A known challenge for the simulation of reacting flow systems is that detailed chemical mechanisms contain hundreds to thousands of species and thousands of reactions, leading to high CPU requirements despite the use of state-of-the-art solvers. For specific conditions of interest (temperature, pressure, and composition), smaller mechanisms can predict the chemistry relatively accurately. One possibility for obtaining such mechanisms is species elimination from a detailed mechanism. Here, an automatic method for kinetic model reduction by simultaneous reaction and species elimination is proposed, based on an integer linear program (ILP) formulation. The solution of the ILP is an optimally reduced kinetic mechanism that reproduces the predictions of a reference mechanism within prespecified tolerances for finitely many reference points in the state space. The method is applied to generate optimally reduced models for isobaric, adiabatic homogeneous combustion. Case studies are presented for the combustion of n-heptane. Comparisons between the full and reduced models are shown and the tradeoff between species and reaction elimination is discussed. Tolerances in the ILP formulation control the error introduced by the model reduction. For increasing acceptable error, more species and/or reactions are eliminated. A method of quantifying this tradeoff between approximation error and reduction achieved is proposed, based on multiobjective optimization, and demonstrated in a case study. The effect of variable initial conditions is investigated. The mechanisms generated achieve significant reduction in the CPU requirement and can accurately predict the trajectories of the state variables (species mass fractions and temperature), as well as other metrics of interest, such as ignition time delay.