In this Fair Labor Standards Act case, we affirm the district court’s ruling that the city of Atlanta properly applied the Act to captains, lieutenants, and firefighters, in its Bureau of Fire Services.
On February 19, 1986, the Supreme Court announced in Garcia v. San Antonio Transit Authority, 469 U.S. 528, 105 S.Ct. 1005, 83 L.Ed.2d 1016 (1985), that the overtime provisions of the Fair Labor Standards Act (“FLSA”) were applicable to municipalities. Prior to that time, the city of Atlanta (the “City”) treated firefighters employed in its Bureau of Fire Services (“BFS”) as quasi-salaried employees in that it paid them a fixed sum bi-weekly, which was subject to adjustment for unexcused absences or for any extra work during the period.1 The City reduced the fixed biweekly amount if a firefighter had unexcused absences and increased the amount if *802a firefighter performed extra work. The City paid the firefighters compensation for extra work on a “straight time” rather than a “time and a half” basis.
The firefighters are divided into three rotation groups — groups “A,” “B,” and “C.” The BFS employed a three-day rotation cycle whereby a firefighter from each group worked one “twenty-four hour day” followed by two days off. Because it is mathematically impossible to schedule the three groups to an equal number of shifts during the twenty-eight work days in a bi-weekly pay period, one group of firefighters worked ten days during a pay period while the other two groups worked nine days.2
Following the Supreme Court’s announcement in Garcia that the statutory provisions of the FLSA applied to municipalities, the City realized that it would have to change its quasi-salaried system. The FLSA required that, except as otherwise provided, employees who worked in excess of a certain number of hours be compensated for the extra hours (“overtime”) at a rate not less than one and one-half times the regular rate. See generally 29 U.S. C.A. § 207. The specific provision governing the firefighters requires that the City pay overtime to the firefighters where, in a work period of 28 consecutive days, the time worked exceeds the lesser of 216 hours or a number of hours established by the Secretary of Labor as being the average number of hours similar employees work in 28 day tours of duty. See 29 U.S.C. § 207(k). On November 14, 1985, Congress enacted a “grace period” whereby municipalities were permitted to delay implementation of the FLSA until April 15, 1986. See 29 U.S.C. § 216 note.
In attempting to comply with the FLSA provisions, the City formulated a plan which allowed firefighters to receive one “relief-day” per pay cycle. Under this plan, firefighters who were scheduled to work 240 hours (10 days) in a 28-day cycle were scheduled to work 216 hours. Firefighters who were scheduled to work 216 hours (9 days) were scheduled to work 192 hours. Despite the reduction in their work hours, the firefighters continued to receive the same bi-weekly pay. Between November 25, 1985, when the City implemented the new plan, and April 15, 1986, the City continued its custom of paying “straight time” when a firefighter worked extra hours beyond the regularly scheduled hours.
According to the City, on April 15, 1986, it was unable to comply with the overtime provisions of the FLSA due to problems with their computerized pay system. On that date, Chief William Haymer of BFS sent out a memorandum informing firefighters that instead of receiving the 24-hour relief day as had been customary for the preceding 5 months, they would receive a 12-hour relief day. This meant that firefighters scheduled to work 240 hours (10 days) during a 28-day cycle were scheduled to work 228 hours instead of 216 hours; firefighters who were scheduled for 216 hours (9 days) during the 28-day cycle were scheduled to work 204 hours. This system continued in effect until September 3, 1986.
On September 3, 1986, the City converted to an hourly system of pay for firefighters, with time and a half being paid once a 212 hour threshold was reached in each 28-day pay cycle. The City determined that, in order to ascertain each firefighter’s hourly rate of pay, it would divide the firefighter’s annual salary by 2,756 hours.3 In September, 1986, the City notified the firefighters that it would pay, on a retroactive basis, any overtime pay earned during the period *803April 15 to September 3, 1986. The City announced that in making computations for this period, it would determine an hourly rate for each firefighter, and this rate would be applied to compensable time.4 Under this scheme, holidays not actually worked and “relief” days would be excluded from “compensable time” and would not be counted in determining whether the 212 hour overtime threshold had been met. The City also decided that those firefighters who had worked less than 212 hours in a given 28-day period between April 15, 1986, and September 3, 1986, would suffer a retroactive decrease in pay because they had not worked the number of hours for which they had been paid.
The City recalculated both base pay and overtime pay for each 28 day cycle during the period April 15 to September 3, 1986. Thereafter, the City mailed checks to those employees who received less pay than they were entitled to under the new method of calculating overtime. Conversely, those employees who had been paid more than they were entitled to under the new method of calculation had to repay the excess to the City.5
PROCEDURAL HISTORY
The Atlanta Professional Firefighters Union, Loeal 134, (the “Union”) instituted this class action lawsuit on behalf of the firefighters, lieutenants and captains in federal district court, pursuant to 29 U.S.C. § 216(b). The Union alleged that (1) the City had violated the FLSA by failing to pay overtime to firefighters during the period April 15, 1986, to September 3, 1986; (2) the lieutenants and captains were entitled to overtime under the provisions of the Act; and (3) the City had intentionally sought to circumvent the provisions of the Act. The Union sought liquidated damages, attorneys fees, and other equitable relief.
After the Union and the City submitted motions for summary judgment, the district court granted partial summary judgment in favor of the Union, concluding that lieutenants were not exempt from the overtime requirements of the FLSA. The district court also awarded attorneys fees to the Union, but only to the extent that fees were earned on the lieutenant exemption issue.
The district court also granted partial summary judgment in favor of the City. The district court concluded that (1) captains were exempt from the overtime requirements of the FLSA, (2) the City did not err in computing the firefighters’ retroactive award of overtime, (3) liquidated damages were not appropriate because the City had established a good faith reason for deciding not to pay overtime to lieutenants, and (4) the claims of office workers in the BFS were not properly before the court.
CONTENTIONS OF THE PARTIES
The Union contends that the district court erred when it concluded that captains are exempt from the overtime requirements of the FLSA. Additionally, the Union contends that the City violated the FLSA by (1) incorrectly computing the amount of overtime payable to the firefighters, and (2) failing to pay firefighters overtime on a timely basis. Finally, the Union contends that the district court erred by concluding that the employees who worked forty-hour weeks could not obtain relief in this class action suit.
The City contends that the district court did not err in its rulings.
*804DISCUSSION
Under the FLSA, an employer is exempt from paying overtime in connection with the work of certain employees. See 29 U.S.C. § 213. The exemption at issue in this case is one which exempts from the overtime requirements of the FLSA “any employee employed in a bona fide executive, administrative, or professional capacity.” 29 U.S.C. § 213(a)(1). The district court concluded that the City had satisfactorily established the applicability of this exemption for the BFS captains, but not for the lieutenants. Only the Union has appealed.
A. Captain’s Exemption
A captain reports to a battalion chief, who is one rank higher and whose duties involve coordinating the efforts of three different fire stations. A captain is an employee who has achieved a higher rank than lieutenant; and a firefighter is lower in rank than either a captain or a lieutenant. Each of the City’s thirty-four fire stations has a captain, whether it is a single or double company station.6 Only double company stations have lieutenants.
In this case, the City had the burden of proving the administrative exemption. Corning Glass Works v. Brennan, 417 U.S. 188, 196-97, 94 S.Ct. 2223, 2229, 41 L.Ed.2d 1 (1974). Additionally, in determining whether an administrative exemption exists, we must narrowly construe the overtime provisions of section 207 against the City. See Brennan v. Sugar Cane Growers Co-Op of Fla., 486 F.2d 1006 (5th Cir.1973).
Federal regulations provide two tests for determining whether an employee qualifies for the administrative exemption of the FLSA — the “short test” and the “long test.” See 29 C.F.R. §§ 541.2, 541.2(e)(2) (1987). Title 29 C.F.R. § 541.2 provides that:
The term “employee employed in a bona fide ... administrative ... capacity” in section 13(a)(1) of the Act [29 U.S.C. § 213(a)(1)] shall mean any employee:
(a) Whose primary duty consists of either:
(1) The performance of office or non-manual work directly related to management policies or general business operations of his employer or his employer’s customers, ... and
(b) Who customarily and regularly exercises discretion and independent judgment; and
(c)(1) Who regularly and directly assists a proprietor, or an employee employed in a bona fide executive or administrative capacity (as such terms are defined in the regulations of this subpart), or
(2) Who performs under only general supervision work along specialized or technical lines requiring special training, experience, or knowledge, or
(3) Who executes under only general supervision special assignments and tasks; and
(d) Who does not devote more than 20 percent ... to activities which are not directly and closely related to the performance of the work described in paragraphs (a) through (c) of this section; and
(e)(1) Who is compensated for his services on a salary or fee basis at a rate of not less than $155 per week ... exclusive of board, lodging, or other facilities, or
(2) ... Provided, That an employee who is compensated on a salary or fee basis of not less than $250 per week ... and whose primary duty consists of the performance or work described in paragraph (a) of this section, which includes work requiring the exercise of discretion and independent judgment, shall be deemed to meet all the requirements of this section.
Under the “long test,” an employer must establish all five elements of the regula*805tion. Under the “short test,” the employer need only establish the requirements of subsection (e)(2). As is readily apparent, an employer seeking to establish an exemption first seeks to qualify under the “short test”; if that effort fails, the “long test” is used.
The “short test” requires that an employee be paid “on a salary basis” and have a “primary duty” as an administrator. 29 C.F.R. § 541.2(e)(2). Federal regulations define “on a salary basis” as follows:
An employee will be considered to be paid ‘on a salary basis’ within the meaning of the regulations if under his employment agreement he regularly receives each pay period on a weekly, or less frequent basis, a predetermined amount constituting all or part of his compensation, which amount is not subject to reduction because of variations in the quality or quantity of the work performed. Subject to the exceptions provided below, the employee must receive his full salary for any week in which he performs any work without regard to the number of days or hours worked. This policy is also subject to the general rule that an employee need not be paid for any workweek in which he performs no work. [Emphasis added.]
29 C.F.R. § 541.118(a).
Captains receive the same pay for each nine-day cycle or ten-day cycle during the year. As indicated earlier, the scheduling needs of the fire department and the number of groups make it impossible for the City to schedule captains to the same number of days each pay cycle. Although captains do not receive the same pay each pay period, this fact does not preclude a finding that they are paid a predetermined amount. Under the BFS system, each captain knows at the beginning of each year the exact amount of pay for each nine-day cycle or ten-day cycle. Consequently, we conclude that captains are paid a predetermined amount.
The focus of the Union’s challenge to the district court’s finding, however, concerns the issue of whether the predetermined compensation is subject to reduction because of variations in the quality or quantity of work performed. The Union argues that because a city ordinance requires that all city employees’ compensation be decreased for arriving late or for violating other BFS regulations, the captains cannot, as a matter of law, qualify for the administrative exemption. As the district court noted, however, the Union presented no evidence to prove that any captain ever suffered a reduction in pay for any of the reasons stated. Accordingly, we conclude that the City has demonstrated that a captain’s pay is not subject to reduction because of the quality or quantity of work.
The second prong of the “short test” requires the City to establish that a captain’s “primary duty” is administrative. An employee’s “primary duty” is administrative if for 50-percent of the time the employee is “responsible for work which is characteristic of employment in a bona fide administrative capacity ... related to management policies or general business operations.” 29 C.F.R. § 541.206; see also 29 C.F.R. § 541.103. The evidence in this case indicates that, although a captain acts upon directions of a battalion chief, a captain generally has discretion in implementing these directions. Moreover, the evidence indicates that a captain can make changes in the daily activity agenda of the fire station. Captains also direct emergency operations, inspect buildings that are potential fire hazards, and inspect fire hydrants. No evidence exists to indicate that a captain performs much of the manual work associated with the traditional role of firefighting. The City presented testimony that the captain’s role involves making strategic decisions on how to fight the fire, and when necessary, to perform manual work. Accordingly, we conclude that a captain’s primary duty is to perform bona fide administrative tasks. Consequently, both prongs of the short test have been met, and we hold that the captains are exempt from the overtime provisions of the FLSA.
*806B. FLSA violations
(i) Firefighters
The Union contends that the City violated the FLSA by incorrectly computing the overtime award to firefighters for the period April 15 to September 3, 1986. The Union also attempts to argue on appeal that the City violated the FLSA by failing to make “timely” overtime payments for the period April 15 to September 3. This timeliness issue was not raised in the complaint and first appeared in the Union’s third supplemental brief in support of its motion for summary judgment. Since the City had no notice of this issue and the district court did not address it, we will not consider it for the first time on appeal.
In computing the overtime award for the period in question, the City applied each firefighter’s hourly rate to the firefighter’s “compensable time” during April 15 to September 3.7 The City did not include holidays and relief days not worked in its determination of whether the 212 hour overtime threshold had been met.
As to liquidated damages, the statute provides: “Any employer who violates the provisions of section 206 or section 207 of [FLSA] shall be liable to the ... employees affected in the amount of their ... unpaid overtime compensation ... and in an equal amount as liquidated damages.” 29 U.S.C. § 216(b).
In any action ... to recover ... liquidated damages, under the Fair Labor Standards Act of 1938 as amended [29 U.S.C.A. § 201 et seq.], if the employer shows to the satisfaction of the court that the act or omission giving rise to such action was in good faith and that he had reasonable grounds for believing that his act or omission was not a violation ... the court may, in its sound discretion, award no liquidating damages or award any amount thereof not to exceed the amount specified in section 216 of [FLSA].
29 U.S.C. § 260.
The Union asserts that the firefighters are entitled to overtime compensation under the FLSA for holiday and relief days. Thus, the Union argues that the City violated the FLSA through its decision to retroactively offset accrued overtime compensation by implementing an hourly rate and excluding holiday and relief days from the overtime compensation. See Blanton v. City of Murfreesboro, 658 F.Supp. 1540 (M.D.Tenn.1987), aff'd, in part and modified in part, 856 F.2d 731 (6th Cir.1988). Under the firefighters’ contract with the City, holidays and relief days are to be counted for compensation purposes. The contract counts the holiday and relief days; the FLSA does not count them. The district court awarded the firefighters compensation for holiday and relief days pursuant to a breach of contract theory. In doing so, the court noted that the FLSA does not require an employer to count hours not actually worked or relief days in determining whether the 212 hour threshold requirement has been met. See Boll v. Federal Reserve Bank of St. Louis, 365 F.Supp. 637, 646-47 (E.D.Mo.1973) (the FLSA does not require employers to compensate employees for holiday time and personal convenience time). Therefore, the City did not violate the FLSA, but violated the contract by not counting holiday and relief days. Only a violation of the FLSA results in a right to liquidated damages under the Act.
The Union’s additional argument is that the City’s retroactive reduction of accrued overtime constitutes discrimination prohibited by the FLSA. See 29 U.S.C. § 215(a)(3). Section 215(a)(3) makes it unlawful for an employer to “discriminate against any employee because such employee has filed any complaint or instituted or caused to be instituted any proceeding under or related to the [FLSA].” The district court concluded that the City institut*807ed the overtime provisions to comply with the requirements of the FLSA and did not discriminate nor intend to discriminate against the employees through the use of these provisions. The Union failed to present evidence to support its assertion that the City in recalculating overtime acted in retaliation against the employees’ for the filing of this lawsuit. No evidence supports such an assertion. Accordingly, we hold that the district court correctly granted summary judgment to the City on this issue.
(ii) Lieutenants
The Union contends that the district court erred by failing to award liquidated damages to lieutenants. According to the Union, the City’s failure to evaluate whether lieutenants were entitled to the administrative exemption belies the City’s claim that it acted in good faith. The City acknowledges that it violated the Act as to lieutenants, but asserts that it has satisfied its burden of demonstrating good faith because it relied on an administrative decision of the Administrator of the Department of Labor’s Wage and Hour Division. The administrator’s decision concluded that the salary test was not applicable to lieutenants. We conclude, as did the district court, that in this case, the City’s reliance on the administrative decision satisfies its burden of demonstrating good faith. Additionally, record testimony indicates that the City did evaluate the job duties of lieutenants.
C. Office workers
Finally, the Union contends that the district court erred by failing to consider and resolve the BFS office workers’ claims. The Union first raised the claims of these employees in its third supplemental brief in support of its motion for summary judgment. The district court declined to consider the claims of these workers based on its finding that the complaint specifically stated that members of the class were “firefighters.” Upon review of the pleadings, we agree with the district court that the office workers are not members of the class. See Fed.R.Civ.P. 23(c)(3).
CONCLUSION
In summary, we hold that captains are exempt from the overtime provisions of the FLSA, the computation of overtime was correct, the City acted in good faith, and office workers are -not members of the class.
AFFIRMED.
. Unexcused time includes absences which are not properly chargeable to sick leave, allowable vacation, military leave, allowable compensable holiday leave (nine days per year), injury on the job time, or jury duty.
. For example, during the first twenty-eight day pay cycle, group "A” firefighters were scheduled to work ten 24-hour shifts while groups "B” and "C" firefighters were scheduled to work nine 24-hour shifts. In the next twenty-eight day pay cycle, group "B” firefighters were scheduled to work ten 24-hour shifts, while groups "A" and "C" firefighters were scheduled to work nine 24-hour day shifts.
. Two thousand seven hundred and fifty-six hours is an average work week of 53 hours (52 X 53 = 2,756). The average hours roughly equate to a year’s worth of 24-hour shifts with 2 days in between each shift but less a 12 hour relief day every 28 days.
. "Time" was defined to include actual hours worked, sick leave, vacation leave, military duty, on-the-job injury time, and jury duty.
. In determining whether an employee had received the proper compensation, the City recalculated the salary for each 28-day cycle during the period. For example, the record indicates that one employee worked 228 hours in pay cycle No. 5 and was credited with unpaid overtime of 16 hours (228-212 = 16). A separate computation revealed that the employee worked only 204 hours in pay cycle No. 6, and therefore, the firefighter owed the City for 4 hours of excess computation (212-204 = 8). The City then computed the net balance of the employee’s account after making similar computations for every 28-day cycle during the period.
. Atlanta has twenty double stations with two firefighter companies housed in the same building, and fourteen single stations. A single station usually has four firefighters, including a captain. A double company station usually has eight firefighters, including a captain and lieutenant.
. “Compensable time” included actual hours worked, sick leave, vacation leave, military duty, on-the-job injury time, and jury duty.