Nonlinear planning and scheduling models for crude-oil atmospheric and vacuum distillation units are essential to manage increased complexities and narrow margins present in the petroleum industry. Traditionally, conventional swing-cut modeling is based on fixed yields with fixed properties for the hypothetical cuts that swing between adjacent light and heavy distillates, which can subsequently lead to inaccuracies in the predictions of both its quantity and quality. A new extension is proposed to better predict quantities and qualities for the distilled products by taking into consideration that we require corresponding light and heavy swing-cuts with appropriately varying qualities. By computing interpolated qualities relative to its light and heavy swing-cut quantities, we can show an improvement in the accuracy of the blended or pooled quality predictions. Additional nonlinear variables and constraints are necessary in the model, but it is shown that these are relatively easy to deal with in the nonlinear optimization.