Olando Juwan Thomas appeals the district court’s 1 adverse grant of summary judgment on his 42 U.S.C. § 1983 complaint. After de novo review, see Beaulieu v. Ludeman, 690 F.3d 1017, 1024 (8th Cir. 2012), we reject Thomas’s arguments for reversal as follows.

We agree with the district court that Thomas did not create a genuine issue of material fact as to whether Lt: D. Davis was deliberately indifferent, as Thomas’s medical authorization did not restrict him from work or from wearing sandals at work, and he did not submit evidence of the work environment or risks, of injury from working in such shoes. See Fed.R.Civ.P. 56(a); Farmer v. Brennan, 511 U.S. 825, 834, 837-38, 847, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994) (official violates Eighth Amendment if he knows of and disregards substantial risk of serious harm to inmate health or safety); Nelson v. Corr. Med. Servs., 583 F.3d 522, 528-29 (8th Cir. 2009) (en banc) (outlining two-prong deliberate-indifference test); Choate v. Lockhart, 7 F.3d 1370, 1374 (8th Cir. 1993) (officials are deliberately indifferent when they knowingly compel prisoners to perform physical labor that is beyond their strength, dangerous to health, or unduly painful; mere negligence or inadvertence, however, does not satisfy deliberate-indifference test). Thomas also failed to establish supervisory liability against Warden James Banks, see Williams v. Davis, 200 F.3d 538, 538-39 (8th Cir. 2000) (per curiam) (absent constitutional violation, there is no basis for § 1983 liability against supervisors); and his allegation that Banks improperly investigated his grievance failed to state a claim, see Buckley v. Barlow, 997 F.2d 494, 495 (8th Cir. 1993) (per curiam) (prison officials’ failure to process or investigate grievances, without more, is not actionable under § 1983). The magistrate judge properly entered final judg *292 ment under 28 U.S.C. § 686(c) without first offering Thomas an opportunity to object, see Roell v. Withrow, 538 U.S. 580, 585, 123 S.Ct. 1696, 155 L.Ed.2d 775 (2003) (referral under § 636(c) gives magistrate judge full authority over dispositive motions, conduct of trial, and entry of final judgment, without district court review); and properly entered final judgment without sua sponte allowing Thomas to amend his complaint.

The judgment is affirmed.