Despite several additive manufacturing techniques are commercially available in market, Fused Deposition Modeling (FDM) is increasingly used by researchers and engineers for new product development. FDM is an established process with a plethora of advantages, but the visible surface roughness (SR), being an intrinsic limitation, is major barrier against utilization of fabricated parts for practical applications. In the present study, the chemical finishing method, using vapour of acetone mixed with heated air, is being used. The combined impact of orientation angle, finishing temperature and finishing time has been studied using Taguchi and ANOVA, whereas multi-criteria optimization is performed using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The surface finish was highly responsive to increase in temperature while orientation angle of 0° yielded maximum strength; increase in finishing time led to weight gain of FDM parts. As the temperature increases, the percentage change in surface roughness increases as higher temperature assists the melt down process. On the other hand, anisotropic behaviour plays a major role during tensile testing. The Signal-to-noise (S/N) ratio plots, and ANOVA results indicated that surface finish is directly proportionate to finishing time because a longer exposure results in complete layer reflowing and settlement.