Model became infeasible after adding "difference to mean" variables and constraints
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The model I'm building includes variables to indicate utilization rates at different facilities. I want to compute the mean utilization rate and add several "difference to mean" variables. I did it as follows:
mean_utilization = m.addVar(name='mean_utilization')
m.addConstr(14 * mean_utilization ==
quicksum(utilization_rate[i] for i in facility_list))
diff_to_mean = m.addVars(facility_list, name='diff_to_mean')
m.addConstrs(
(diff_to_mean[i] == utilization_rate[i] - mean_utilization)
for i in facility_list
)
The problem is, when the two constraints are used simultaneously, the model would immediately return infeasible. I couldn't understand why, since mean_utilization and diff_to_mean don't seem to affect any other parts of the model, and the constraints look perfectly fine and linear. I didn't even add any of these parts into the objective function. They're simply extra variables that don't really do stuff and the model became infeasible.
I would appreciate any help! Thank you very much!
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Variables added with Model.addVar() or Model.addVars() are nonnegative by default. Thus, the \( \texttt{diff_to_mean} \) variables are all nonnegative. There almost certainly exists \( \texttt{i} \) for which \( \texttt{utilization_rate[i] - mean_utilization} \) is negative, which would result in an infeasible model. To resolve this, you can try setting the \( \texttt{lb} \) keyword argument when defining the \( \texttt{diff_to_mean} \) variables:
diff_to_mean = m.addVars(facility_list, lb=-gp.GRB.INFINITY, name='diff_to_mean')
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