I am working on a nonlinear scheduling problem that minimizes the electricity cost of a facility. This system includes a number of identical machines that consume power and produce a product. When the product demanded by these machines is low (i.e. near the low bound for one machine) this causes an infeasibility. I think this is occurring because in reality only one machine should be on, but the way I have the problem written, mathematically this decision is impossible to reach. In general what is the best way to model identical equipment?
I could make one machine just slightly more efficient than the other...but that's not ideal. Is there a more elegant way to handle this?