depends on how much time you want to spend on this and how much traffic you're expecting.
the fastest way to implement this imho is to have a column for the date/time the auction started ( now() )and a column for when the auction ends( dateadd( now() + 1 week). whenever the page loads, first run a sql update setting the status of the auction to closed where auction_closed_date > now(). next, show all open auctions sorting by the auctions that will soon close.
if you're expecting a bit more traffic, then have a php page run as a cron job updating the auction status every couple of minutes.