Directional stream value analysis system and server

A optimization modeling system comprising:

• one or more computers comprising one or more processors and one or more non-transitory computer readable media, the one or more non-transitory computer readable media comprising instructions stored thereon that when executed cause the one or more computers to:
• generate, by the one or more processors, a model of an industrial process comprising a linear program comprising one or more equations that includes one or more flow variables associated with one or more flow components;
• store, by the one or more processors, a relation of each of the one or more flow variables to any of the one or more equations in which the one or more flow variables are incident with a nonzero coefficient;
• compute, by the one or more processors, changes in the one or more flow variables in in response to a material injection into the model;
• and
• determine, by the one or more processors, a stream value by summing a downstream impact or an upstream impact of the material injection.