indicates that there is a significant potential for real-life applications of robust optimization, and Slack states that flexibility is an important concept that must be taken into account in productive industries due to the lack of stability and predictability of the environment. This factor determines the ability of the equipment to perform cost-effectively and rapidly a set of different tasks. An important issue, like setup flexibility, is sometimes neglected during the acquisition process. Many aspects need to be considered, among which one finds: product demand, quality, cost, production efficiency, and capital expenditure. However, decision-makers need to ponder several complex factors at the moment of deciding the adequate machinery and the optimal moment to invest in.
To remain competitive, companies must improve their productivity, reducing fixed and variable costs, which the investment in new manufacturing technologies can achieve. Among its limitations can be found difficulty in cutting sheets of large thicknesses (e.g., above 25 mm), processing reflective materials such as copper and its alloys, and the high investment cost associated with it. Some of its advantages consider high cutting speeds and dimensional precision as well as complex geometry contouring, ease of automation through the use of computer numerical control (CNC), and the fact that the LASER is considered a green manufacturing tool. LASER beam cutting, in particular of metals, has been on the market for over 40 years. Benefits from investing in AMT arise from: reduced inventory, less floor space, improved return on equity, reduction in unit production cost and cycle time, increased flexibility, improved product quality, increased productivity, quick response to customer demand, increased ease of operation, and enhanced employee relationship. Investment in new technologies, such as AMT, has become a requirement for companies to stay competitive. For this specific application of the model, results showed that the optimal robust solution could increase the company’s expected profits by 6.4%. The case study validates the effectiveness of the proposed model and proves the robustness of the solution. As a case study, we decided on the investment and productive plan for a company that offers Laser-Beam Cutting (LBC) services.
Second, we determine the optimal production plan based on the results of the robust optimization model and assuming that demand follows a normal distribution. The model is then transformed into a robust optimization model which considers demand uncertainty. We propose a linear investment model based on historical demand information and take physical process parameters for a LASER cutting equipment, such as cutting speed and gas consumption. In this work, we present a robust model that optimizes equipment investing decisions, considers the process’s technical constraint and finds an optimal production plan based on the available machinery. Its payback period is usually more extended, and there is a moderate-to-high risk involved in adopting these technologies. The acquisition of Advanced Manufacturing Technologies (AMT), such as high-power fiber or CO 2 laser cutting equipment, generally involves high investment levels.
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