Abstract: The invention relates to linear programming methods and systems. The linear programming model has at least one input streams, at least one intermediate stream, and at least one output stream. The linear programming model is utilized for simulating the effect of withdrawing at least a portion of an intermediate steam on one or more of the model's outputs.

Abstract: Methods and systems for withdrawing a stream from a linear programming model of a manufacturing facility. In one embodiment, one or more independent input variables and one or more key output variables are specified within the linear programming model. A stream within the model to be at least partially withdrawn is identified, and a stream is preferably added to the model immediately downstream of the withdrawal point. The added stream has one or more component rates that are perturbed. The one or more key output variables are solved in response to the perturbation of the component rates to create a derivative for the perturbed component rates. The derivatives are negated, and an amount of withdrawal for the identified stream is specified. The resulting component rates of the stream to be at least partially withdrawn can be determined based on the specified amount of withdrawal and the negated derivatives to simulate an effect on the one or more key output variables.