Manufacturing industries contribute to 16.7% of CO2 emissions globally [1]. Any waste generated during manufacturing processes such as defective products, poor tolerances, or rejected products due to quality issues, result in excessive energy consumption and unnecessary carbon emission. Most of the manufacturing waste and quality fluctuations are generated due to uncertainty and variation in raw material and process conditions [2]. For this purpose, uncertainty quantification, robust optimization as well as real-time monitoring and optimization are among the promising methods to reduce the waste during manufacturing processes. Robust optimization and inverse robust optimization, so-called tailored scatter, are generally implemented offline [3] due to computational complexities, process non-linearities and problem dimensionality. In this work, an efficient implementation of robust optimization is presented using closed-form solutions of uncertainty propagation and sensitivities to realize the potential of real-time robust optimization. This method is applied on an industrial wipe-bending manufacturing process. A Gaussian-process surrogate model of this non-linear manufacturing process is constructed to test the efficiency of the proposed method. The results demonstrate not only increased accuracy in uncertainty propagation and evaluating sensitivities but also a notable reduction in computational expenses compared to conventional methods, such as quasi Monte Carlo (MC). By applying this method and using a gradient-based solver (SQP), solving a full robust optimization problem becomes feasible within seconds representing a reduction in computation time by more than one order of magnitude compared to SQP and quasi MC. The results clearly show the potential of this approach to be implemented in online robust optimization and paves the way towards real-time implementation of robust optimization in industrial applications to reduce their carbon footprint.