Exploitation of edible oils for biodiesel production has become a debatable issue. This article aims at developing a statistical model for optimized biodiesel production from a mixture of two non-edible oils, namely, pongamia and neem oils. Central composite design was used to design batch experiments in order to examine main and interaction effects of reaction time, catalyst concentration (NaOH) and methanol–oil molar ratio on biodiesel yield. Based on the experimental data, a reduced cubic model was chosen to represent the response surface (R2 = 0.995). Analysis of variance indicated that catalyst concentration had a significant effect on the biodiesel yield (F = 746.91, p < 0.0001). Numerical optimization (using fmincon in Matlab®) of the reduced cubic model predicted maximum biodiesel yield of 86.2% at reaction time: 77 minutes, catalyst concentration: 0.67% (w/w) and methanol–oil molar ratio: 6:1. A close agreement between the predicted and observed biodiesel yields (86.3%) in validation experiment (under optimal settings) confirmed the accuracy and applicability of the model for industrial process optimization. The properties of biodiesel produced under optimal settings, i.e. flash point, cloud and pour points, were within the specifications of ASTM 6751 and EN 14214 biodiesel standards. © 2018 Informa UK Limited, trading as Taylor & Francis Group.