1. A computer modeling apparatus, comprising: an input module enabling: (i) user specification of inventory information including one or more rundown blending components without an intermediate storage tank but with splitters that separate the one or more rundown blending components, and (ii) user specification of refinery product commitments; a processor routine executable by a computer and coupled to the input module, the processor routine responding to the user specification by sequencing refinery operations into an optimized multi-period, multi-event schedule that matches the refinery product commitments with (a) the inventory information and (b) rundown blending component operations without intermediate storage tanks, wherein the processor routine optimizes scheduling of the rundown blending component operations directly off a process unit to a finished product tank without having intermediate storage tanks; the processor routine sequencing the refinery operations into the optimized refinery operations schedule by comprehensively modeling nonlinear properties, linear properties, nonlinear constraints, and discrete constraints of the rundown blending component operations as an optimization problem, the modeling formulating the optimized refinery operations schedule to simultaneously optimize each of: (i) sequence and timing of refinery operations events, including determining optimal number and duration of event periods for the sequencing of the refinery operations events, (ii) split ratio of splitters, and according to the optimum split ratio, scheduling the splitters to separate the rundown blending component operations into multiple component streams of different flow and quality, the splitters changing properties of at least one of the multiple component streams, and (iii) recipes for product blends in the refinery product commitments, the optimal recipes including optimal components and optimal amounts; and an output module including: a display member receiving the optimized refinery operations schedule from the processor routine and providing a display of the optimized refinery operations schedule; and a blending control system receiving the optimized refinery operations schedule from the processor routine, wherein the blending control system adjusts parameters of the rundown blending component operations based on the received optimized refinery operations schedule, such that the blending control system controls the rundown blending components in a manner that simultaneously optimizes the sequence and timing of the refinery operations events, the split ratio of the splitters, and the recipes for the product blends.