Primal-dual methods for solving optimization problems applied to industrial an logistic contexts

Abstract

Operations Research (OR) has shown to have an important role in the scope of Production Engineering, when the goal is to make efficient the activities that emerge from industrial and logistic contexts. As one of the several OR branches, Optimization offers mathematical and computational tools with big potential to model and solve problems. Currently, the optimization softwares are able to solve many types of problems within a reasonable amount of time. However, many classes of large-scale and/or combinatorial nature problems are still a challenge even for the best softwares in the market. This way, the search for more efficient solution methods is still very active in the Optimization literature. The purpose of this project is to study the main linear optimization methods and to propose method combinations with the aim of improving the efficiency of the current methods. We intend to address the most common variants of simplex-type methods and interior point methods and to investigate how their main advantages can be combined in order to obtain more efficient methods. The development of the methods will be focused on classes of problems that arise from the modeling of usual situations addressed in Production Engineering. Benchmark instances from the literature will be used in computational experiments to analyze the performance of the proposed methods. This research belongs to the scope of an ongoing FAPESP Regular Project Grant and intends to involve a foreigner researcher who has remarkable contributions in the literature regarding linear optimization methods. (AU)