When it begins, remember to file at all levels. Make as much noise and problems as you can. You can sue UPS and you can sue the Union for failure to represent. Even if you just go to small claims court for both it is definitely worth it. Last I checked small claims cost $60 to file and had a $15,000 max.
You can also call the UPS Corporate Human Resources hotline at 1-800- 220-4126. You can report a complaint against your supervisor or manager, and then follow that up with a Union grievance. This will help get the Company’s attention at a higher level.