It is possible to set an end date for an experiment. You only have to go into the "Summary" screen of your experiment and select the "Stats" section.
Within there you can specify the number of days you want the experiment to finish. So, if your starting date is January 1st and you want to run it until January 15th, then just set the "Maximum Days" to "15".
Note that the cutoff date is in on defined on the GTM time zone.