Decomposition methods used in operations research

Question

I want to know when and where to use the decomposition methods such as lagrangean decomposition, Dantzig-wolfe decomposition and Bender's decomposition are used and advantageous. I also want to know the application areas where these techniques are widely used. I also want to know whether I can apply any one of the above three methods and solve a bigger problem ( having say 3500 integer variables and 2000 constraints) with a trail version of soft wares such as GAMS or LINDOS which have limited capacity of 50 integer variables and 100 constraints.

Answer 1

Yes, they are used but more in academic studies than in practical applications. MIP solvers and computer hardware have become very fast so we can handle many problems with straight MIP models that previously required decomposition techniques.

Typically decomposition methods are used where there is a reason to do so: large and difficult MIP models that have some structure that is amenable to decomposition. Googling must give you a good indication if decomposition is used in your specific application area.

You can also run your larger GAMS models on NEOS. That allows you to develop your model on a small data set locally and then run the GAMS model with a larger data set on NEOS.