I am working on a problem which involves optimizing for minimum power consumption in a large compressor network interconnected through pipelines (think of a connected graph with nodes as compressors and arcs as pipelines). I need to impose a constraint. when more than one compressors share a single pipeline on their discharge side i.e. their individual discharge pressures should ideally be equal.
Now, when I read in the historical plant operational data recorded through the sensors, I notice that these variables are fairly close but not precisely equal already. This could likely be due to sensor error. My question is how to model such constraints in an optimization problem so that you account for the slight variability among the variables instead of imposing a strict equality constraints.