1. A method for simultaneous synthesis of combined heat and power utility and process subsystems for a process facility, the method comprising the steps of: defining model input data for a combined heat and power utility and process subsystem mathematical program model, the model comprising a cost function configured to minimize a total cost of combined heat and power utility and process subsystems of a process facility, the combined heat and power utility and process subsystems comprising a utility subsystem configured to generate steam and a process subsystem configured to consume steam generated by the utility subsystem, and the model input data comprising a plurality of rigorously bounded process variables for one or more key process of the process facility, the plurality of rigorously bounded process variables comprising, for each of the one or more key processes: process steam demand intervals for the key process, the process steam demand intervals comprising a process steam demand interval for each of a plurality of different steam pressure levels, wherein each process steam demand interval for a steam pressure level comprises an upper bound and a lower bound of process steam demand for the key process at the steam pressure level; and a process power generation interval for the key process, the process power generation interval comprising an upper bound and a lower bound of power generation for the key process; and processing, by a computer, the model input data through application of the combined heat and power utility and process subsystem mathematical program model to determine model output data comprising process subsystem conditions and utility subsystem conditions, the process subsystem conditions comprising, for each of the one or more key processes: process steam demand load values corresponding to the process steam demand intervals for the key process, the process steam demand load values comprising a process steam demand load value for each of the plurality of different steam pressure levels; and a process power generation value corresponding to the process power generation interval.