As many BEE SIGgers have found, it is quite possible to have an odourless compost bin even on a balcony to get rid of their food waste. Here is a summary information about composting shared on our mailing list.
The high-tech solution to your problem is a curious white powder containing Effective Microorganisms (EM). These little blighters will speed up the decomposition process and reduce the smell. They're quite popular in Japan, so you should be able to get them in a gardening centre. I know some people who use them, but I'm not sure if it's really necessary or desirable to be adding foreign organisms to your pristine compost, unless you can't get rid of the smell with normal aeration techniques.
The only purchase you'll need to make is two plastic garbage cans. Ideally the largest should be about 100 litre capacity and the smaller about 60 litres. The larger the volume, the faster your compost will heat up, thus aiding decomposition.
Make about 15 small holes in the bottom of the smaller can. Next, make three rows of holes along the side of the same can about 15cm apart, leaving approximately 10ch between the rows. Place a brick or a similar large solid object in the bottom of the large can. This is to allow leachate to drain out of the smaller can. Rich in nutrients, it can be diluted with water and added to pot plants or added back to the compost as is. Into the smaller can, lay a base of carbon-rich materials like twigs or pine needles, then layer with nitrogen-rich materials such as kitchen peelings or green leaves. The smaller the pieces, the faster the breakdown. Finally, top with soil and give the whole thing a generous sprinkling with water. Secure the lids and go and make a cup of tea… In winter, insulate your compost bin by surrounding it with old newspapers.
You can buy aerated compost bins at garden centers and from Japan Agriculture.
Vermiculture is an excellent apartment-friendly way of disposing of food waste also. There are products called "The Worm Factory" and "Can-O-Worms", made by a Sydney company called Reln Plastics, and both are available in Japan through their distributor Sagami Jyoka Service in Kanagawa Prefecture, (Telephone 0463-90-1332 and Fax 0463-95-9667. A big part of Reln's energy goes into education and there is a teacher's activities page on their site, and also a Japanese language page which explains all about their products (which may even lend itself to a low cost eco-project for ALTs!).
With worms, you will need a deep tray with rocks at bottom and an ashen bag to prevent the little worms from falling out. Then some earth, most preferably with no nutrients or fertilizer in it, or this will kill the worms. Then we place dry food only mixed amongst the earth so the worms can access it and we cover the lot with an ashen bag so that the air and sun do not burn and dehydrate the little things. Now with worms after one month (depending on tray size) we do another tray to put on top so that the worms can migrate out of the previous box with their little babies into the new box. then we throw the first box into the garden or pot plants and start again.