| Summary: | 碩士 === 實踐大學 === 資訊科技與管理學系碩士班 === 100 === In various manufacturing industries (for examples, paper, glass, steel, wood etc.), one of the difficulties faced during the production process is the cutting of stock to the appropriate sizes to meet the demands of different customers. The recent global economic recession—exacerbated by rapid changes in the business environment, global financial crisis, and pressures due to inflation—showed that refinements to the stock cutting process is increasingly important for minimizing wastage and reducing cost. This study investigates the trim loss optimization problems in the paper industry. There are currently two approaches to handle this issue, namely, heuristic and deterministic. Although the former can provide the best solution within a limited amount of time, there is no guarantee that the solution will be globally optimal. Conversely, the latter can be used to determine the globally optimal solution by solving mathematical programming models. This study first examines the various deterministic methods, which transform the original trim loss optimization problem into either a mixed-integer linear programming or convex mixed-integer non-linear programming problem. The most efficient method is then used to develop a new system, which automatically generates the required mathematical programming model according to the parameters specified by the users. Next, the system calls the optimization software to derive the globally optimal solution of the constructed model. The results are displayed in the form of graphs, allowing the users to easily identify the best method to minimize wastage during the stock cutting process. Lastly, several examples are used to validate the accuracy and feasibility of the developed system.
Keywords: Cutting stock problem, mathematical programming model, linear transformation, optimization system
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