Troubleshooting methods for batch sizing problems

Abstract

This research project is associated to the development of two other more general projects coordinated by the candidate (Jovem Pesquisador FAPESP, Process: 2006/01665-2, Period: 01/2007 to 12/2010 and Bolsa de Produtividade em Pesquisa CNPq, Process 307033/2006-6, Level 2; Period: 03/2007 to 02/209). In these two general projects the aim is to study and develop mathematical models and solution methods for different extensions of lot sizing problems. Such extensions arise from practical problems in different industrial sectors where the lot sizing problems appear to be integrated to other problems of the production process. In 2007, Professor Zeger Degraeve published, with Raf Jans, the paper Degraeve e Jans (2007) where a Dantzid-Wolfe Reformulation for a Lot Sizing problem is presented. The authors also show that the new reformulation is equivalent to the original one. To solve the problem, a branch-and-price method was developed. They speeded up the column generation process by using a combination of simplex and subgradient optimization. The computational tests show that the method provides good results. Among the possibilities for future research, the authors propose the adaptation of the method for different extensions of lot sizing problems. Considering the future research proposals of Degraeve e Jans (2007) and according to the planning in the general projects coordinated by the candidate, in this current post-doctorate project (to be developed from February/2009 to July/2009, with the cooperation of Professor Zeger Degraeve) the aim is to adapt their solution method, initially, for the problem that allows Backlog. Further, the problem with Parallel Machines and the Integrated Lot Sizing and Cutting Stock could also be studied. (AU)