
    William HOWE, et al., PlaintiffsAppellees/Cross-Appellants, v. CITY OF AKRON, Defendant-Appellant/Cross-Appellee.
    Nos. 14-3352, 13-4172, 13-4268.
    United States Court of Appeals, Sixth Circuit.
    Argued: June 17, 2015.
    Decided and Filed: Sept. 17, 2015.
    
      ARGUED: Benjamin C. Sassé, Tucker Ellis LLP, Cleveland, OH, for Appel-lanVCross-Appellee. Bruce B. Elfvin, Elfvin & Besser, Cleveland, OH, for Ap-pellees/Cross-Appellants. ON BRIEF: Benjamin C. Sassé, Irene C. Keyse-Walker, Tucker Ellis LLP, Cleveland, OH, Cheri B. Cunningtham, Patricia Ambrose-Rubright, Michael J. Defibaugh, City of Akron, Akron, OH, Aretta K. Bernard, Karen D. Adinolfi, Roetzel & Andress, LPA, Akron, OH, for Appellant/Cross-Ap-pellee. Bruce B. Elfvin, Barbara Kaye Besser, Stuart Torch, Elfvin & Besser, Cleveland, OH, Dennis R. Thompson, Christy B. Bishop, Thompson & Bishop Law Offices, Akron, OH, for Appel-lees/Cross-Appellants.
    Before: MOORE and COOK, Circuit Judges; COHN, District Judge.
    
    
      
       The Honorable Avern Cohn, Senior United States District Judge for the Eastern District of Michigan, sitting by designation.
    
   OPINION

KAREN NELSON MOORE, Circuit Judge.

In 2004, Defendant-Appellant City of Akron administered promotional examinations for firefighters for the ranks of Lieutenant and Captain. The Plaintiffs-Appel-lees are Akron firefighters who took the examinations, but were not promoted. They filed this lawsuit, alleging that the promotional process disparately impacted firefighters over the age of forty in violation of the Age Discrimination in Employment Act, 29 U.S.C. § 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. In addition, they allege that the Lieutenant promotional process adversely impacted African-American applicants, and the Captain promotional process adversely impacted Caucasian candidates in violation of Title VII, 42 U.S.G. § 2000e et seq., and Ohio Revised Code § 4112.02(A).

On December 23, 2008, a jury found that the two promotional processes adversely impacted applicants over the age of forty, and that the exams and promotional processes were not justified by business necessity. On October 2, 2009, the district court entered findings of fact and conclusions of law consistent with the jury’s verdict with respect to the Plaintiffs’ Title VII race-discrimination claims, finding that Akron’s promotional process adversely impacted African-American Lieutenant candidates and Caucasian Captain candidates. Following the parties’ post-judgment motions, the district court ordered a new trial on the sole issue of damages. On August 30, 2013, -after a retrial, the district court entered an award of back pay in the amount of $616,217.75. On March 27, 2014, the district court entered a permanent injunction and appointed a court monitor.

The parties have been litigating this case with remarkable vigor and venom since 2008. After two trials and multiple appeals, the parties remain unwilling to settle their differences. Akron now appeals the liability judgment, back-pay award, permanent injunction, and the appointment of a court monitor. The Plaintiffs have cross-appealed the district court’s back-pay award, and argue that Akron has forfeited any challenge to the liability judgment because of this court’s opinion in Howe v. City of Akron (“Howe I”), 723 F.3d 651 (6th Cir.2013). Both parties seek — at the very least — a new trial on the issue of back pay and reassignment of the case to a different district judge.

For the reasons expressed in this opinion, we AFFIRM the liability judgment. However, we REVERSE the back-pay award and REMAND the case for reassignment to a different district judge and a new trial on the issue of back pay. In addition, we MODIFY the district court’s order appointing a court monitor to limit the court monitor’s involvement to one promotional cycle.

I. FACTS & PROCEDURAL HISTORY

A. Akron’s 2004 Promotional Process

The Plaintiffs are all members of the Akron Fire Department who took the 2004 promotion exam for either the rank of Lieutenant or Captain. Their claims arise out of the results of the Akron Fire Department’s 2004 promotional process.

Akron hired E.B. Jacobs LLC to develop, administer, and score the December 2004 Lieutenant and Captain promotional exams for the Akron Fire Department. R. 277 at 7 (Findings of Fact and Conclusions of Law (“FFCL”) ¶¶ 70-71) (Page ID # 7742). Each examination included a 100-question multiple-choice component about technical job requirements. Id. (FFCL ¶ 72). In addition to the written component, candidates for the Lieutenant position had to complete “a written work sample exercise” and undergo two oral assessments, including “a subordinate conference and incident command.” Id. (FFCL ¶ 73). The Captain promotional examination had three oral exercises: “a subordinate conference, group exereise[,] and [an] incident command.” Id. at 8 (FFCL ¶ 74) (Page ID # 7743).

After the examiners scored the exams, they converted the scores to a scale for which 100 was the highest score, and then created lists of eligible candidates for promotion. To be eligible for a promotion, the candidate had to achieve a final average test score of at least 70%. R. 80 at 10 (Def.’s Mot. for Summ. J.) (Page ID # 513). The test administrators combined the written and oral test scores and standardized those scores by converting them to a ninety-point scale. R. 196 at 84 (Trial Tr. Vol. 3) (Page ID # 4882); R. 211 at 141 (Trial Tr. Vol. 8) (Page ID # 5916). Next, the Fire Department awarded up to ten additional points based on seniority to the candidates’ final test scores, and then the candidates were ranked in order of the combination of their test score plus seniority. R. 196 at 83 (Trial Tr. Vol. 3) (Page ID # 4881); R. 211 at 141 (Trial Tr. Vol. 8) (Page ID # 5916). Candidates with the highest scores were at the top of the list; candidates with the lowest scores were at the bottom. See R. 212 at 127 (Trial Tr. Vol. 9) (Page ID # 6164). This final list was called the “eligibility list.” R. 99 at 11 (Pis.’ Resp. in Opp’n to Def.’s Mot. for Summ. J.) (Page ID # 2517).

When there was a vacant Lieutenant or Captain position, the Personnel Director for the Fire Department submitted a certified list of candidates to the Mayor, which included. the names of those candidates with the three highest scores on the eligibility list — the so-called “Rule of Three.” R. 213 at 178 (Tr. Trial Vol. 7) (Page ID # 6502). Next, the Personnel Director interviewed the three candidates before submitting a recommendation about whom among the three candidates the Mayor should promote to the vacant position. Id.;' R. 212 at 128 (Tr. Trial Vol. 9) (Page ID # 6165). To fill the next available vacancy, the Personnel Director selected the top three names on the eligibility list, and the interview process began anew. R. 213 at 182-84 (Trial Tr. Vol. 7) (Page ID # 6506-08). If a candidate was interviewed and passed over three times, then his or her name would be removed from the list. R. 99 at 11 (Pis.’ Opp’n to Def.’s Mot. for Summ. J.) (Page ID #2517). Under this system, it is possible that a candidate with the top score might never receive a promotion. Id.

On April 5, 2005, the Akron Civil Service Commission completed the eligibility list, which remained active for two years. R. 277 at 8 (FFCL ¶¶ 75-76) (Page ID # 7743). During that two-year period, twenty-eight candidates were promoted to the rank of Lieutenant and twelve to the rank of Captain. Id. (FFCL ¶¶ 78-79). Of the twenty-eight candidates who became Lieutenants only three were African Americans. Id. (FFCL ¶ 78). Of those twelve who became Captains seven were Caucasians. Id. (FFCL ¶ 79-80). The following Table represents the pass and promotion rates for each rank and protected group at issue:

Rank Class Pass Rate Promotion Rate
Over-40 76% (29/38) 24% (7/29)
Lieutenant Under-40 87% (55/63) 38% (21/55)
Caucasian 85% (69/81) 36% (25/69)
African-American 75% (15/20) ' 20% (3/15)
Captain Caucasian 81% (26/32) 27% (7/26)
African-American 78% (7/9) 71% (5/7)

Howe I, 723 F.3d at 656.

B. The Claims

On November 16, 2006, the Plaintiffs filed this lawsuit, alleging age and race discrimination in violation of federal statutory law. See R. 1 at 9-10 (Compl.Hf 30-37) (Page ID # 9-10). On October 19, 2007, the Plaintiffs amended their complaint to include claims of age and race discrimination in violation of Ohio law and violations of the Equal Protection Clause. R. 23 at 12-16 (1st Amend.Compl.1ff 49-68) (Page ID # 147-51).

The Age-Discrimination Claims. Eleven plaintiffs, Mike Reed, Brenda Chapman, Michael Harvey, William Roy Wilkinson, Jeffrey Layne, James Farina, Jeff Schueller, Jerry Elie, Frank Poletta, Kerry Briggs, and Bruce Clough allege that the promotional process adversely impacted candidates for the rank of Lieutenant who were over the age of forty. See R. 277 at 1-5 (FFCL ¶¶ 1-47) (Page ID # 7736-40). In Counts I, III, and V, the Plaintiffs allege that the promotional exams had an adverse impact on twenty-three candidates for promotion to the ranks of Lieutenant and Captain because of their age in violation of the ADEA, 29 U.S.C. § 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. R. 23 at 11-13 (1st Amend.CompLIffl 45-46, 49-50, 53-54) (Page ID # 146-48). Counts II, IV, and VI allege that the candidates for promotion to the rank of Lieutenant and Captain were subjected to disparate treatment because of their age “in the administration and scoring of the promotional examinations” in violation of the ADEA, 29 U.S.C. §§ 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. Id. (1st Amend. Compl.lffl 47-48, 51-52, 55-56).

The Race-Discrimination Claims. Three plaintiffs, Brenda Chapman, Michael Harvey, and Jerry Elie, allege that the promotional process for the rank of Lieutenant adversely impacted African-American candidates. See R. 23 at 14-15 (1st Amend.Compl.Hf 57-58, 61-62) (Page ID # 149-50). A group of twelve plaintiffs, William Howe, James Freeman, Leslie Geiser, John Triolo, Jeffrey Derenber-ger, David Hull, David O’Neil, Jerome Crawford, Bradley Robson, Michael Hausch, Bradley Carr, and Gregory Snyder allege that the promotional process adversely impacted Caucasian candidates for the rank of Captain. See id. at 14-15 (1st Amend.Compl.1ffl 59-60, 63-64) (Page ID # 149-50). Counts VII and IX alleged that the promotional examinations for the rank of Lieutenant had a disparate impact on African-American candidates in violation of Title VII, 42 U.S.C. § 2000e et seq., and Ohio Revised Code § 4112.02(A). Id. at 14-15 (1st Amend.Compl.W 57-58, 61-62) (Page ID # 149-50). Counts VIII and X alleged that the promotional exam adversely impacted Caucasian candidates for the rank of Captain. Id. at 14-15 (1st Amend.Compl.lffl 59-60, 63-64) (Page ID # 149-50). Counts XI and XII alleged that the administration of the promotional examinations violated the Equal Protection Clause of the Fourteenth Amendment. Id. at 15-16 (1st Amend. CompLIffl 65-68) (Page ID # 150-51).

On December 1, 2008, the district court entered summary judgment in favor of Akron for Counts XI and XII, the equal-protection claims. R. 176 at 1 (Order on Mot. for Recons.) (Page ID # 4196). A jury trial regarding the remaining claims commenced on December 3, 2008. During the trial, the plaintiffs dismissed their disparate-treatment claims (Counts II, IV, and VI) and the Captain candidates’ dispa- „ rate-impact, age-discrimination claims (Counts I, III, and V), which related to the plaintiffs who were candidates for the rank of Captain. R. 216 at 1 (Pis.’ Notice of Stipulation of Dismissal) (Page ID # 6585); R. 218 at 1 (Order Dismissing Disparate Treatment Claims) (Page ID # 6590); R. 309 at 2 (Tr. Trial Vol. 13) (Page ID # 16338). The jury’s task was to determine whether Akron’s promotional process had a disparate impact on African-American or over-forty candidates for the rank of Lieutenant and Caucasian candidates for the rank of Captain. R. 309 at 2 (Tr. Trial Vol. 13) (Page ID # 16338).

C. The Trial

The Plaintiffs and Akron presented evidence about the statistical significance of the disparities between the promotion of each protected group and argued about whether the statistical tests were appropriate tools to evaluate the disparate-impact claims. The Plaintiffs also offered expert opinion testimony that the examinations and the promotion processes were not job related. Akron’s experts offered opinion testimony to the contrary — that the promotional process was justified by business necessity.

On December 23, 2008, the jury returned a unanimous verdict in favor of all of the Plaintiffs and specifically found that business necessity did not justify the promotion process. See R. 237 at 1-44 (Jury Verdict) (Page ID # 7312-55). The jury awarded each candidate for the rank of Lieutenant $9,000 in compensatory damages and $72,000 in front pay. See id. at 10-20 (Page ID # 7321-31). The jury awarded each candidate for the rank of Captain $10,000 of compensatory damages and $80,000 in front pay. Id. at 21-32 (Page ID # 7332-43).

On October 2, 2009, the district court filed its findings of fact and conclusions of law, noting that it was “bound by the jury’s factual findings to the extent that the jury and non-jury claims overlapped.” R. 277 at 10 (FFCL ¶92) (Page ID # 7745) (citing Gutzwiller v. Fenik, 860 F.2d 1317, 1332-33 (6th Cir.1988); Lewis v. Sears, Roebuck & Co. (In re Lewis), 845 F.2d 624, 628-29 (6th Cir.1988)). The district court concluded that the Plaintiffs had “established a prima facie case of disparate impact on both their [ADEA] age and [Title VII] race claims.” Id. at 11 (FFCL ¶ 99) (Page ID # 7746). In addition, the district court concluded ■ that “[b]ased upon the jury’s findings ... Akron failed to prove that its employment practices in making selections for promotions to Lieutenant in 2004 were based on reasonable factors other than age or race.” Id. (FFCL ¶ 101). Thus, the district court found that Akron’s “2004 promotional process for promotion to Lieutenant” and Captain discriminated against the Plaintiffs on the basis of race in violation of 42 U.S.C. § 2000e-2(k)(l)(A)(i) and the Ohio Revised Code §§ 4112.02(A) and .99. Id. at 11-12 (FFCL ¶¶ 102-03) (Page ID # 7746-47). The district court awarded the Plaintiffs “front pay as determined by the jury,” as well as attorney fees and costs and further relief to be addressed after full briefing. Id. at 12 (FFCL ¶¶ 104-05) (Page ID # 7747).

D. The Post-Verdict Motions

On October 19, 2009, the Plaintiffs and Akron filed post-judgment motions. The Plaintiffs filed a motion pursuant to Federal Rule of Civil Procedure 59(e) to alter or amend the judgment, requesting additional relief: (1) back pay calculated through the date of judgment or promotion; (2) “grossing up” for tax liability on the wages paid in a lump sum; (3) prejudgment interest; (4) permanent injunctive relief in the form of a promotion for any prevailing plaintiff electing to be promoted; (5) pension adjustments; (6) post-judgment interest from the date of judgment until payment; (7) a posthumous promotion .and adjustment for Crawford; (8) permanent injunc-tive relief in the form of a new equitable, valid promotional process; appointment of a receiver to oversee the development of a new promotional process; (9) court monitoring until all issues related to the case are fully resolved; and (10) “any other relief as set forth in Plaintiffs’ motions for equitable relief.” R. 280 at 1-2 (Pis.’ Rule 59(e) Mot. to Amend. J.) (Page ID # 7756-57).

Akron filed two motions: A renewed motion for judgment as a matter of law, new trial, or remittitur pursuant to Federal Rules of Civil Procedure 50(b) and 59; and a Rule 59(e) motion to alter or amend the judgment, new trial, or remittitur. See R. 282 (Def.’s Renewed Mot. for J. as a Matter of Law “JMOL” or Mot. for a New Trial, or- Remittitur) (Page ID # 7761-69); R. 283 (Def.’s Rule 59(e) Mot. to Amend J. or Mot. for New Trial, or Remittitur on Pis.’ Title VII Claims) (Page ID # 7771-74). Akron argued, inter alia, that the evidence of adverse impact was insufficient. To this end, Akron argued four theories. First, Akron argued that the disparities between the various groups who went through the promotion process were hot statistically significant. Second, Akron asserted that pass rates were the appropriate measure of adverse impact— not promotion rates — and the evidence did not support a finding that there was a-four-fifths-rule violation when the experts compared the different pass rates of each group. R. 285 at 11-14 (Def.’s Mem. in Support of JMOL) (Page ID # 7788-91). Third, Akron also faulted the Plaintiffs for failing to introduce statistical evidence other than a violation of the four-fifths rule and argued that evidence of a violation of the four-fifths rule was insufficient because the sample size was small. Id. at 16-19, 22-24 (Page ID # 7793-96, 7800-01). Finally, Akron complained that the Plaintiffs had not established that Akron was an “unusual employer,” i.e., an employer who discriminates against the majority. See id. at 14-16 (Page ID # 7791-93).

Alternatively, Akron asserted that it was entitled to a new trial because the jury’s verdict was against the manifest weight of the evidence and the district court made legal errors and admitted certain evidence in error. R. 282 at 7-8 (Def.’s Renewed Mot. for JMOL, New Trial, or Remittitur) (Page ID # 7767-68); R. 283 at 3 (Def.’s Rule 59(e) Mot. to Alter or Amend J., New Trial, or Remittitur) (Page ID # 7773). Akron also sought a new trial on the issue of damages for two reasons. First, Akron argued that the lock-step damages award for each class of plaintiff was inconsistent with the Plaintiffs’ testimony about their individual damages. R. 285 at 27 (Def.’s Br. in Support of JMOL or Mot. for New Trial) (Page ID # 7804). Second, Akron asserted that the jury had not considered that not all of the Plaintiffs would have been promoted had the process been fair. Id. (citing Biondo v. City of Chi., 382 F.3d 680, 688-89 (7th Cir.2004)).

On December 30, 2010, the district court filed a memorandum opinion granting in part and denying in part the Plaintiffs’ and Akron’s Rule 59(e) motions to amend the judgment, denying Akron’s motion for judgment as a matter of law, and granting in part Akron’s motion for a new trial on the issue of damages alone. See R. 311 at 1-2 (D.Ct.Mem.Op.) (Page ID # 16399-16400). First, the district court concluded that Akron had waived its argument that promotion rates were not an appropriate metric to use because Akron had not advanced this argument in its pre-verdict motion for judgment as a matter of law. Id. at 16-17 (Page ID # 16414-15). In the alternative, however, the district court held that promotion rates were appropriate criteria for application of the four-fifths rule in a case challenging promotion policies. Id. at 18 (Page ID # 16416) (citing Phillips v. Cohen, 400 F.3d 388, 399 (6th Cir.2005)). Second, the district court found that Akron had “waived” the argument that the Plaintiffs had to prove that Akron is the unusual employer that engages in “reverse discrimination.” Id. at 20-21 (Page ID # 16418-19). Although Akron had requested a jury instruction requiring a showing of “background circumstances” that a facially neutral policy adversely impacted the majority, the district court found waiver because Akron had not furthered its argument for the proposed instruction during the charging conference. Id. at 20-21 (Page ID # 16418-19) (citing R. 138 at 30 (Proposed Joint Jury Instrs.) (Page ID # 3967); R. 148 at 14 (Def.’s Proposed Jury Instrs.) (Page ID #4036); R. 309 at 4-44 (Tr. Trial Yol. 13) (Page ID # 16340-80)). Third, the district court rejected Akron’s argument that even if there were violations of the four-fifths rule, the disparities were not statistically significant because of the small size of the sample. Id. at 21-24 (Page ID # 16419-22).

When the district court turned to Akron’s motion for a new trial, it rejected the bulk of Akron’s arguments, see id. at 29-34 (Page ID # 16427-32), but agreed with Akron that “the jury recognized, but failed to follow, their duty to award damages based on the testimony of the individual Plaintiffs” because the jury had awarded the individual Plaintiffs the same amounts in compensatory damages and front pay, id. at 29 (Page ID # 16427) (internal quotation marks omitted). The evidence at trial established that some of the Plaintiffs spent more time preparing for the examinations than other Plaintiffs, and some Plaintiffs failed multiple examinations. Id. at 29-30 (Page ID # 16427-28). Accordingly, the district court granted Akron’s motion for a new trial “solely on damages.” Id. at 34 (Page ID # 16432). The district court did not address the Plaintiffs’ Rule 59(e) motion to alter or amend the judgment.

Soon thereafter, Akron filed a motion to alter or amend the judgment to include a statement seeking certification of an interlocutory appeal pursuant to 28 U.S.C. § 1292(b) for one legal question: “Does ‘selection’ refer to pass rates or promotion rates in adverse impact promotional testing cases?” R. 314 at 1 (Def.’s Mot. to Amend J.) (Page ID # 8076). The district court denied the motion, in part because it doubted that Akron had preserved the issue, but also because Akron had not satisfied the § 1292(b) standard for certification. See R. 324 at 1-4 (D. Ct. Order Re § 1292(b) Certification) (Page ID # 8168-71).

E. Plaintiffs’ Motion for Promotion

On February 9, 2009, soon after the district court entered the liability judgment, the Plaintiffs filed a motion for a permanent injunction. The Plaintiffs requested “a permanent injunction prohibiting ... Akron from utilizing or otherwise acting upon any promotional process, including but not limited to the process developed and administered in December, 2004, for filling the ranks of Lieutenant and Captain.” R. 256 at 1 (Pis.’ Mot. for Permanent Inj.) (Page ID # 7528). The Plaintiffs also requested an injunction

requiring] the development of a job-related non-discriminatory promotion process, under the supervision and guidance of a receiver appointed by this Court, that selects qualified candidates without adverse impact because of race or age and complies with Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. § 2000e et seq., the ADEA, 29 U.S.C. § 621, et seq., and the Uniform Guidelines on Employee Selection, 29 C.F.R. § 1607, et seq.

Id. In the interim, the Plaintiffs sought “the promotion of each Plaintiff to the rank of Lieutenant and Captain,” and for the fire department to appoint “all acting officers for the ranks of Lieutenant and Captain, until the actual promotion of the Plaintiffs, exclusively from the pool of Plaintiffs, rotated on a seniority basis, with the incremental base pay set at the full-step in-grade level pending the development of the new promotion process.” Id. at 2 (Page ID # 7529).

On September 29, 2009, the district court denied without prejudice the Plaintiffs’ motion for a permanent injunction because the relief sought related to the Title VII claim for which the district court had not yet entered its findings of fact and conclusions of law. R. 276 at 1 (D. Ct. Order Re Permanent Inj.) (Page ID # 7734).

E. Renewed Damages Discovery

The parties disagreed about how the new trial on the issue of damages should proceed, so the district court ordered the parties to provide briefing about whether they would need additional discovery. R. 315 at 1 (D. Ct. Order Re Damages Disc.) (Page ID # 8081). On April 5, 2011, the district court set the jury trial for July 18, 2011, and reopened discovery to be completed by June 17, 2011. R. 326 at 1 (Pretrial Order) (Page ID #8173). The renewed discovery period was intended to provide Akron with an opportunity to explore issues related to the Plaintiffs’ calculation of damages. R. 322 at 4-5 (Def.’s Position Statement Re: New Trial on Damages) (Page ID # 8159-60).

On June 23, 2011, the district court ordered the Plaintiffs.to disclose “their damage calculation and how they arrive at those numbers.” R. 357 at 24-25 (Tr. Telephone Conference) (Page ID #8298-99). Plaintiffs’ counsel assured the court that the formula involved “basically multiplication, division, addition and subtraction and that’s all it is.” Id. at 24 (Page ID # 8298). Akron had not provided the Plaintiffs with the payroll documents needed to perform the necessary calculations, however, and so the district court ordered Akron to produce those documents. Id. at 27-28 (Page ID # 8301-02).

Akron redeposed all twenty-three Plaintiffs, who revealed that they had calculated their back pay using a formula created by Plaintiff Gregory Snyder, who had been the employee-benefits officer in the Akron Fire Department. Snyder used the average salaries of officers promoted in 2005 beginning with the date of the first promotions from the eligibility lists to produce back-pay calculations for each plaintiff. R. 370-2 at 16-17, 40-44 (Snyder Dep. at 15-16, 39-43) (Page ID # 8902-03, 8926-30). During these depositions, the Plaintiffs claim that they became aware of some errors in their computations of back pay and notified the district court and Akron’s attorneys that they intended to adjust the calculations. Specifically, Plaintiff Carr reviewed Snyder’s calculations to determine whether the issues that Akron raised during the depositions warranted adjustments. R. 469 at 60 (Tr. Carr Testimony) (Page ID # 12852).

On June 16, 2011, one day before the close of discovery, Akron disclosed the identity of its witness who would testify about the Plaintiffs’ back pay. Pis.’ Br. at 5 n. 3. After that disclosure, Carr recalculated the back pay based on the Plaintiffs’ real pay. R. 469 at 60 (Tr. Trial Vol. 3 at 383) (Page ID #12852). The Plaintiffs produced Carr’s new calculations on June 17, 2011, which was the final day of discovery. Pis.’ Br. at 6.

G. The District Court Sets a Start Date for Back Pay and Promotes the Plaintiffs

On July 7, 2011, approximately one week before the retrial, the district court entered an order holding that the Plaintiffs had forfeited the right to a trial by jury on the issue of back pay. R. 403 at 1 (D. Ct. Order Re Bench Trial and Mot. for Promotion) (Page ID # 10937). The district court further held that the promotions ordered by July 18, 2011, made the question of front pay no longer one for the jury. Id. The district court based the decision about the start date for calculating back pay on the Plaintiffs’ failure to request a jury instruction on the issue of back pay during the first trial, id. at 2 (Page ID # 10938), and because the Plaintiffs had not timely requested a jury trial in accordance with Federal Rule of Civil Procedure Rule 38, id. at 4 (Page ID # 10940). Moreover, the district court found that the Plaintiffs “ha[d] treated the calculation of back pay damages as a matter to be decided by” the district court because they had filed motions to alter or amend the judgment in which they had asked the court to add the back pay calculations to the total award of damages. Id. at 3 (Page ID # 10939). The court further noted that it had similarly prohibited Akron from arguing lost opportunities during the retrial for the same reason. Id. at 4 (Page ID # 10940).

In addition, the district court “revisited” the Plaintiffs’ earlier motion for promotion and ordered that Akron promote all of the Plaintiffs no later than July 18, 2011, the date on which the trial would commence. Id. at 1 (Page ID # 10937). The district court cited drastic changes to Akron’s fire department as one of the motivating reasons for the injunction promoting the Plaintiffs and noted that there “are over 25 vacancies in the lieutenant position and five vacancies at the captain position.” R. 416 at 2 (D. Ct. Order Re Mot. for Promotion) (Page ID # 11105). The court noted that “[o]ver half of the Plaintiffs have retired or are no longer seeking promotion” or are “currently acting in the capacities for which they seek promotion.” Id. Although the district court’s opinion addressed the Plaintiffs’ motion for a permanent injunction, the district court did not mention whether the promotions were intended to be temporary or permanent. See id. at 1-3 (Page ID # 11104-06).

On July 14, 2011, Akron filed a notice of appeal of the district court’s July 7 oral order and July 13 supplemental order to promote the Plaintiffs effective July 18, 2011. R. 419 at 1 (Page ID # 11115). The Sixth Circuit issued a temporary stay to allow time for the Plaintiffs to respond to the motion for an emergency stay. In the meantime, Akron moved to suspend the promotions pending the appeal of the injunction. R. 423 at 1 (Def.’s Mot. to Suspend Inj.) (Page ID # 11187). The district court granted a continuance of the retrial, R. 434 (Marginal Order) (Page ID # 11342), and denied Akron’s request for a stay, finding that Akron was not likely to succeed in showing that the district court abused its discretion to promote the Plaintiffs after they had obtained a judgment in their favor, R. 435 at 1-11 (D. Ct. Order Re Stay) (Page ID # 11343-53). On July 21, 2011, the Sixth Circuit dissolved the temporary stay and denied Akron’s motion to stay the promotions pending the resolution of the interlocutory appeal. R. 443 at 2-3 (6th Cir.Order).

During the status conference before the retrial, the district court altered the injunction to make the Plaintiffs’ promotions effective July 22, 2011. R. 444 at 1 (D. Ct. Order Re .Alteration of Inj.) (Page ID # 11415). Akron had requested to treat the promotions as “provisional” promotions. Id. at 1-2 (Page ID # 11415-16). The district court initially granted that request, noting that if the “ ‘provisional’ promotion process somehow provides less than the relief ordered,” then the district court reserved the ability-to “take any other steps necessary to ensure compliance with its prior orders.” Id. at 2. The Plaintiffs objected to provisional promotions to the extent that they were not permanent promotions. R. 446 at 2 (Pis.’ Objection as to “Provisional” Appointments and Supplemental to Pis.’ Mot. to Enforce) (Page ID # 11466). The district court acknowledged that the “provisional promotions” would rely upon informal agreements and therefore were not the type of promotion the court had envisioned. R. 454 at 3 (D. Ct. Order Re Objection to “Provisional” Appointment) (Page ID # 11523). Despite Akron’s assertions that “provisional promotions” were necessary to ensure that it would not have to “demote” the Plaintiffs in the event that the Sixth Circuit reversed judgment or the injunction, the district court sustained the Plaintiffs’ objections and ordered Akron to “FORMALLY PROMOTE each Plaintiff to the appropriate rank” permanently. Id. at 3-4 (Page ID # 11523-24).

H. The District Court’s Order Regarding Back-Pay Start Dates

On July 13, 2011, after the district court had ordered Akron to promote all of the Plaintiffs, the district court issued an order stating that the back-pay calculations would commence on April 5, 2007, the date the eligibility list expired and the Plaintiffs could no longer be promoted based on the 2004 promotional exam. R. 416 at 3 (D. Ct. Order Re Back Pay Start Date) (Page ID # 11106). The district court noted that the Plaintiffs had previously argued that the statute of limitations did not bar their claims because the claims did not accrue until “the completion of the ‘total selection process.’ ” Id. (quoting R. 290 at 23 (Pis.’ Mem. in Opp’n to Mot. for JMOL) (Page ID # 7965)). Accordingly, the district court found that “[t]he promotional process was not completed until the expiration of the list generated by the test,” and therefore the Plaintiffs were not harmed until the list expired. Id. at 4 (Page ID # 11107). The Plaintiffs filed a motion for reconsideration regarding the dates for back pay. R. 441 at 1-7 (Mot. for Recons.) (Page ID # 11399-494). The district court summarily denied the motion for reconsideration. R. 449 at 1 (D.Ct.Order) (Page ID # 11486).

I. The Discovery Sanctions

On July 15, 2011, the Plaintiffs filed supplemental trial exhibits, including Exhibit 208, which was a document prepared by Carr reflecting his calculations of the Plaintiffs’ back pay losses with a differential starting April 4, 2007. R. 429 .at 3 (Pis.’ Amend. Ex. List Rerial) (Page ID # 11284). That same day, Akron disclosed its final back-pay calculations. R. 457-2 at 3 (Elfin Decl. ¶ 17) (Page ID #11673). The difference between Akron’s and the Plaintiffs’ computation of back pay was approximately $14,000. R. 467 at 4 (Tr. Retrial Vol. 1) (Page ID # 12473).

The retrial commenced on July 25, 2011, and the district court addressed Akron’s concern that the Plaintiffs had disclosed their back-pay calculations late. See id. at 37-38 (Page ID # 12506-07). The Plaintiffs’ original calculation of back pay required taking the average salary of all Lieutenants or Captains promoted using the 2004 examination and resulting eligibility list. R. 448 at 1 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11482). The Plaintiffs who were candidates for the rank of Lieutenant would compare their actual salary with that of a promoted candidate for each year after the promotion. Id. Those Plaintiffs who were candidates for the rank of Captain would compare their actual salaries with the average salary of a promoted Captain. See id.

Carr’s new formulation took a different approach: each Plaintiff used the paycheck he or she personally received and “incorporate[d] step increases into each paycheck” to reflect the pay increase they would have received had they been promoted. Id. at 1-2 (Page ID # 11482-83). Thus, in the first year after the promotion, a Plaintiff would receive a percentage pay increase of her actual salary, and then in subsequent years receive additional percentage increases. Carr indicated that he preferred his method of calculating back pay, but he abandoned his calculations because the other Plaintiffs intended to use Snyder’s method. See R. 469 at 60-63 (Tr. Retrial Vol. 3) (Page ID # 12852-55).

The Plaintiffs claimed that they had to change their calculations because the district court had promoted them and thus they could no longer compare their paychecks to promoted firefighters who had already received step increases. R. 448 at 3 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11484); see also R. 467 at 42-43 (Tr. Retrial Vol. 1) (Page ID # 12511-12). Nevertheless, the district court found that Carr’s formula had existed prior to the court’s order promoting the Plaintiffs, but Akron had not deposed Carr about how he had made his calculations because it had been clear that the Plaintiffs intended to use Snyder’s method. R. 448 at 3-4 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11484-85). In order to permit Akron to inquire into the Plaintiffs’ new method for calculating back pay, the district court reopened the depositions of Carr and Snyder. Id. 'at 4 (Page ID # 11485).

After the depositions and before the retrial resumed, the district court conducted a voir dire examination of Carr to determine why the Plaintiffs had changed their back-pay calculations. The district court asked Carr, “[W]hat if anything at all did the Court’s order of promotion have to do with the change in methodology by the plaintiffs?” R. 469 at 74 (Tr. Retrial Vol. 3) (Page ID # 12866). Carr answered:

Front pay got taken out of play. And there was a question of whether the start day. If the start date changed, then we couldn’t use Mr. Snyder’s calculations because it would have inflated the numbers if we would have kept it that way, because we would have only had one person to compare to, and that would have been a highly — one of the highest paid captains, Captain Willough-by.

Id. at 74-75 (Page ID # 12866-67). The district court clarified: “So, in essence, the methodology didn’t change. Just simply the fact-the dates in essence changed, correct?” Id. at 75 (Page ID # 12867). Carr replied, “Yes, sir.” Id.

On July 28, 2011, at the close of the Plaintiffs’ case, the district court entered an order excluding Carr’s calculations from evidence. The district court found that the Plaintiffs had “engaged in a classic bait-and-switch maneuver,” allowing Akron to conduct discovery on the Snyder method without indicating that the Plaintiffs might use the Carr method for their final calculations. R. 484 at 7 (D. Ct. Order Excluding Ex. 208) (Page ID # 13413). In addition, the district court rejected the Plaintiffs’ contention that the court’s promotion order had caused them to change course because Carr had computed back pay using his method before the promotion order went into effect. Id. The district court concluded that the late disclosure of Carr’s calculations had prejudiced Akron because, at their depositions, all the Plaintiffs stated that they had relied on Snyder’s calculation of back pay, but at trial, they stated that they had recalculated their back pay to verify Carr’s calculations. Akron had not been able to depose Plaintiffs other than Carr about their individual calculations based on this new information. Id. at 8 (Page ID # 13414). And the district court decided that it was highly suspicious that the Plaintiffs had calculated their own back pay only after the district court had expressed doubt that the Plaintiffs could rely on Carr’s methodology. Id. Finally, the district court found that the “Plaintiffs’ damages ha[d] been a moving target,” id. at 9 (Page ID # 13415), concluding that “[w]hether this [was] a strategic choice or simply poor trial preparation, it is improper and prejudicial,” id. at 10 (Page ID # 13416). Therefore, the district court excluded Carr’s back-pay calculations, Exhibit 208, as a sanction pursuant to Federal Rule of Civil Procedure 37(b)(2). Id. at 11-12 (Page ID # 13417-18). As an additional sanction, the district court indicated that it would likely award attorney fees for the costs of litigating the motion to exclude Carr’s testimony. Id. at 12 (Page ID # 13418).

J. The Retrial

After excluding Exhibit 208, the district court suspended the retrial. Akron filed a motion for judgment on partial findings pursuant to Federal Rule of Civil Procedure 52(c), arguing that the Plaintiffs had not presented competent evidence to substantiate back pay, among other issues. See R. 499 at 1-30 (Def.’s Mem. in Supp. of Mot. for J. on Partial Findings) (Page ID # 14626-55). On September 24, 2012, the district court denied Akron’s Rule 52(c) motion, concluding that the Plaintiffs had presented evidence from which the court could determine back pay for each Plaintiff. R. 531 at 3 (D. Ct. Order Re Mot. for J. on Partial Findings) (Page ID # 15372).

On November 28, 2012, nearly four years after the first trial and fifteen months after the retrial first began, the trial resumed. Akron moved to admit exhibits into evidence, rested, and renewed its motion for a directed verdict pursuant to Federal Rule of Civil Procedure 52. R. 565 at 4-7 (Tr. Retrial Vol. 5) (Page ID # 15881-84). Akron argued that the only evidence in the record was the testimony of Mark McLeod, Akron’s witness, who had not performed back-pay calculations, but had reduced the Plaintiffs’ lost earnings calculations to reflect a loss of chance. Id. at 8-11 (Page ID # 15885-88).

K. Howe I: Appeal of the Injunction Ordering Promotions

While the parties were relitigating the issue of damages in the district court, this court was considering whether the district court had abused its discretion by issuing the injunction that permanently promoted the Plaintiffs. See Howe I, 723 F.3d 651. In Howe I, Akron advanced two arguments: (1) that the Plaintiffs had failed to present a prima facie case of disparate impact liability; and (2) that “the district court abused its discretion in issuing the injunction.” Id. at 657. On July 22, 2013, following briefing and argument, we held that “the district court did not abuse its discretion in issuing the preliminary injunction requiring [Akron] to promote certain Plaintiffs.” Id. at 663-64. In order to reach that conclusion, we held “that all of the promoted Plaintiffs had demonstrated substantial likelihood of success on the merits with regard to the adverse effect element of their disparate impact claims.” Id. at 661.

L. The Back-Pay Award

On August 30, 2013, the district court entered its findings of fact and conclusions of law with respect to the Plaintiffs’ back pay. The district court used McLeod’s calculations to compute the Plaintiffs’ back pay, see R. 588 at 2-6 (Findings of Fact ¶¶ 9-23) (Page ID # 16480-84), noting that the “computations involved simple mathematical functions and were not expert calculations,” id. at 8 (Conclusions of Law ¶ 12) (Page ID # 16486). The back-pay calculations began on April 4, 2007, and continued until July 17, 2011, the day before the Plaintiffs’ promotions went into effect. Id. at 3-4 (Findings of Fact ¶ 21-22) (Page ID # 16481-82). Accordingly, the district court found that there was sufficient evidence to award the Plaintiffs a total of $616,217.75 in back pay. Id. at 9 (Conclusions of Law ¶ 14) (Page ID # 16487). The district court calculated each Plaintiffs individual back-pay award. See id. at 9-12 (FFCL ¶¶ 14A-U) (Page ID # 16487-90). To the extent that the district court’s calculations may include some front pay, the court noted that it would still award that amount. Id. at 8 (Conclusions of Law ¶ 11) (Page ID # 16486). In addition, the district court dismissed Plaintiff Michael Harvey’s claim to back pay because he never testified and the record did not support a back-pay award. Id. at 12 (Conclusions of Law ¶ 15) (Page ID # 16490). Finally, the district court found no just reason for delay pursuant to Federal Rule of Civil Procedure 54(b). Id. (Conclusions of Law ¶ 16).

On September 3, 2013, the district court denied Akron’s renewed motion for judgment under Rule 52(c). R. 589 at 1 (D. Ct. Order Re Def.’s Renewed Mot. for J. on Partial Findings) (Page ID # 16491). The district court found that Akron had waived its legal theory that the Plaintiffs’ back pay had to be reduced based on the probability that they would not be promoted because Akron had not presented that testimony or argument during the first trial. Id. at 2 (Page ID # 16492). Moreover, the court concluded that the Plaintiffs had not opened the door to that theory 'during their cross-examination of McLeod. Id.

On September 27, 2013, Akron filed a Notice of Appeal of (1) “the Findings of Fact and Conclusions of Law entered in this action on the 30th day of August, 2013 (Doc. 588), that awards Plaintiffs $616,217.75 and includes ‘no just reason for delay’ (2) the Order (“Doc.589”) denying Akron’s renewed Rule 52(c) motion;' and (3) “interlocutory orders that issued prior to August 30, 2013 and are merged into the August 30, 2013 Findings of Fact and Conclusions of Law.” R. 590 at 1 (Notice of Appeal Case No. 13-4172) (Page ID # 16494). On October 10, 2013, the Plaintiffs filed their cross-appeal for Case No. 13-4172 regarding back pay.

On February 19, 2014, the Plaintiffs filed a motion for prejudgment and post-judgment interest. R. 613 at 1-9 (Pis.’ Mot. for Pre & PosNJ. Interest) (Page ID # 16646-54). Akron opposed the motion. R. 638 at 1-14 (Def.’s Opp’n to Mot for Pre & Post-J. Interest) (Page ID # 17301-14). To date, the district court has not yet ruled on the Plaintiffs’ motion.

M. The Permanent Injunction and Appointment of a Court Monitor

On December 28, 2012, after the retrial ended, the Plaintiffs filed a renewed motion for a permanent injunction after they learned that the Akron Fire Department planned to promote firefighters to the ranks of Lieutenant and Captain. R. 573 at 1 (Pis.’ Renewed Mot. for Permanent Inj. and Appointment of a Receiver) (Page ID # 16065). They asked the ' district court to enter an order barring Akron “from utilizing or otherwise acting upon any promotional process, including but not limited to the process developed and administered in December, 2004, for filling the ranks of Lieutenant and Captain.” Id. at 1-2 (Page ID # 16065-66). In addition, the Plaintiffs requested that the district court mandate that Akron “develop[] a job-related nondiscriminatory promotion process, under the supervision and guidance of a receiver appointed by [the district court].” Id. at 2 (Page ID # 16066). Akron opposed the Plaintiffs’ motion. See R. 577 at 1-11 (Def.’s Br. in Opp’n to Pis.’ Renewed Mot. for Permanent Inj.) (Page ID # 16083-93).

On March 27, 2014, the district court entered a permanent injunction and appointed David R. Cohen to serve as the Court Monitor. The district court found that the promotions and back-pay award did not make the Plaintiffs whole because they had been “deprived of a fair process and a fair opportunity to be promoted at the outset of the creation of the eligibility list.” R. 643 at 6 (D. Ct. Order Re Permanent Inj.) (Page ID # 17331). The district court specially noted that, although the promotions addressed some of the harm they suffered, there remained questions about how the denial of the fair process at the outset would impact the Plaintiffs’ access to fair promotions in the future. See id.

The permanent injunction forbade Akron to do the following: (1) to use the 2004 examination or promotion process or hire any of the entities involved in the creation of the examination or promotion process; (2) to use “any promotional examination process” that “results in disparate impact upon any protected group of applicants and is not job related for the promotional position”; (3) to “take any step” in the promotion process for any firefighters, or use any promotional examination without the approval of the Court Monitor; (4) to retaliate against any employee who has complained of discrimination “on the basis of their race or age in the promotional process, or has participated in the investigation or litigation of any claim or allegation of such discrimination, or has sought or obtained relief from the court in this case”; (5) to discriminate on the basis of race or age “in the development or implementation of its promotional process.” Id. at 7 (Page ID # 17332).

The permanent injunction required “[t]he Parties” to “timely comply with the orders of the Court Monitor.” Id. The district court also required the appointed Court Monitor to do the following: (1) “adopt a schedule which requires [Akron] to notify the [Court] Monitor and the Parties before commencing any step in creating a new promotional process”; (2) to develop a process, “which allows Plaintiffs to review [Akron’s] proposals, provide objections or input where appropriate, and be compensated for that review,” and which “specifies] any and all limitations placed on Plaintiffs with regard to both content and compensation”; and (3) to prepare a Document Retention Order. Id. at 8. The district court gave the Court Monitor the discretion to require Akron “to disclose any information relating to any step in its proposed new promotional process before allowing [Akron] to proceed to any step in the process,” or “to establish that it has satisfied conditions specified by the [Court] Monitor, or to obtain the [Court] Monitor’s explicit approval before commencing any step in the proposed new promotional process.” Id.

Failure to comply with any provision of the permanent injunction could “be punished by court-ordered sanction if another party moves for such sanction,” which may include contempt proceedings. Id. at 9. The district court gave the parties ten days to file objections to the permanent injunction. Id. at 12. Because neither party objected to Cohen’s appointment as the Court Monitor, the district court entered the Order of Appointment on April 8, 2014. R. 653 at 1 (Order of Appointment) (Page ID # 17373). Three days later, on April 11, 2014, Akron filed a notice of appeal of the permanent injunction and order of appointment. R. 654 at 1 (Notice of Appeal Case No. 14-3352) (Page ID # 17383).

After filing the notice of appeal, Akron sought a stay of the permanent injunction from the district court, which was denied. R. 666 at 1 (D. Ct. Order Re Stay of Permanent Inj.) (Page ID # 17440). The ■ district court rejected the request for a stay because Akron had not made “even a meager showing of likelihood of success on the merits.” Id. at 5 (Page ID # 17444). Tellingly, the district court reiterated that it “found that [a permanent injunction] was necessary for complete relief,” that the “Plaintiffs will never know with any certainty whether they could have been promoted much sooner,” and that “obstacles remain for them for future testing, such as lacking the proper amount of time in grade to qualify for that future testing.” Id. at 4 (Page ID # 17443). Moreover, the district court emphasized that Akron’s conduct— “even post-verdict conduct” — had caused the court to believe that it should oversee the promotion process, citing Akron’s “attempt ] to segregate Plaintiffs from all others in their rank by attaching a ‘provisional’ term to their title.” Id. In response to Akron’s argument that the court lacked the authority to enter a permanent injunction absent a showing of intentional discrimination, the district court noted that the Plaintiffs had “presented a strong argument that the evidence of disparate impact was so overwhelming that one could infer intentional discrimination,” but declined to make that specific finding. Id. at 5 (Page ID # 17444). The district court also emphasized that Akron had “offer[ed] no argument of any kind to suggest how the relief could be narrowed to more fully respect the principles of federalism or comity,” and “[i]nstead, ... [Akron] stubbornly adheres to its pre-verdict belief that no relief of any kind should be afforded these Plaintiffs.” Id.

Akron has never asked this court to issue a stay of the permanent injunction. See 6th Cir. Docket, Case No. 14-3352. The Court Monitor continues to work with the parties and file status reports with the district court. See, e.g., R. 676 at 1-3 (Special Master Quarterly Report No. 1) (Page ID # 17706-08).

N. Appeals No. 13-4172 and No. 14-3352

This is a consolidated appeal. Case No. 13-4172 involves the appeal of a liability judgment in favor of the Plaintiffs with respect to their disparate-impact age- and race-discrimination claims and the award of back pay. Akron challenges the liability judgments on three grounds. First, Akron challenges the sufficiency of the evidence of disparate impact. In particular, Akron argues that the district court erroneously relied up on the EEOC’s so-called four-fifths rule, which provides that “[a] selection rate for any race, sex, or ethnic group which is less than four-fifths (4/5) (or eighty percent) of the rate for the group with the highest rate will generally be regarded ... as evidence of adverse impact....” 29 C.F.R. § 1607.4(D). Akron challenges the four-fifths rule in this context because it believes that the dataset in this case is too small. Akron Br. at 32-38. Second, Akron contends that it is entitled to judgment as a matter of law with respect to the twelve Caucasian Plaintiffs who applied for the rank of Captain because the “Plaintiffs offered no evidence of background circumstances suggesting [Akron] is the unusual employer who discriminates against the majority (Caucasians).” Id. at 38. Akron also requests a new trial on the issue of liability because the district court issued an erroneous jury instruction and because the verdict was against the manifest weight of the evidence. See id. at 44-48.

Akron also challenges the district court’s award of back pay. See id. at 49-52. The Plaintiffs filed a cross-appeal in Case No. 13-4172, challenging the back-pay award on the basis that the district court utilized an incorrect date to begin calculating back pay and failed to calculate step increases. See Pis.’ Br. at 60-64. In addition, the Plaintiffs argue that the district court abused its discretion by excluding their back-pay calculations as a sanction for alleged discovery violations during the retrial. Id. at 64-71. Finally, the Plaintiffs contend that the district court made various errors when calculating back-pay awards for Plaintiffs Snyder, Harvey, and Sehueller. Id. at 71-72.

In Case No. 14-3352, Akron appeals the district court’s order entering a permanent injunction and appointing a Court Monitor because it contends that the injunction'is not narrowly tailored to address the harm to the Plaintiffs or sufficiently limited in scope or duration. Akron Br. at 52-60.

II. THE LIABILITY JUDGMENTS

A. The Impact of Howe I: Law of the Case

The Plaintiffs contend that we should not review Akron’s challenges to the liability judgment either because we have already decided the issues in Howe I, or because Akron could have raised the arguments in its appeal of the promotion order, but did not. See Pis.’ Br. at 31-41. We agree.

In Howe I, we noted that the district court had not yet entered a final judgment and “may yet revisit its decision regarding promotions,” and so “we reviewed] only the question of whether the district court abused its discretion in issuing the injunction and reaeh[ed] the merits of the case only as necessary to do so.” Howe I, 723 F.3d at 657-58. We therefore analyzed Akron’s challenges to the liability judgments to determine whether Akron was “ ‘likely to prevail on the merits.’ ” Id. at 658 (quoting Samuel v. Herrick Mem’l Hosp., 201 F.3d 830, 833 (6th Cir.2000) (listing the four factors we consider when reviewing the propriety of a preliminary injunction)).

Using this framework in Howe I, we examined Akron’s three challenges to the validity of the liability judgments. First, Akron argued that the Plaintiffs had not identified a specific employment practice that caused a disparate impact. Howe I, 723 F.3d at 658-59 (citing Grant v. Metro. Gov’t of Nashville & Davidson Cnty., 446 Fed.Appx. 737 (6th Cir.2011)). We held that the “Plaintiffs sufficiently identified a specific employment practice.” Id. at 659. Second, Akron contended “that the district court erred as a matter of law in permitting Plaintiffs to demonstrate adverse ef.fect by applying the ‘four-fifths rule’ to promotion rates instead of exam pass rates.” Id. at 659. Akron did not contest the validity of the four-fifths rule. See id. at 659-60. We held that the Plaintiffs could use the four-fifths rule with respect to promotion rates, and therefore the Plaintiffs had demonstrated that the promotion process had an adverse effect on African-American and over-forty candidates for the rank of Lieutenant. Id. at 660. Third, Akron challenged the liability judgment in favor of the Caucasian candidates for Captain because the “Plaintiffs failed to show that [Akron] is that unusual employer who discriminates against the majority.” Id. (internal quotation marks omitted). We held that Akron had waived that argument, but we also concluded that “[e]ven if the argument had not been waived, it is far from clear that the unusual-employer requirement” is applicable in the case of a disparate-impact—rather than disparate-treatment—claim. Id. at 661.

Akron argues that our holding that Akron had waived its argument that the Plaintiffs were required to prove that Akron is the “unusual employer who discriminates against the majority” was “clear error and should not be followed.” Akron Br. at 38. Akron also urges us to consider all of their challenges to the liability judgments because Howe I was a review of a preliminary injunction, and therefore was not a full review of the liability judgment. Akron Reply Br. at 8. We will not address either issue, however, because the doctrine of law of the case counsels against reconsideration of issues that have already been decided.

The doctrine of law of the case provides that the courts should not “reconsider a matter once resolved in a continuing proceeding.” 18B Chaeles Alan Wright, Arthur R. Miller, and Edward H. Cooper, Federal PRACTICE And Prooedure: JurisdictioN And Related Matters § 4478 (4th ed.2015). “The purpose of the law-of-the-case doctrine is to ensure that ‘the same issue presented a second time in the same case in the same court should lead to the same result.’ ” Sherley v. Sebelius, 689 F.3d 776, 780 (D.C.Cir.2012) (quoting LaShawn A. v. Barry, 87 F.3d 1389, 1393 (D.C.Cir.1996)). For a prior decision to control, the prior tribunal must have actually decided the issue. Weight et al„ supra, § 4478. “A position that has been assumed without decision for purposes of resolving another issue is not the law of the case.” Id. “An alternate holding, however, does establish the law of the case.” Id. Unlike claim preclusion, the law of the case does not apply to issues that a party could have raised, but did not. Id. The law-of-the-case doctrine is a prudential practice; a court may revisit earlier issues, but should decline to do so to encourage efficient litigation and deter “indefatigable diehards.” Id.

Whether a panel should treat a pri- or panel’s ruling on a preliminary injunction as the law of the case is tricky, however. Rulings on preliminary injunctions are generally “‘tentative deeision[s] on the merits,’ ” which “change[ ] the ‘incentives’ of the parties that inform their litigation strategies.” Gooch v. Life Investors Ins. Co. of Am., 672 F.3d 402, 433 (6th Cir.2012) (quoting Bieneman v. City of Chi., 838 F.2d 962, 964 (7th Cir.1988)). But when the appellate panel considering the preliminary injunction has issued “[a] fully considered appellate ruling on an issue of law,” then that opinion becomes the law of the case. Wright et al., supra, § 4478.5.

This case presents an unusual circumstance because we considered the issues presented in Howe I with a completely developed record; we had transcripts from a completed jury trial available for review. “[W]here the earlier ruling, though on preliminary-injunction review, was established in a definitive, fully considered legal decision based on a fully developed factual record and a decisionmaking process that included full briefing and argument without unusual -time constraints,” then the law-of-the-case doctrine applies. Sherley, 689 F.3d at 782. In Sherley, the D.C. Circuit vacated a preliminary injunction in favor of the plaintiffs and remanded the case to the district court for further proceedings, after which the district court entered summary judgment in favor of the defendants. Id. at 779. The plaintiffs appealed the entry of summary judgment and offered “precisely the same argument” that the prior panel had rejected, arguing that the preliminary nature of a review of a denial of a preliminary injunction made the law-of-the-case doctrine inapplicable. Id. at 781. The D.C. Circuit held that the doctrine of law of the case prevented reconsideration of that prior holding because “[t]he time constraints and limited record” that usually make the law-of-the-case doctrine inappropriate in most cases involving preliminary injunctions were “not present.” Id. at 788.

The D.C. Circuit’s conclusion is not novel; other circuits facing similar procedural issues have reached the same conclusion. See id. at 782-83 (citing Naser Jewelers, Inc. v. City of Concord, 538 F.3d 17, 20 (1st Cir.2008) (“[T]he [law-of-the-case] doctrine applies when [the] court has previously ruled on a motion for preliminary injunction and the record before the prior panel was sufficiently developed and the facts necessary to shape the prior legal matrix were sufficiently clear.”) (internal quotation marks omitted); This That & The Other Gift & Tobacco, Inc. v. Cobb Cnty., 439 F.3d 1275, 1284-85 (11th Cir.2006) (same); Entergy, Ark., Inc. v. Nebraska, 241 F.3d 979, 987 (8th Cir.2001) (same); Royal Ins. Co. of Am. v. Quinn-L Capital Corp., 3 F.3d 877, 880-81 (5th Cir.1993) (same)). We therefore join the other circuits and hold that, when a court reviewing the propriety of a preliminary injunction issues a fully considered ruling on an issue of law with the benefit of a fully developed record, then the conclusions with respect to the likelihood of success on the merits are the law of the case in any subsequent appeal.

In Howe I, Akron appealed the promotion of all of the Plaintiffs with the benefit of a complete record that “was sufficiently developed and the facts necessary to shape the proper legal matrix were sufficiently clear.” Naser Jewelers, 538 F.3d at 20 (internal quotation marks and bracket omitted). We “carefully considered” each argument that Akron raised as to why the Plaintiffs’ liability judgment would not be upheld on appeal and issued a reasoned judgment. Entergy, 241 F.3d at 987. We therefore conclude that the holdings of Howe I are the law of the case. That means that unless Akron provides compelling reasons to revisit those holdings, we will not address Akron’s contention that the Plaintiffs’ evidence that Akron’s promotional process adversely impacted Caucasian Captain candidates was insufficient because they did not prove that Akron is an “unusual employer.” See Howe I, 723 F.3d at 660-61.

Akron has not demonstrated that “extraordinary circumstances” militate in favor of abandoning our prior holdings. Christianson v. Colt Indus. Operating Corp., 486 U.S. 800, 817, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988). ‘We generally will not disturb these [holdings] unless there is ‘(1) an intervening change of controlling law; (2) new evidence available; or (3) a need to correct a clear error or prevent manifest injustice.’ ” Entm’t Prods., Inc. v. Shelby Cnty., 721 F.3d 729, 742 (6th Cir.2013), cert. denied, — U.S. -, 134 S.Ct. 906, 187 L.Ed.2d 778 (2014) (quoting Louisville/Jefferson Cnty. Metro Gov’t v. Hotels.com, L.P., 590 F.3d 381, 389 (6th Cir.2009)). But there have been no intervening changes in the law since Howe I. Nor has the record changed in any way; it is exactly the same. We therefore hold that any legal error the Howe I panel made — if any at all — was neither clear nor manifestly unjust, and that the holdings of Howe I are binding on this panel.

B. The Impact of Howe I: Forfeiture

We next consider whether Akron’s failure to challenge in Howe I the legal sufficiency of the evidence of adverse impact, the jury instructions, and the district court’s conclusion that the jury verdict was not against the manifest weight of the evidence precludes Akron from making those arguments now. In general, “question[s] that could have been but [were] not raised on one appeal cannot be resurrected on a later appeal to the same court in the same case.” Weight et al., supra § 4478.6. “Part of the price paid for the final-judgment rule is that trial-court proceedings may be tainted by an unappeala-ble ruling and require expensive and time-consuming reconstruction after the opportunity for appeal finally becomes available. There is no reason to pay this price when there was an opportunity for review in the course of an appeal that was actually taken.” Id.

The Plaintiffs refer to this as a “waiver,” some courts have referred to this principle as the “law of the case,” and others use the term “res judicata.” The Sixth Circuit has not defined the proper terminology to use in this situation or when it applies, and so we endeavor to define the appropriate terms and boundaries now.

Res judicata bars relitigation of final judgments. Under federal common law,

[r]es judicata has four elements: (1) a final decision on the merits by a court of competent jurisdiction; (2) a subsequent action between the same parties or their privies; (3) an issue in the subsequent action which was litigated or which should have been litigated in the prior action; and (4) an identity of the causes of action.

Rawe v. Liberty Mut. Fire Ins. Co., 462 F.3d 521, 528 (6th Cir.2006) (internal quotation marks and alteration omitted). Howe I did not involve an appeal of a final judgment, however. Because the liability judgment was not “final,” res judicata does not bar appellate review of the liability judgments now.

Nevertheless, Akron had the opportunity to litigate fully the merits of the liability judgment. Most courts apply a waiver/forfeiture principle to situations like the one presented in this case. In JGR, Inc. v. Thomasville Furniture Industries, Inc., 550 F.3d 529, 533 (6th Cir.2008), we held that a plaintiff who did not challenge during their first appeal the jury’s finding that the plaintiffs had suffered no lost profits had “waived any right to relitigate the issue in the retrial for damages.” Our sibling circuits have used a similar approach. For example, in Lindquist v. City of Pasadena, 669 F.3d 225, 238 (5th Cir.2012), in the plaintiffs’ first appeal, they argued that the statute at issue was facially unconstitutional, which the Fifth Circuit rejected before remanding the case to the district court. After the remand, the plaintiffs argued to the district court that the statute was unconstitutional as applied to them. Id. When the plaintiffs appealed again, the Fifth Circuit clarified that their as-applied challenge was not barred from appellate review because of the law-of-the-case doctrine; the first panel had addressed only the facial challenge, and not the as-applied challenge to the statute. See id. at 239. Instead, applying “waiver doctrine,” the Fifth Circuit held that the plaintiffs could not pursue their as-applied challenge because they could have raised that argument during the first appeal but had “waived” their as-applied challenge to the statute. Id. at 240. “Only plain error justifies departure from the waiver doctrine” in the Fifth Circuit. Med. Ctr. Pharmacy v. Holder, 634 F.3d 830, 836 (5th Cir.2011) (internal quotation marks omitted); see also United States v. Zahursky, 668 F.3d 456, 459 (7th Cir.2012) (“By failing to raise the issue in his first appeal, Zahursky forfeited his right to challenge the application of the pseudo-count enhancement under § 2G1.3(d), and the district court was not obligated to consider this new argument on remand”)- But see Beazer E., Inc. v. Mead Corp., 525 F.3d 255, 263 (3d Cir.2008) (“Mead cannot now, after a remand on an unrelated issue, raise objections that it previously waived,” unless “when an intervening decision from a superior court changes the controlling law.”).

We believe, however, that “waiver” is an inappropriate term to use to describe the failure to litigate an issue during a prior appeal. The terms “waiver” and “forfeiture” are often misused. See Wright et al., supra § 4478.6. In most cases, the decision not to press an argument is the result of “an unreflected failure to think about the procedural need to make a choice (forfeiture),” rather than “a conscious choice to abandon a position (waiver).” Id. Therefore, we hold that a party who attempts to raise in a second appeal an issue, which could have been raised and fully litigated in the first appeal, has forfeited the issue. We will review a new issue in a second appeal only if the party seeking review demonstrates that the error was plain. Med. Ctr. Pharmacy, 634 F.3d at 836 (holding that the waiver rule prevents consideration of an issue raised in a second appeal absent plain error).

Akron has forfeited any arguments that the liability judgment is flawed that it did not raise in Howe I to challenge the Plaintiffs’ likelihood of success on the merits. Therefore, absent plain error, we will not review Akron’s challenges to the sufficiency of adverse impact, the jury instruction about the four-fifths rule, and the district court’s denial of the motion for a new trial. Akron could have — and should have — raised each of these arguments to support its assertion that the order promoting the Plaintiffs was an abuse of discretion. Had Akron asserted that these errors undermined the liability judgment, then we could have taken those arguments into consideration in Howe I. Akron chose to challenge other aspects of the liability judgment instead.

We do not believe that any of the errors that Akron asserts now were plain, and therefore we affirm the liability judgments. Akron presented evidence that, under 29 C.F.R. § 1607.4(D), Akron’s promotional process had a disparate impact on protected groups. Akron challenged the reliability of the four-fifths rule and offered testimony that other statistical tests showed that Akron’s promotional process did not disparately impact protected groups. The jury listened to testimony about the strengths and weaknesses of the four-fifths rule, and concluded that, in this case, the Plaintiffs had demonstrated that the promotional process had a discriminatory effect. The Supreme Court has never said what kind of statistical evidence courts may rely on to find adverse impact. Isabel v. City of Memphis, 404 F.3d 404, 412 (6th Cir.2005). Indeed, in Ricci v. DeStefano, 557 U.S. 557, 586, 129 S.Ct. 2658, 174 L.Ed.2d 490 (2009), the Supreme Court indicated that a violation of the four-fifths rule was prima facie evidence of disparate-impact liability, citing 29 C.F.R. § 1607.4(D). And we have used the four-fifths rule as the starting point to determine whether plaintiffs alleging disparate impact have met their prima facie burden, although we have used other statistical tests as well. See Isabel, 404 F.3d at 410. Accordingly, without more guidance from the Supreme Court, we are loath to overturn the jury’s conclusion that the Plaintiffs’ proof of disparate impact was persuasive.

III. BACKPAY

Akron and the Plaintiffs challenge the district court’s back-pay award. When a plaintiff has demonstrated that an employer “has intentionally engaged in or is intentionally engaging in an unlawful employment practice charged in the- complaint,” Title VII empowers the court to “order such affirmative action as may be appropriate, which may include, but is not limited to, reinstatement or hiring of employees, with or without back pay ... or any other equitable relief....” 42 U.S.C. § 2000e-5(g)(l). If a court concludes that back pay is appropriate, then “[b]ack pay liability shall not accrue from a date more than two years prior to the filing of a charge with the [Equal Employment Opportunity] Commission. Interim earnings or amounts earnable with reasonable diligence by the person or persons discriminated against shall operate to reduce the back pay otherwise allowable.” Id. The ADEA authorizes the award of back pay in the same manner as unpaid minimum wages and overtime compensation are paid under the Fair Labor Standards Act. See 29 U.S.C. § 626(b); Tyler v. Union Oil Co. of Cal., 304 F.3d 379, 399 (5th Cir.2002). And Ohio Revised Code § 4112.99 permits courts to award to victims of an unlawful employment practice “damages, injunctive relief, or any other appropriate relief,” which may include back pay.

The purpose of back pay under Title VII and the ADEA is to “make whole” the victim of an unlawful employment practice, Albemarle Paper Co. v. Moody, 422 U.S. 405, 419, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975), by “restoring] the employee to the position he or she would have been in absent the discrimination,” McKennon v. Nashville Banner Publ’g Co., 513 U.S. 352, 362, 115 S.Ct. 879, 130 L.Ed.2d 852 (1995); see also Albemarle, 422 U.S. at 419-21, 95 S.Ct. 2362 (discussing the legislative history of the “make whole” provision of Title VII).

The Supreme Court has held that “given a finding of unlawful discrimination, back-pay should be denied only for reasons which, if applied generally, would not frustrate the central statutory purposes of eradicating discrimination throughout the economy and making persons whole for injuries suffered through past discrimination.” Albemarle, 422 U.S. at 421, 95 S.Ct. 2362. “Where racial discrimination is found, ‘the (district) court has not merely the power but the duty to render a decree which will so far as possible eliminate the discriminatory effects of the past as well as bar like discrimination in the future.’ ” Isabel, 404 F.3d at 414 (quoting Louisiana v. United States, 380 U.S. 145, 154, 85 S.Ct. 817, 13 L.Ed.2d 709 (1965)).

The back pay award should completely redress the economic injury the plaintiff has suffered as a result of discrimination. It should include the salary, including any raises, which plaintiff would have received but for the discrimination, as well as sick leave, vacation pay, pension benefits and other fringe benefits she would have received but for discrimination.

Gutzwiller, 860 F.2d at 1333.

“We review a district court’s award of back pay for abuse of discretion.” Madden v. Chattanooga City Wide Serv. Dep’t, 549 F.3d 666, 678 (6th Cir.2008). Our task, as an appellate court, is to ensure that district courts exercise the equitable power to award back pay consistently and with an eye towards the statutory objectives of the back-pay provisions of Title VII and the ADEA. See Albemarle, 422 U.S. at 421, 95 S.Ct. 2362.

Akron and the Plaintiffs offer five separate reasons for why they believe the district court abused its discretion to award back pay. The Plaintiffs argue that the district court did not adequately make them whole because (1) the district court used an incorrect start date to calculate back pay; (2) the back-pay award did not incorporate step increases; (3) the district court excluded the Plaintiffs’ back-pay calculations, which included the incremental step increases, as a sanction for alleged discovery violations; and (4) the back-pay award did not include prejudgment interest. Akron contends that the district court “failed to discount [the back-pay .awards] based on Plaintiffs’ actual lost opportunity for promotion.” Akron Br. at 49.

Start Date. The first step when calculating back pay is to identify the starting and ending dates for the back-pay award period. 1 SusaN M. OmiliaN & Jean P. Kamp, Sex-Based Employment Discrimination § 14:4 (2015). Back-pay calculations begin from the date of the injury. Palasota v. Haggar Clothing Co., 499 F.3d 474, 483 (5th Cir.2007) (“[B]ack pay accrues from the date of the commencement of the discriminatory course of conduct causing financial loss until the date damages are ‘settled.’ ”). In the case of a continuing unlawful employment practice, however, the statute limits back pay to no “more than two years prior to the filing of a charge with the [EEOC].” 42 U.S.C. § 2000e-5(g)(l). Thus, the start date for each Plaintiffs back pay will depend on either the date of injury or when he or she filed a complaint with the EEOC. To address the appropriate back-pay award adequately, the district court should have made an individualized inquiry as to when to start each Plaintiffs back-pay calculations.

In this case, the Plaintiffs and Akron disagree about when the discriminatory conduct began. The district court held that back-pay calculations would commence on April 5, 2007, the date the eligibility list expired, on the basis that the Plaintiffs had argued that their claims were not barred by the statute of limitations because the claims did not accrue until the promotional process was completed. R. 416 at 3-4 (D. Ct. Order Re Back Pay) (Page ID # 11106-07). The Plaintiffs contend that the back-pay calculations should begin on May 16, 2005, the date when the Akron Fire Department promoted firefighters using the discriminatory promotional process (the exams, eligibility lists, the Rule of Three, and the interviews). Pis.’ Br. at 62; R. 572-1 at 36-37 (Pis.’ Proposed Findings of Fact and Conclusions of Law Retrial ¶ 16) (Page ID # 16059-60). To determine when back-pay calculations should begin, we must identify when the injury to the Plaintiffs occurred.

“[A] plaintiff establishes a prima facie disparate-impact claim by showing that the employer ‘uses a particular employment practice that causes a disparate impact’ on one of the prohibited bases.” Lewis v. City of Chi., 560 U.S. 205, 212, 130 S.Ct. 2191, 176 L.Ed.2d 967 (2010) (quoting 42 U.S.C. § 2000e-2(k) (defining disparate-impact claims)). Thus, under a disparate-impact theory of liability, injury occurs and back-pay calculations commence when the employer uses the discriminatory practice for the first time. See id. Here, that date was May 16, 2005. Although the Plaintiffs could not assess the discriminatory effects of Akron’s promotional process until the promotion lists expired, it does not follow that they were not injured earlier.

Nevertheless, Akron insists that the Plaintiffs were not injured until April 2007, when the that their claims were not barred by the statute of limitations. See Akron Reply Br. at 38-41. But Title VII requires “only that a Title VII plaintiff must show a ‘present violation’ within the limitations period,” Lewis, 560 U.S. at 214, 130 S.Ct. 2191, which the Plaintiffs did by relying on the dates when Akron finished using the promotional process that disparately impacted protected groups; each time Akron used the promotional process, the Plaintiffs were injured. Thus, the district court committed two errors. First, the district court concluded incorrectly that the injury to the Plaintiffs did not accrue until the eligibility list expired. Second, the district court calculated all of the Plaintiffs’ back pay by using the same start date. The Plaintiffs filed multiple EEOC complaints, see, e.g., R. 441-1 at 1 (Howe’s EEOC Charge) (Page ID #11406); R. 441-2 at 1 (Carr’s EEOC Charge) (Page ID # 11407), and therefore the district court should have calculated each Plaintiffs back pay from the date no more than two years before he or she filed a charge of discrimination with the EEOC.

After the court determines the starting date of the back-pay award period, the court must determine the ending date for the period. 1 Sex-Based Employment DISCRIMINATION § 14:4. The district court selected July 16, 2011, the date that the district court ordered that the Plaintiffs be promoted, as the ending date. R. 588 at 3 (FFCL ¶ 21) (Page ID # 16481). The parties do not challenge the district court’s selection of an ending date, and therefore we do not review the district court’s decision to end the back-pay award period on that date.

Once the district court has selected starting and ending dates for the back-pay award period, the court must calculate the wages each plaintiff would have earned had he or she been promoted, before subtracting the wages he or she actually earned without the promotion. See 2 FaiR Employment Praotioes § 15:24 (2015). Determining each plaintiffs actual and projected wages will depend upon the employer’s compensation scheme, and any back-pay award “should completely redress the economic injury the claimant has suffered as a result of discrimination.” Rasimas v. Mich. Dep’t of Mental Health, 714 F.2d 614, 626-27 (6th Cir.1988). Consequently, “Host pay, lost pension rights, lost benefits, or lost seniority must all be rectified, if they result from illegal discrimination.” Thompson v. Sawyer, 678 F.2d 257, 290 (D.C.Cir.1982). “An award of back pay, therefore, should ordinarily consist of lost salary, including anticipated raises, and fringe benefits.” E.E.O.C. v. Joint Apprenticeship Comm. of Joint Indus. Bd. of Elec. Indus., 164 F.3d 89, 101 (2d Cir.1998).

Step Increases. Step increases are ' among the types of compensation that a district court must consider when calculating the back-pay award in order to make the plaintiff whole.

When discrimination continues over time, ... the harms it causes' are compounded. An employee denied a raise in one year will fall further behind if raises in subsequent years are a function of prior salaries. Likewise, an employee denied a promotion in a given year may be frozen out of additional promotional opportunities, unless the missed rung on the promotion ladder is somehow replaced.

Thompson, 678 F.2d at 290; see also Salone v. United States, 645 F.2d 875, 878 (10th Cir.1981) (holding that the plaintiff could recover the benefit of periodic step increases as part of a back-pay calculation).

In this case, the back-pay calculations should have included step increases. Under the Akron Fire Department’s Salary Plan, firefighters who are promoted to the ranks of Lieutenant and Captain begin at Step 4. After each year in the rank, the firefighter receives an additional step up; thus, they achieve Step 5 after the first year in the rank, and Step 6 after the second year, and so on. See Pis.’ Br. at 21; R. 467 at 26-29 (Tr. Retrial Vol. 1) (Page ID # 12495-98). Akron introduced an exhibit that lists each of these step increases in accordance with the salary plan, see R. 736-1 at 1-3 (Def.’s Tr. Ex. 1117) (Page ID # 18730-32), and therefore the district court had all of the information necessary to compute step differentials. Because the back-pay calculations did not incorporate step increases, the back-pay award did not make the Plaintiffs whole.

Discovery Sanction. Akron contends that the record does not include any evidence necessary to compute step increases. Akron Reply Br. at 56-57. As explained above, we disagree. Even so, any deficiency in the evidentiary record was the result of the district court’s decision to exclude the Plaintiffs’ final back-pay calculations as a sanction for alleged discovery violations. The Plaintiffs contend that the district court abused its discretion by excluding this evidence. See Pis.’ Br. at 64-69.

Federal Rule of Civil Procedure 26(a)(l)(A)(iii) requires the party seeking damages to “make available for inspection and copying ... the documents or other evidentiary material, unless privileged or protected from disclosure, on which each computation is based, including materials bearing on the nature and extent of injuries suffered[.]” “If a party fails to provide information or identify a witness as required by Rule 26(a) or (e), the party is not allowed to use that information or witness to supply evidence on a motion, at a hearing, or at a trial, unless the failure was substantially justified or is harmless.” Fed.R.Civ.P. 37(c)(1). Although exclusion of late or undisclosed evidence is the usual remedy for noncompliance with Rule 26(a) or (e), Rule 37(c)(1) provides the district court with the option to order alternative sanctions “instead of’ exclusion of the late or undisclosed evidence “on motion and after giving an opportunity to be heard.” Id.; see also Roberts ex rel. Johnson v. Galen of Virginia, Inc., 325 F.3d 776, 783-84 (6th Cir.2003) (“Rule 37(c)(1) does not compel the district judge to exclude testimony in its entirety.”). A noncompliant party may avoid sanction if “there is a reasonable explanation of why Rule 26 was not complied with or the mistake was harmless.” Bessemer & Lake Erie R.R. Co. v. Seaway Marine Transp., 596 F.3d 357, 370 (6th Cir.2010) (internal quotation marks omitted).

“We review a district court’s decision to impose sanctions for any such noncompliance under an abuse-of-discretion standard.” Jordan v. City of Cleveland, 464 F.3d 584, 600 (6th Cir.2006). The Advisory Committee Notes to the 1993 Amendments, which include Rule 37(c)(1), explain that

[l]imiting the automatic sanction to violations “without substantial justification,” coupled with the exception for violations that are “harmless,” is needed to avoid unduly harsh penalties in a variety of situations: e.g., the inadvertent omission from a Rule 26(a)(1)(A) disclosure of the name of a potential witness known to all parties; the failure to list as a trial witness a person so listed by another party; or the lack of knowledge of a pro se litigant of the requirement to make disclosures. In the latter situation, however, exclusion would be proper if the requirement for disclosure had been called to the litigant’s attention by either the court or another party.

Fed.R.Civ.P. 37, 1993 advisory committee’s note. “[The] Advisory Committee Notes to [the] 1993 Amendments (including Rule 37(c)(1)) ... strongly suggest!] that ‘harmless’ involves an party.” Vance ex rel. Hammons v. United States, 182 F.3d 920, at *5 (6th Cir.1999). In order to assess whether a party’s omitted or late disclosure is “substantially justified” or “harmless,” the Fourth Circuit considers five factors, which we now also adopt:

(1) the surprise to the party against whom the evidence would be offered; (2) the ability of that party to cure the surprise; (3) the extent to which allowing the evidence would disrupt the trial; (4) the importance of the evidence; and (5) the nondisclosing party’s explanation for its failure to disclose the evidence.

Russell v. Absolute Collection Servs., Inc., 763 F.3d 385, 396-97 (4th Cir.2014) (quoting S. States Rack & Fixture, Inc. v. Sherwin-Williams Co., 318 F.3d 592, 597 (4th.Cir.2003)).

We first address whether the Plaintiffs’ alleged late disclosure was a surprise to Akron. A district judge’s decision to exclude evidence of the plaintiffs back-pay calculations as a sanction is an abuse of discretion when the defendant “had all the information relevant to the computation of damages in its possession” and “had a full opportunity during [the plaintiffs] deposition to question him about damages.” Jordan, 464 F.3d at 601 & n. 22. Here, Akron had all of the Plaintiffs’ salary information in its possession. Akron knew that the Plaintiffs intended to use Excel simple math—addition, subtraction, multiplication, and division-to calculate back pay. And Akron was aware that the Plaintiffs had considered two methods for computing back pay—Carr’s method and Snyder’s method. Akron deposed both Carr and Snyder about their methods for calculating back pay, and therefore Akron had adequate time to explore the methodology Carr and Snyder used.

The record establishes that the Plaintiffs were relying on Snyder’s back-pay calculations throughout the discovery period. But the record also reveals that the Plaintiffs acknowledged that their original back-pay calculations may have been flawed and that they may need to recalculate their back pay. After receiving information from Akron, the Plaintiffs calculated their back pay using Snyder’s method. During the depositions, the Plaintiffs realized that there may have been problems with their method of calculating back pay, and the Plaintiffs disclosed that to the district court. See R. 358 at 7 (Tr. Pretrial Conference) (Page ID # 8322) (“If [Akron] is going to say that [the Plaintiffs’ calculation of back pay] is incorrect, they have to assume that there is something that is correct.... That’s why some of the revisions that we are making in the damage computations are based on the depositions that have happened so far based on some of the inquiries they have made.... ”). Thus, Akron was aware that the Plaintiffs had considered Carr’s method and that the Plaintiffs were reconsidering their calculations.

Second, we address whether Akron had adequate opportunity to remedy the surprise. Despite the Plaintiffs’ last-minute decision to alter their method for calculating back pay, it appears that the change brought the parties closer to agreement: under the Carr method, the Plaintiffs’ back-pay calculation apparently resulted in a $120,000 reduction. Pis.’ Br. at 68. Akron had been complaining that the Plaintiffs had overstated their entitlement to back pay, see Akron Br. at 49, and therefore it seems that this correction should have been welcome news to Akron; the only issue to be litigated during the retrial was how much Akron would have to pay, not whether they must. Moreover, Akron could have explored the problems with Carr’s method for calculating back pay by cross-examining Carr and the other twenty-two Plaintiffs during the retrial.

Third, we consider whether introduction of the evidence would disrupt the hearing or trial. When the Plaintiffs disclosed Exhibit 208, the retrial had not commenced, and therefore Akron still had an opportunity to cross-examine Carr, Snyder, and the other twenty-one Plaintiffs. In addition, McLeod, an Akron employee, testified about the Akron Fire Department’s compensation scheme and he calculated each Plaintiffs back pay, and therefore the record suggests that Akron believed that there was a “proper” method for calculating back pay. Akron could have compared the strengths and weaknesses of each method, which it apparently did by including evidence about the probability that the Plaintiffs would not have been promoted at all. See R. 565 at 10 (Tr. Retrial Vol. 5) (Page ID # 15887) (“[I]f plaintiffs want to embrace Mr. McLeod’s calculations, they must embrace all of them, including the loss of chance reduction of 28 percent for the lieutenants, 29 percent for the captains.”). We therefore conclude that the Plaintiffs’ untimely disclosure did not significantly impact the trial.

Fourth, we consider the importance of the evidence excluded. We have already held that the district court should have considered the step increases when calculating the Plaintiffs’ back pay in order to make them whole. We thus believe that this evidence was crucial to establishing an accurate back-pay award.

Fifth, we consider the Plaintiffs’ explanation for the late disclosure. The Plaintiffs argue that the district court’s last-minute orders promoting the Plaintiffs and establishing the start date for calculating back pay substantially justified the late disclosure of Exhibit 208. See Pis.’ Br. at 66-68. The Plaintiffs contend that their “damages amount inevitably needed to change to comply with the July 12, 2011 Order,” setting the start date for calculating back pay. Id. at 67. They explain that “the basic formula never changed — it always involved the [Plaintiffs’] weekly payroll data provided by Akron multiplied by the incremental step increases,” id. at 67-68, but they now could not use “the average salaries of promoted officers in 2005” to calculate the back pay, id. at 66. Akron points out that this is not an adequate explanation for the late disclosure because the start date for calculating back pay would not affect the formula used to calculate back pay, see Akron Reply Br. at 53-54, and we agree.

Nevertheless, we believe that the record suggests that the Plaintiffs’ late disclosure was more likely the result of negligence, confusion, and lack of information than underhanded gamesmanship. Our review of the record suggests that the discovery period before the retrial was a rushed, confusing nightmare. The Plaintiffs complain that Akron wasted everyone’s time by continuing to focus on the Lability component of the case. Akron accuses the Plaintiffs of, first, trying to inflate their back pay; and, second, trying to conceal their back-pay calculations. The Plaintiffs requested information about the actual hours and pay rates of all of the Lieutenants and Captains who had been promoted in order to compare the promoted firefighters’ earnings to the Plaintiffs’ actual earnings. See R. 357 at 21-22 (Tr. Pretrial Conference) (Page ID # 8295-96). Akron refused to provide that information until the last possible day, but insisted that the Plaintiffs provide their back-pay calculations before that time. See id. at 22-23 (Page ID # 8296-97). The record farther reveals that the attorneys for both sides engaged in a childish withholding game, rather than providing necessary information to determine how best to make the Plaintiffs whole. See id. at 24-25 (Page ID #8298-99). The district court chastised both sides and,. required that “the plaintiffs quickly provid[e] to the defendant their damage calculation and how they arrive at those numbers.... [I]n order for the plaintiffs to do that, the city must promptly and timely provide documentation outlining lieutenants’ pay and the overtime.... ” Id. at 24 (Page ID #8298). Thus, the Plaintiffs could not calculate and verify their back-pay calculations until they looked at the data in Akron’s possession, and Akron bears at least some responsibility for the delayed disclosure.

In addition, the record strongly suggests that the district court also caused some of the confusion leading up to the retrial. The district court set short deadlines for discovery and made it difficult for the Plaintiffs to calculate accurately their back pay by (1) promoting all of the Plaintiffs without notice, and (2) setting the date to commence back-pay calculations very shortly before trial. The hurried nature of the second discovery period, rancor between the parties, and the last-minute decisions that substantially affected back-pay calculations contributed to the confusion. Although the Plaintiffs are not blameless, we believe that the district court caused many of the problems that led to the late disclosure of the Plaintiffs’ final back-pay calculations. We therefore conclude that the Plaintiffs’ late disclosure was harmless, and thus the district court’s decision to exclude Carr’s testimony and Exhibit 208 was an overreaction and an abuse of discretion.

Prejudgment Interest. Finally, the district court’s back-pay award did not adequately make the Plaintiffs whole because the back-pay award did not include prejudgment interest. Akron claims that we may not review this portion of the Plaintiffs’ appeal because they have “waived” their claim to prejudgment interest because they did not file a motion to alter or amend the judgment pursuant to Rule 59(e) within the time period described in the rule. Although the Plaintiffs did not file a motion to alter or amend the back-pay findings of fact and conclusions of law, they raised the issue of prejudgment interest in this appeal. “Parties are not required to make a motion for a new trial challenging the supposed errors as a prerequisite to appeal,” and therefore the Plaintiffs’ notice of cross-appeal was sufficient to preserve the prejudgment-interest issue for appeal. 11 Chaeles AlaN Wright, Arthur R. Miller, Mary Kay KaNe, Federal Praotioe and ProCedure § 2818 (3d ed.2015); see also Richardson v. Oldham, 12 F.3d 1873, 1377 (5th Cir.1994) (“Filing a Rule 59 motion is not a prerequisite to taking an appeal. ...”). The Plaintiffs have preserved their claim to prejudgment interest, and we may review the district court’s failure to award that interest for an abuse of discretion. United States v. City of Warren, 138 F.3d 1083, 1096 (6th Cir.1998).

“Prejudgment interest, of course, is ‘an element of complete compensation.’ ” Loeffler v. Frank, 486 U.S. 549, 558, 108 S.Ct. 1965, 100 L.Ed.2d 549 (1988) (quoting West Virginia v. United States, 479 U.S. 305, 310, 107 S.Ct. 702, 93 L.Ed.2d 639 (1987)). “Indeed, ‘it is ordinarily an abuse of discretion not to include prejudgment interest in a back-pay award’ ” because prejudgment interest is part and parcel of complete compensation for past discrimination. E.E.O.C. v. Ky. State Police Dep’t, 80 F.3d 1086, 1098 (6th Cir.1996) (quoting Clarke v. Frank, 960 F.2d 1146, 1154 (2d Cir.1992)). A district court does not abuse its discretion by failing to award prejudgment interest, however, if the plaintiff does not request it. See Scales v. J.C. Bradford & Co., 925 F.2d 901, 909 (6th Cir.1991) (“Because [the plaintiff] did not request any prejudgment interest in her damage calculation, we find no abuse of discretion in this case.”).

That is not the case here, however; the Plaintiffs have consistently pursued prejudgment interest in the district court, and the district court led the Plaintiffs to believe it would consider their request for prejudgment interest at the conclusion of the retrial, but did not do so. After the first trial, the Plaintiffs filed a motion pursuant to Rule 59(e) to alter or amend the judgment to include prejudgment interest. R. 280 at 1-2 (Pis.’ Rule 59(e) Mot. to Amend. J.) (Page ID # 7756-57). When the district court granted the new trial on damages, it chose to “take up each of plaintiffs’ requests [for additional relief] at the new trial on damages.” R. 311 at 11 (Mem.Op.) (Page ID # 16409). But when the district court entered its findings of fact and conclusions of law after the second trial, the court did not mention prejudgment interest. See R. 588 at 7-12 (Conclusions of Law ¶¶ 1-16) (Page ID # 16485-90). The delays in this case have been considerable. The Plaintiffs “should not be penalized for delays in the judicial process,” nor should Akron “benefit from such delays.” City of Warren, 138 F.3d at 1096. Accordingly, we hold that the district court abused its discretion by failing to award prejudgment interest to the Plaintiffs.

Lost-Chance Theory. Finally, Akron argues that the district court’s back-pay award was erroneous, and therefore an abuse of discretion, because the district court did not reduce the Plaintiffs back-pay award by sixty-seven percent for Lieutenant candidates and seventy-one percent for Captain candidates, which are the respective probabilities that the Plaintiffs would not have been promoted had the promotional process been completely fair. Akron Br. at 50. The lost-chance theory of back-pay calculations, if applicable, would require the finder of fact to estimate the probability that the plaintiffs would have been promoted using a non-discriminatory process, and then reduce the back-pay award to the percentage of the back pay the plaintiff would have received had he or she been certain to be promoted. See Bishop v. Gainer, 272 F.3d 1009, 1016— 17 (7th Cir.2001); Doll v. Brown, 75 F.3d 1200, 1205-06 (7th Cir.1996) (describing the lost-chance theory in the field of medical negligence). The theory is that plaintiffs’ chances at promotion “are inherently uncertain because of the competitive setting” of the promotional process.” Doll, 75 F.3d at 1206.

As an initial matter, we note that Akron did not forfeit its arguments regarding back pay by not raising the issues in Howe I, as the Plaintiffs argue; the district court had not yet entered its findings of fact and conclusions of law with respect to the Plaintiffs’ back pay, and therefore Akron did not have an opportunity to challenge the back-pay award. Nor did Howe I decide whether the Plaintiffs’ back pay should be reduced by the probability that they would not be promoted. Howe I addressed whether the Plaintiffs had demonstrated “a reasonable likelihood of promotion,” such that promotion of all of the Plaintiffs was not an abuse of discretion. 723 F.3d at 661-62. Accordingly, we may address Akron’s challenge to the district court’s back-pay award on a clean slate.

The district court did not employ a lost-chance method of calculating the Plaintiffs’ back pay because it concluded that Akron “previously waived that legal theory.” R. 589 at 2 (D.Ct.Order) (Page ID # 16492). In addition, the district court found that “[t]he door was not reopened on this legal theory by virtue of [the] Plaintiffs[ ]....” Id. Akron contends that the district court’s exclusion of lost-chance evidence is “fundamentally unfair and wrong” because the Plaintiffs did not request a back-pay jury instruction during the first trial, and once the Plaintiffs requested a back-pay instruction, Akron began arguing that the Plaintiffs’ back-pay award should be reduced. Akron Br. at 51.

Akron has a point. When the district court held that the Plaintiffs had waived their right to a jury trial on the issue of back pay, the district court specifically found that the Plaintiffs (1) did not argue for back pay during the initial trial, (2) did not request a back-pay jury instruction during the first trial, and (3) that the jury awarded front pay, not back pay. R. 403 at 2 (D. Ct. Order Re Back Pay Jury Trial Waiver) (Page ID # 10938). We cannot reconcile these conclusions with the district court’s finding that Akron waived the right to present an argument for lost-chance back-pay calculations. We therefore conclude that the district court erred.

However, we do not address now whether back-pay calculations must include a lost-chance reduction. Only the Seventh Circuit uses the lost-chance method for calculating back pay in adverse-impact discrimination cases. The sole time we have confronted the question whether to apply lost-chance theory to back-pay calculations, we declined to do so because it would have been unnecessary to the holding. See City of Warren, 138 F.3d at 1098-99. Although the Seventh Circuit has offered a plausible argument in favor of applying the lost-chance methodology to back pay, see, Biondo, 382 F.3d at 685-88, at least one scholar has offered an argument against the application of the lost-chance methodology, see Paul M. Secunda, A Public Interest Model for Applying Lost Chance Theory to Probabilistic Injuries in Employment Discrimination Cases, 2005 WIS. L. REV. 747, 777-83 (2005) (arguing that the lost-chance theory of back-pay calculations “fail[s] to give sufficient attention to the public interests that such laws are also intended to serve” and “gives zealous defense counsel an additional opportunity to confuse the remedial issues for the fact finder, and by extension, may significantly add to the administrative costs associated with the litigation of such disputes”). We believe that appellate review will benefit from a district court opinion that addresses whether Akron has presented credible evidence that the lost-chance method of calculating back pay is appropriate in this case, and therefore we do not address that issue now.

We vacate the district court’s award of back pay to the Plaintiffs and remand the case for a new trial on the sole issue of back pay, and therefore we see no cause to address whether the district court made errors with respect to any specific back-pay calculation. See Pis.’ Br. at 71-72.

IV. PERMANENT INJUNCTION AND COURT MONITOR

Akron appeals the district court’s order entering a permanent injunction and appointing a court monitor. “A district court has broad discretionary powers to craft an injunction to the specific violations found to ensure that the employer complies with the law.” E.E.O.C. v. Wilson Metal Casket Co., 24 F.3d 836, 842 (6th Cir.1994) (citing Lemon v. Kurtzman, 411 U.S. 192, 201, 93 S.Ct. 1463, 36 L.Ed.2d 151 (1973)). “Congress deliberately gave the district courts broad authority under Title VII to fashion the most complete relief possible.... ” Local 28 Sheet Metal Workers’ Int’l Ass’n v. E.E.O.C., 478 U.S. 421, 465, 106 S.Ct. 3019, 92 L.Ed.2d 344 (1986) (plurality opinion). “Once liability for racial discrimination has been established, a district court has the duty to render a decree that will eliminate the discretionary effects of past discrimination and prevent like discrimination in the future.” United States v. City of New York, 717 F.3d 72, 95 (2d Cir.2013) (citing Albemarle, 422 U.S. at 418, 95 S.Ct. 2362).

We review the district court’s grant of a permanent injunction for abuse of discretion. United States v. Miami Univ., 294 F.3d 797, 806 (6th Cir.2002). “A district court abuses its discretion when it relies on clearly erroneous findings of fact or when it improperly applies the law.” Id. (internal quotations marks omitted). The district court should limit the scope of the injunction to the conduct “which has been found to have been pursued or is related to the proven unlawful conduct.” Wilson Metal Casket, 24 F.3d at 842. “In fashioning relief against a party who has transgressed the governing legal standards, a court of equity is free to proscribe activities that, standing alone, would have been unassailable.” Ky. Fried Chicken Corp. v. Diversified Packaging Corp., 549 F.2d 368, 390 (5th Cir.1977).

After two trials and extensive briefing, the district court concluded that a permanent injunction and the appointment of a court monitor were necessary to make these Plaintiffs whole, and that the promotions alone did not make the Plaintiffs whole. R. 643 at 5-6 (D. Ct. Permanent Inj. Order) (Page ID # 17331). The district court found that the Plaintiffs continued to experience lingering, harmful effects as a result of Akron’s discriminatory promotional process. See id. at 6 (Page ID # 17331). Cognizant of the complexities of this case, the district court noted that numerous questions remain about how the district court can ever make the Plaintiffs whole: “Are there any plaintiffs that deserve additional time in grade? If so, how much? Should there be some type of carve out for the next round of testing to put the victims of the discrimination on equal footing as to those promoted earlier off of the discriminatory test?” Id. Given these lingering questions, the district court concluded that the proper course of action was to appoint a court monitor to work with Akron and the Plaintiffs to create a new nondiscriminatory promotional process that will avoid the injury the Plaintiffs suffered as a result of the 2004 exam and process. See id. at 9-11 (Page ID # 17334-36).

The permanent injunction prohibits Akron from using a promotional process similar to that which it used in 2004 or any other promotional process that has a disparate impact on protected groups. Id. at 7 (D. Ct. Permanent Inj. Order ¶¶ 1-2). Akron may not promote firefighters without the approval of the Court Monitor, who is responsible for reviewing Akron’s proposed promotional process and developing a system by which the Plaintiffs can review the proposed promotional process. Id. at 7-8 (D. Ct. Permanent Inj. Order ¶¶ 3, 8-9 (Page ID #17332-33)). The Court Monitor is also responsible for working with Akron to create a system for reviewing Akron’s compliance with the injunction and creating a document-retention policy. Id. at 8 (D. Ct. Permanent Inj. Order ¶¶ 9-10). Finally, the district court forbade Akron from retaliating against the Plaintiffs, discriminating on the basis of race or age, or defying the Court Monitor’s orders. Id. at 7 (D. Ct. Permanent Inj. Order ¶¶ 4-6) (Page ID # 17332).

Akron first complains that the Plaintiffs had not presented evidence that Akron will use the discriminatory promotional process again, and therefore there is no need for future oversight. Akron Br. at 54. Permanent injunctions may be appropriate remedies even when the defendant has taken remedial action because “[a]n employer that takes curative actions only after it has been sued fails to provide sufficient assurances that it will not repeat the violation.” E.E.O.C. v. Goodyear Aerospace Corp., 813 F.2d 1539, 1544 (9th Cir.1987). But the district court specifically found that Akron had shown “reluctance to afford Plaintiffs relief, even when it is court-ordered relief,” R. 666 at 4 (D. Ct. Order Re Stay of Permanent Inj.) (Page ID # 17443)—a factual finding which is not clearly erroneous. The district court did not abuse its discretion by prohibiting Akron from future unlawful discrimination.

Akron also argues that the permanent injunction was not necessary to make the Plaintiffs whole. See Akron Br. at 54-55. In Sharpe v. Cureton, 319 F.3d 259, 273 (6th Cir.2003), we held that a permanent injunction granting relief to all firefighters, when the plaintiffs had asserted only individual claims, was an abuse of discretion. But this case is distinguishable from Sharpe. First, only the parties in this case—the Plaintiffs and Akron—have access to the deliberative process with the Court Monitor and the ability to consult with the Court Monitor about the next promotion cycle. See R. 643 at 8 (D. Ct. Permanent Inj. Order ¶¶ 7-8, 10) (Page ID # 17333) (“The Court Monitor shall ... notify ... the Parties before commencing any step in creating a new promotional process”; “The Court Monitor shall develop a process ... which allows Plaintiffs to review the City of Akron’s proposals....” (emphases added)). This interactive process remains subject to court oversight. Id. at 9 (Page ID # 17334). Second, the district court has found that the Plaintiffs face future irreparable harm in the next promotion cycle. Moreover, the district court’s finding that the effects of Akron’s 2004 discriminatory promotional process on the individual Plaintiffs’ careers and compensation continue through the present day is not clearly erroneous. See id. at 6 (D. Ct. Permanent Inj. Order) (Page ID # 17331).

In order to redress the individual harms presented in this case and the complexities involved with crafting a promotional process, the district court concluded that it was best to require that the Plaintiffs work with the Court Monitor. That determination is reasonable. The district court believed that requiring Akron to consult with the Plaintiffs would ensure that they could address any “obstacles [that] remain for them for future testing, such as lacking the proper amount of time in grade to qualify for that future testing.” R. 666 at 4 (D. Ct. Order Re Stay of Permanent Inj.) (Page ID # 17443). This conclusion is reasonable, too, and the factual findings to support it are not clearly erroneous.

Akron next contends that the permanent injunction is overly broad. Principles of federalism “have applicability where injunctive relief is sought ... against those in charge of an executive branch of an agency of state or local governments,” which means that permanent injunctions should be tailored to redress the harm without hamstringing local government. Rizzo v. Goode, 423 U.S. 362, 380, 96 S.Ct. 598, 46 L.Ed.2d 561 (1976). Akron complains that the permanent injunction infringes on its ability to run the fire department because the injunction is of “unlimited duration” and is not “tailored] to the promotional processes and type of discrimination at issue in this case,” and that the appointment of a court monitor imposes “unwarranted court oversight” on the inner workings of the Akron fire department. Akron Br. at 58-60. The Plaintiffs respond that the permanent injunction “is limited to the ‘next cycle of promotions,’ ” and is therefore not too broad. Pis.’ Br. at 56. In reply, Akron “accepted] [the] Plaintiffs’ concession that the injunction should be confined to the ‘next cycle of promotional examinations,’ ” but insisted that “this limitation appear in the injunction itself.” Accordingly, to the extent that the district court’s permanent injunction is not so limited, we modify the permanent injunction to say so explicitly; the district court’s permanent injunction shall be in effect for one promotional cycle.

In all other respects, we conclude that the permanent injunction is sufficiently narrow to address the issues in this case. The injunction that the district court entered is similar to a permanent injunction approved by the Second Circuit. In City of New York, 717 F.3d 72, after the district court found that New York City had used written exams that disparately impacted minority candidates seeking entry-level firefighter positions, the district court entered a permanent injunction, inter alia, (1) prohibiting the use of the challenged exams; (2) requiring that the City obtain the approval of a court monitor before “taking any step in the hiring process”; (3) barring retaliation for complaining against discrimination; (4) requiring compliance with the court monitor’s requests; (5) requiring prior notice to the court monitor and the parties about new hiring and preparation of new eligibility tests; and (6) authorizing sanctions for noncompliance with the permanent injunction. Id. at 96-97. Each of these provisions is strikingly similar to the provisions of the district court’s permanent injunction in this case. Compare id. at 96-97, with R. 643 at 7-10 (D. Ct. Permanent Inj. Order) (Page ID #17332-35). The Second Circuit affirmed each of the above-listed provisions because the injunction proscribed the challenged examinations and sought to address the harmful effects of the examinations. See City of New York, 717 F.3d at 97.

We believe that, like the provisions of the permanent injunction at issue in City of New York, each of the provisions in the district court’s order is sufficiently tailored to the jury’s and district court’s findings that Akron used a faulty testing and promotional process that disparately impacted protected groups. An injunction is not overly broad because it requires that a defendant comply with federal law. See Goodyear Aerospace, 813 F.2d at 1544 (“[T]he district court found that an injunction against retaliation was superfluous because Title VII already prohibits that conduct. We disagree.”). Such provisions are commonplace and reflect the belief that an employer’s “eleventh hour change of heart” following being sued for violating federal law is insufficient assurance that the employer will not violate federal law again. Id. at 1544-45. All of the other provisions of the permanent injunction here are tailored to ensure that Akron uses a promotional process in the next promotional cycle that does not have a disparate impact on protected groups. This was a case about a discriminatory promotional process, and the district court has appropriately limited the scope of the injunction to address promotional processes.

Finally, Akron contends that oversight by a court monitor is unnecessary. Federal Rule of Civil Procedure 53(a)(l)(B)(i) gives courts the power to appoint masters to “hold trial proceedings and make or recommend findings of fact on issues to be decided without a jury if appointment is warranted by “some exceptional condition.” “Rebanee on a master ... may be appropriate when a complex decree requires administration or complex policing, particularly when a party has proved resistant or intransigent or special skills are needed.” 9C ARTHUR R. Miller, Federal Practice and Procedure § 2602.1 (3d ed.2015). The district court concluded that the complex, intertwining issues presented by this case made this case “exceptional” and warranted the appointment of a court monitor. In addition, the district court found that the complexities involved in creating a promotional process and the existence of a collective bargaining agreement required the skill of a tactful court monitor. R. 643 at 10-11 (D. Ct. Permanent Inj. Order) (Page ID # 17335-36). The record supports the district court’s conclusions; and therefore the district court did not abuse its discretion by appointing a court monitor.

Y. REASSIGNMENT

Perhaps the only issue upon which the parties agree is that we should reassign the case to a different district judge. We have interpreted 28 U.S.C. § 2106 (2012) as authorizing the courts of appeals to reassign a case to a different district judge on remand if necessary. Rorrer v. City of Stow, 743 F.3d 1025, 1049 (6th Cir.2014). Reassignment is “[a]n extraordinary power,” which we hesitate to invoke. Lavin v. Husted, 764 F.3d 646, 652 (6th Cir.2014). We consider the following factors to determine whether reassignment of a case is necessary:

(1) whether the original judge would reasonably be expected to have substantial difficulty in putting out of his or her mind previously expressed views or findings;
(2) whether reassignment is advisable to preserve the appearance of justice; and
(3) whether reassignment would entail waste and duplication out of proportion to any gain in preserving the appearance of fairness.

United States ex rel. Williams v. Renal Care Grp., Inc., 696 F.3d 518, 532-33 (6th Cir.2012) (quoting Solomon v. United States, 467 F.3d 928, 935 (6th Cir.2006)).

We believe that this case is an extraordinary case that warrants reassignment to a different district judge. First, this district judge has made it clear that he would have “substantial difficulty ... putting out of his mind previously expressed views” about the Plaintiffs’ counsel’s conduct during the retrial. Id. at 532. After we dismissed for lack of jurisdiction the Plaintiffs’ counsel’s appeal of the district court’s order awarding sanctions, see Howe v. City of Akron (“Howe II”), 557 Fed.Appx. 402 (6th Cir.2014), the district judge acknowledged that Judge Gilman’s concurring opinion criticizing the • district judge’s handling of the discovery and sanctions, see id. at 405-06, required revisiting the sanctions ordér. Nevertheless, the district judge stated that the Plaintiffs’ conduct would “remain under the Court’s consideration when it evaluates attorney fees in this matter.” R. 722 at 4 (D. Ct. Order Re Sanctions) (Page ID # 18053). The district judge was similarly disinclined to reconsider any portion of the permanent injunction when Akron sought a stay. See, e.g., R. 666 at 5 (D. Ct. Order Re Stay of Permanent Inj.) (Page ID # 17444) (“[T]he City stubbornly adheres to its pre-verdict belief that no relief of any kind should be afforded these Plaintiffs.”). Accordingly, the first factor weights in favor of reassignment.

The second factor also tilts in favor of reassignment because “the history of the case reveals an alarming lack of timely progress toward resolving” this ease — a case that began nearly a decade ago. John B. v. Goetz, 626 F.3d 356, 364 (6th Cir.2010). After the jury rendered its verdict in December 2008, the district judge waited nine months before entering his findings of fact and conclusions of law and the judgment, on October 2, 2009. See R. 277 at 1 (FFCL) (Page ID # 7736); R. 278 at 1(J.) (Page ID # 7748). In addition, the parties waited another fifteen months before, on December 30, 2010, the district judge ruled on their post-verdict motions for judgment as a matter of law, new trial, or to amend the judgment, and he has never addressed many of the issues raised in those motions, such as the Plaintiffs’ request for prejudgment interest. The district judge was also slow to enter findings of fact and conclusions of law on the issue of back pay. We understand that judicial dockets are relentless and these parties have been extremely litigious, but district judges have a “responsibility for moving a case forward,” John B., 626 F.3d at 364, and this district judge has not done that. In the meantime, the City of Akron has not been able to promote firefighters and some Plaintiffs died or retired.

The final factor — whether reassignment would be too difficult — gives us pause. This case is complex, unlike other cases in which we have ordered reassignment. See Rorrer, 743 F.3d at 1050-51 (“This is not a case with a ‘complex factual record.’ ”) (quoting Villegas v. Metro. Gov’t of Nashville, 709 F.3d 563, 580 (6th Cir.2013)). The parties have been litigating this case since 2006, and this district judge is the only judge who is fully aware of this ease’s complicated factual and procedural history.

Nevertheless, we believe that reassignment is proper here. A new district judge will have to preside over yet another trial and make findings of fact with respect to a very limited issue — back pay. We hope that this opinion gives the new district judge sufficient guidance so that the trial can proceed in an orderly and efficient manner: We understand that the new district judge will have to undertake the difficult task of calculating and awarding attorney fees to the Plaintiffs’ attorneys. Although we have acknowledged that fee applications are usually best handled by the district judge “intimately familiar with the facts,” Lavin, 764 F.3d at 652, we have confidence that the new district judge will be up to the task. A magistrate judge might streamline the process and alleviate some of the burden as well. See id.

We do not make the decision to reassign this case lightly, acknowledging that the district judge faced parties who have engaged in petty, scorched-earth litigation tactics. The parties’ appellate briefs have provided a taste of the unpleasant and unnecessarily bitter dynamic of this litigation. But the discord appears to be, at least in part, the result of the protracted nature of this litigation to which the district judge has contributed greatly. “Going forward, resolution of key issues should govern progress in the case.” John B., 626 F.3d at 365.

YI. CONCLUSION

At some point, this litigation needs to end. Unfortunately, we cannot give the parties finality today. We sincerely hope that the parties will resolve this case sooner rather than later.

For the foregoing reasons, we AFFIRM the liability judgments. We REVERSE the district court’s back-pay award and REMAND the case for reassignment and a new trial on the issue of back pay. We AFFIRM the district court’s entry of a permanent injunction and appointment of a Court Monitor, but MODIFY the injunction to clarify that the injunction will be in effect only until the end of the next promotional cycle. 
      
      . The Plaintiffs did not have a right to a jury trial on their Title VII claims, and thus the ' jury was "advisory only,” but the district court's final disposition of the Title VII had to be consistent with the jury’s findings as to the other counts. See Gutzwiller v. Fenik, 860 F.2d 1317, 1332-33 (6th Cir.1988) (holding that when there is a Title VII claim tried with a claim for which there is a right to a jury trial, based on the same underlying facts such that the principle of collateral estoppel would apply, the district court is bound by the jury’s express findings when resolving the Title VII claim).
     
      
      . The four-fifths rule provides that "[a] selection rate for any race, sex, or ethnic group which is less than four-fifths 00 (or eighty percent) of the rate for the group with the highest rate will generally be regarded by the Federal enforcement agencies as evidence of adverse impact, while a greater than four-fifths rate will generally not be regarded by Federal enforcement agencies as evidence of adverse impact.” 29 C.F.R. § 1607.4(D).
     
      
      . Back pay and compensatory damages are different. Back pay includes "[t]he wages or salary that an employee should have received but did not because of an employer’s unlawful action...Black’s Law Dictionary 166 (10th ed.2014). "Compensatory damages may in-elude future pecuniary losses, emotional damages, suffering, inconvenience, mental distress, hedonic losses, and other nonpecuniary losses.” Reeb v. Ohio Dep’t of Rehabilitation & Con., 435 F.3d 639, 646 (6th Cir.2006).
     
      
      . Federal Rule of Civil Procedure 54(b) provides:
      When an action presents more than one claim for relief — whether as a claim, counterclaim, crossclaim, or third-party claim— or when multiple parties are involved, the court may direct entry of a final judgment as to one or more, but fewer than all, claims or parties only if the court expressly determines that there is no just reason for delay. Otherwise, any order or other decision, however designated, that adjudicates fewer than all the claims or the rights and liabilities of fewer than all the parties does not end the action as to any of the claims or parties and may be revised at any time before the entry of a judgment adjudicating all the claims and all the parties’ rights and liabilities.
     
      
      . In Akron's Response Regarding Appointment of David R. Cohen as Court Monitor, it interpreted the district court's statement about the deadline to file objections "as soliciting any reason within the parties' knowledge as to why Mr. Cohen would be unqualified or unable to fill the position that this Court created.” R. 652 at 1 (Def.’s Resp. Re: Appointment of David R. Cohen as Ct. Monitor) (Page ID # 17370). Akron specifically noted that it did not believe the district court was soliciting objections to the "decision to appoint a Court Monitor in general, or to the scope, duration, costs, compensation, or nature of the duties and powers assigned to the Court Monitor....” Id.
      
     
      
      . The Second Circuit has referred to the practice of refusing to consider an issue that could have been raised during the first appeal of a judgment as both "law of the case” and "waiver” in the context of'successive criminal appeals:
      The law of the case ordinarily forecloses relitigation of issues expressly or impliedly decided by the appellate court. And where an issue was ripe for review at the time of an initial appeal but was nonetheless foregone, it is considered waived and the law of the case doctrine bars the district court on remand and an appellate court in a subsequent appeal from reopening such issues unless the mandate can reasonably be understood as permitting it to do so.... For similar reasons, ... the law of the case ordinarily prohibits a party, upon resen-tencing or an appeal from that résentenc-ing, from raising issues that he or she waived by not litigating them at the time of the initial sentencing.
      
        United States v. Quintieri, 306 F.3d 1217, 1229 (2d Cir.2002) (internal quotation marks, citations, and footnote omitted).
      In the civil context, the Seventh Circuit held that a plaintiff's failure to appeal an entry of summary judgment during an earlier appeal prevented a challenge to the adverse summary-judgment order on a subsequent appeal. Fed’n of Adver. Indus. Representatives, Inc. v. City of Chi., 326 F.3d 924, 929 (7th Cir.2003).
     
      
      . For example, in United States v. Gov’t of Virgin Islands, 363 F.3d 276, 292 (3d Cir.2004), the Third Circuit invoked the principles of issue preclusion and res judicata to hold that the defendant's failure to appeal an order to deposit funds “barr[ed] its challenge to the deposit requirement.”
     
      
      . Federal common law governs whether the Howe I appeal precludes Akron's claims that the liability judgments are defective because those judgments involve federal questions and federal judgments. See Taylor v. Sturgell, 553 U.S. 880, 891, 128 S.Ct. 2161, 171 L.Ed.2d 155 (2008) ("For judgments in federal-question cases—for example, Herrick's FOIA suit—federal courts participate in developing uniform federal rules, of res judicata, which this Court has ultimate authority to determine and declare." (internal quotation marks and alteration omitted)).
     
      
      . The best method for calculating back pay depends on each individual case. We therefore limit our discussion of back-pay calculations to the situation presented in this case.
     
      
      . Akron argues that this was an impermissible attempt to offer expert testimony. Akron Reply Br. at 46-48. The Plaintiffs claim that their calculations involve simple math-addition, subtraction, multiplication, and division. Pis.' Br. at 65-66. Because we are remanding this case to the district court for a new trial on the issue of back pay, we believe the district court should address whether expert testimony will facilitate proper calculation of back pay.
     
      
      . On February 19, 2014, while this appeal was pending, the Plaintiffs filed a motion for pre- and post-judgment interest with the district court. See R. 613 at 1-8 (Pis.' Mot. for Pre- and Post-J. Interest) (Page ID # 16646-53). To date, the district court has not ruled on the Plaintiffs’ motion to amend the judgment to add prejudgment interest.
     
      
      . Although this appeal has focused on back pay, the original jury verdict included awards for compensatory damages.
     
      
      . The Second Circuit modified numerous provisions that are not similar to the provisions at issue in this case. See City of New York, 717 F.3d at 97-99.
     