What are the disadvantages of making a large Java non-static method synchronized? Large method in the sense it will take 1 to 2 mins to complete the execution.
If you synchronize the method and try to call it twice at the same time, one thread will have to wait two minutes.
This is not really a question of "disadvantages". Synchronization is either necessary or not, depending on what the method does.
If it is critical that the code runs only once at the same time, then you need synchronization.
If you want to run the code only once at the same time to preserve system resources, you may want to consider a counting Semaphore, which gives more flexibility (such as being able to configure the number of concurrent executions).
Another interesting aspect is that synchronization can only really be used to control access to resources within the same JVM. If you have more than one JVM and need to synchronize access to a shared file system or database, the synchronized keyword is not at all sufficient. You will need to get an external (global) lock for that.
Since your method takes a huge amount of time to run, the relatively tiny amount of time it takes to acquire the synchronized lock should not be important.
A bigger problem could appear if your program is multithreaded (which I'm assuming it is, since you're making the method synchronized), and more than one thread needs to access that method, it could become a bottleneck. To prevent this, you might be able to rewrite the method so that it does not require synchronization, or use a synchronized block to reduce the size of the protected code (in general, the smaller the amount of code that is protected by the synchronize keyword, the better).
You can also look at the java.util.concurrent classes, as you may find a better solution there as well.
If the object is shared by multiple threads, if one thread tries to call the synchronized method on the object while another's call is in progress, it will be blocked for 1 to 2 minutes. In the worst case, you could end up with a bottleneck where the throughput of your system is dominated by executing these computations one at a time.
Whether this is a problem or not depends on the details of your application, but you probably should look at more fine-grained synchronization ... if that is practical.
If the method takes on the order of minutes to execute, then it may not need to be synchronized at such a coarse level, and it may be possible to use a more fine-grained system, perhaps by locking only the portion of a data structure that the method is operating on at the moment. Certainly, you should try to make sure that your critical section isn't really 2 minutes long - any method that takes that long to execute (regardless of the presence of other threads or locks) should be carefully studied as a candidate for parallelization. For a computation this time-consuming, you could be acquiring and releasing hundreds of locks and still have it be negligible. (Or, to put it another way, even if you need to introduce a lot of locks to parallelize this code, the overhead probably won't be significant.)