The acquisition of Advanced Manufacturing Technologies (AMT), such as high-power fiber or CO2 laser cutting equipment, generally involves high investment levels. Its payback period is usually more extended, and there is a moderate-to-high risk involved in adopting these technologies. 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. 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. The model is then transformed into a robust optimization model which considers demand uncertainty. Second, we determine the optimal production plan based on the results of the robust optimization model and assuming that demand follows a normal distribution. As a case study, we decided on the investment and productive plan for a company that offers Laser-Beam Cutting (LBC) services. The case study validates the effectiveness of the proposed model and proves the robustness of the solution. For this specific application of the model, results showed that the optimal robust solution could increase the company's expected profits by 6.4%.