It's fairly obvious that either you will have to buy an off-the-shelf solution (of which there are several), or get someone to write you a customised program.
Both of these options are expensive, but the latter will be horrendously so. What goes on server-side is extremely complex, and I would definitely not advise you to have anything custome-written unless you can use the Asian prgramming services you mention.
Some time ago I designed a very similar site for clients in the travel business in Australia, and we bought in the reservation software from a company called Datalex. These people specialise in reservation/booking systems (including flights) for the travel industry, and they have exactly what you want. It will not be cheap, but it will probably be cheaper/better than starting from scratch.