A zero-dimensional model of the positive column in Ar/Ne/Xe gas mixtures has been developed to help understand the measured dependence of the efficacy on operating conditions in a mercury-free flat fluorescent lamp in a dielectric barrier geometry. The experimental conditions are such that the radiation from the discharge is homogeneous over most of the discharge voltage. The model uses as input the discharge current waveform from the experiments, and it yields the time variations of the mean electron energy and the species densities. From these quantities we calculate the number of vacuum ultraviolet (VUV) photons emitted by the xenon resonance atoms and excimers during one current pulse and the efficiency for generation of VUV radiation in the positive column, which are compared with the measured luminance and efficacy for various voltages, pulse intervals, and lamp sizes. Over the range of conditions studied, we find that most electrical energy dissipated in xenon excitation is converted to VUV radiation; i.e. the losses of xenon excitation in stepwise and associative ionization processes are small. When the mean electron energy is low, energy dissipation in elastic momentum transfer collisions leads to a decrease in the efficiency. On the other hand, ionization and excitation of argon degrade the efficiency when the mean electron energy is high. To a lesser extent, stepwise excitation of the xenon metastables also decreases the efficiency for high current densities.