Lot sizing problems: integrations and solution methods

Abstract

In 2007 the applicant has started to develop financial supported projects on lot sizing problems integrated to other problems of optimization of the productive system. The applicant has done several contributions on the integration of the lot sizing problem with the scheduling problem, with the cutting and packing problem and with decisions related to the transportation of the produced items. In general, such contributions to present heuristics methods specifics to each investigated problem.Following the planning of these projects and aiming to study solution methods, the applicant engaged in a post-doctorate with Professor Zeger Degraeve from London Business School with financial support of Fapesp. In this occasion the applicant also met Professor Raf Jans from Department of Logistics and Operations Management/HEC Montréal. Professors Zeger Degraeve and Raf Jans have published several papers on integrated lot sizing problems and also on solution methods for the lot sizing problems. Such methods are related to reformations and Lagrange relaxation combined (or not) with column generation.In this project we intent to carry on the research related to the projects developed, as well as, the studies related to the post-doctorate. To do so, we intend to study the integrated lot sizing problem amplifying the studies related to mathematical models and solution methods applied to several industrial sectors. The aim is to propose and evaluate the efficiency of mathematical models that combine several aspects of the production planning. Related to the solution methods studied during the post-doctorate, we aim to continue the research on the application of these methods to the lot sizing problem. Moreover, we intend to start the investigation to apply these methods to extensions of the classical lot sizing problem, such as, the parallel machines case; the case with several plants; and the integrated lot sizing problems with emphasis to the lot sizing problem integrated to the cutting and packing problem. (AU)