I have a blended model with multiple goals and a number of constraints.
Some of the constraints can be relaxed if the model is infeasible. Which it frequently is.
The goals are (sadly) one - two orders of magnitude apart, so a small change to one can make the other irrelevant without normalizing somehow.
I can make the goals (kinda, sorta) equivalent in importance by normalizing the weights in the sum of linexps that make up the target using the maximum possible values I calculated for each. It's not perfect, and if there's a better way to do it I'm all ears, but it's good enough for this problem.
I can't seem to figure out a way to do the same for relaxing the constraints in a way that makes them equally valuable. Is there something ootb that can help with this at all?
A concrete example might help.
So let's say I'm buying widgets from 3 suppliers A,B,C. Stocks at all 3 are constrained. Prices are different at all 3.
I have two conflicting requirements -
1. minimize my spend for a set number of widgets.
2. try to get a selected split across suppliers. So (say) a gets 25%, B gets 45% and C gets the rest. Count of widgets bought not spend (and this is important as this is a contrived example).
I modelled (2) as sum of widgets bought and constrained it to the target percentage. Clearly the two goals are incompatible.
In this case the constraints can both be relaxed. I'm trying to figure out a way to make the two sets of roughly equivalent import using the rhspen values in feasRelax.
This is a contrived example for illustration. My problem has more than two sets of constraints that compete, so I'm looking for something generic if it exists.
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