Over the past years, the data envelopment analysis (DEA) methodology has registered widespread use among researchers from many fields. Furthermore, it is important to note that the non-Archimedean infinitesimal, ϵ, is a key concept in DEA models. Nevertheless, it is known that some computational difficulties arise when using ϵ in DEA. In this short communication, we show how the non-Archimedean may be voided using a directional distance function approach. Thus, our approach avoids choosing a real number (10-5 or 10-6) as a value for ϵ or estimating the same.