As Wookie says, cron does not set up an environment unless you tell it to. That can be done at the head of the crontab file.

Obligatory pickiness: use strict;. That would show that all your variables are global. That is not causing problems in your script since all the names are different. Later modifications could give puzzling failures if a generic temp like $i or $time were reused.

After Compline,
Zaxo