As far as I know, a single-level CLSP is an NP-hard problem. Multi-level CLSPs are more complex than single-level ones.
What is the main strategy in solving a Multi-level CLSP?
What's the difference between the strategies for Single-level ones and those for Multi-level ones?
When you say 'level', do you mean 'item' or do you refer to the levels of a BOM structure? Because a problem can be single-level but multi-item (and still hard to solve).
If you mean with 'solving' finding a 'good solution', obviously there are many heuristic methods that work very well in practice. If you are aiming to find the 'optimal' solution, then it's of course not to be expected with a realistic size problem -- there are some inequalities (such as the classical (l,S) inequalities) and reformulations (such as the facility location reformulation) that might well in practice to close the gap (I'd advice the first in practice as the problems can get messy with reformulations due to increase in dimension). Also other exact methods such as Benders decomposition and Lagrangean relaxation can be very handy.
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