hello,
i am trying to solve a rather complicated scheduling problem formulated
as a binary integer program. i have formulated the model in a way that
it is obvious which general constraint can be relaxed (the one that
prevents separability). so far so good. during the modelling process,
it became apparent, that anotehr "overall" constraint is needed. That
leaves me with two sets of constraints, which both partition my
variable set in different manner. So teh lagrangian relaxation i
defined previously doesn't work anymore. i hope the rough problem
setting is clear enough now.
my intention is to relax both sets of constraints, with different
multipliers. my question here is:
since i am not sure on how to proceed in finding the multiplier values
because of different variable partitionings, can anyone give me a hint
at: 1) whether this approach makes any sense, and 2) where to look at
for an example. I have searched the web so far, but haven't found any
paper on dealing with two different types of multipliers.
Thanks a lot in advance,
Cheers,
Ina