Well, this is something you could do to make a cheap trip from Rajasthan to Andaman Islands.
Firstly, get your flight thing sorted out. Usually, you get good deals on flight tickets, if you book your flight 3 Months earlier. The only commercial airport in Andaman is at Port Blair (IXZ) where you land. Well, there is one more thing you need to know is that the direct flight to Port Blair, currently is only from Chennai and Kolkata. You may choose how you wish to travel from Rajasthan to Chennai/Kolkata. We believe Kolkata will be much cheaper. Usually, as the date approaches near the flight tickets get expensive and then the overall tour cost to Andaman Islands gets expensive as well.
Once the above thing gets sorted out then you can plan an extremely customized and cheap tour for yourself in the Andaman Islands.
There are a lot of Andaman tour Package options that you can browse
Trips from budget, standard to luxury tours are available. The cheapest and most comfortable trips will be the standard tours, however if you wish to make your trip more cheaper then you can select budget tours as well. Try to travel before 25 December and after 15 January to make it a little more cheaper. Usually, 25-Dec to 15 January is a peak season when the price rises significantly.
Hope this helps and hope to see you in the Andaman Islands soon.