Estudo da otimização linear e aplicações do método simplex e pontos interiores

Abstract

Many small-scale industries work with manufacturing processes, such as the cutting and packing materials of varying sizes and quantities, to meet the demands of customers. However, in this process, can be generated undesirable residue of materials that often cannot be reused to meet other demands, characterizing the loss of raw material. Therefore, the goal of this work is to apply Linear Programming Methods for modeling and solution of real problems and to study the resolution methods of a linear programming problem: Simplex Method and Interior Points Method, identifying the optimal solutions of applications for manufacturer real problems In this scenario, three case studies of three small industries are presented. The first study describes the application of the packaging problem in an industry that packs peanuts. The goal of the second study is to minimize the waste of raw materials used by a graphical during the cutting process and paper labels making. The third and last study also addresses the application of the cut-ting problem into a graphical that cuts sheets of ream of varying sizes to meet the requests. For the conclusion of this work, these problems were modeled by using Linear Programming and the resolution methods with computational support were applied to obtain the optimal solution. From the obtained results, we observe that the implementation of the cutting and packing problems in these small-scale industries was effective to reduce the wasted raw material and to reduce costs. Minimizing the waste of raw material in the cutting and packaging process, the results contribute to the reduction of waste and environmental impact, thus presenting a positive contribution to the environment and providing the maximum use of raw materials in the manufacturing process.