ABSTRACT Consumption of energy in any manufacturing operation contributes significantly to the ultimate production cost. The study is focused on optimising various CNC milling input variables like depth of cut, round edge radius, feed rate and spindle speed during machining of Inconel 625 alloy for responses such as power consumption, axial force, torque and surface roughness. The experimental results are optimised with MOGA and RSM approaches. It is observed that increases in spindle speed, depth of cut, feed rate and round edge radius increased power consumption, axial force, torque and surface roughness. Optimum machining parameters for MOGA were depth of cut: 0.299 mm, round edge radius: 25 µm, feed rate: 197.31 mm/min and spindle speed: 3000 rpm and output responses were power consumption 1199.63 W, surface roughness 2.16 µm, axial force 176.15 N and torque 0.336 Nm. For RSM, optimum machining parameters were depth of cut: 0.1 mm, round edge radius: 61.36 µm, feed rate: 172.72 mm/min and spindle speed: 3000 rpm and output responses are power consumption 1124.53 W, surface roughness 0.3438 µm, axial force 166.53 N and torque 0.132 Nm with composite desirability of 0.8421. Impact of individual input parameters on response has been examined using 3D surface view.