Hey Afsarul, The cheapest would be through government aided ferries from Chennai which will take you more than two days (60 hrs) to reach port Blair and from Kolkata which will take you 70 hours to reach port Blair.... Have not been in this, but local andamanese say that this is the most beautiful way to reach Andaman and its also lovely to view sea for this long time ... This would be the cheapest for you to reach Andamans ... Check this link for the departure time and the rates ... http://www.andamanbeacon.com/andaman_ship_schedule_fare.html If at all you carry this journey don't forget to post it on your Tripoto page ... Happy Travelling !!!
Basically cost will depends on how you want to spend your tour. If you tell me how long days for you are going, then I can suggest you as per my experience.