For high-performance operations in crude oil refinery processing, it is important to properly determine yields and properties of output streams from distillation units. To address such complex representation, we propose a cutpoint temperature-modeling framework using a coefficient setup MIQP (mixed-integer quadratic programming) technique to determine optimizable surrogate models to correlate independent X variables (crude oil compositions, temperatures, etc) to dependent Y variables (such as stream yields and properties of distillates). The X inputs are systematically generated by Latin hypercube sampling (LHS), and the experiments to obtain the synthetic Y outputs are simulated using the well-known conventional and improved swing-cut methods. By using these optimizable surrogate models (which are suitable to handle continuous data from the process) with measurement feedback (for adjustments and improvements), distillation outputs can be continuously updated when needed. The proposed approach successfully builds accurate surrogates for the distillation unit, which can be embedded into complex planning, scheduling, and control environments. Moreover, this MIQP surrogate identification technique may also be applied to other types of downstream process optimization problems such as reacting and blending unit operations, as well as other separating processes.