Not a perl answer, but it's simpler with a shell script... 
#!/bin/bash
for f in customer*.xml
do
  /usr/bin/zip ${f%xml}zip ${f} ${f%xml}pdf ${f%xml}xls;
done

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In reply to Re: Grouping files with the same name... by shoness
in thread Grouping files with the same name... by A200560

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