulo M. França,et al.  The combined cutting stock and lot-sizing problem in industrial processes , 2006, Eur. J. Oper. Res..

[13]  Anders Thorstenson,et al.  A combined cutting-stock and lot-sizing problem , 2000, Eur. J. Oper. Res..

[14]  Reinaldo Morabito,et al.  Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem , 2009 .

[15]  M. P. Reinders,et al.  Cutting stock optimization and integral production planning for centralized wood processing , 1992 .

[16]  Anders Thorstenson,et al.  Solving a combined cutting-stock and lot-sizing problem with a column generating procedure , 2008, Comput. Oper. Res..

[17]  Claudio Arbib,et al.  Integrating process optimization and inventory planning in cutting-stock with skiving option: An optimization model and its application , 2005, Eur. J. Oper. Res..

[18]  Reinaldo Morabito,et al.  Performance Of Two Heuristics For Solving Large Scale Two-Dimensional Guillotine Cutting Problems , 1995 .