Kinetic modeling based on continuum lumping is a powerful methodology for working with complex petroleum mixtures. The concentration of the lumped species in the reaction mixture, characterized by reactivity, is expressed as a continuous function. The continuous concentration-reactivity function can be constructed from the experimental data, which involves inverting an integral equation. A simple methodology based on a piecewise linear interpolation formulates the inversion problem as a constrained optimization problem. The proposed method is applied to two different vacuum gas oil feedstocks, and the weight fraction values calculated from the continuous concentration-reactivity function are compared with the actual weight fraction values from the true boiling point (TBP) curve.