 United States Court of Appeals
          FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued September 19, 2019           Decided November 22, 2019

                         No. 18-1250

          NATIONAL TREASURY EMPLOYEES UNION,
                      PETITIONER

                               v.

          FEDERAL LABOR RELATIONS AUTHORITY,
                     RESPONDENT


       On Petition for Review of a Decision and Order
          of the Federal Labor Relations Authority


     Paras N. Shah argued the cause for petitioner. With him
on the briefs were Gregory O’Duden and Larry J. Adkins.

     Tabitha G. Macko, Deputy Chief Counsel, Federal Labor
Relations Authority, argued the cause for respondent. On the
brief was Rebecca J. Osborne, Acting Deputy Solicitor. Noah
B. Peters, Attorney, entered an appearance.

    Before: TATEL and SRINIVASAN, Circuit Judges, and
GINSBURG, Senior Circuit Judge.

Opinion for the Court filed by Circuit Judge Tatel.

     TATEL, Circuit Judge: When federal employees travel for
official business, federal law entitles them to compensation for
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certain time and expenses. The labor union representing
Customs and Border Protection (CBP) employees proposed a
new way to determine an employee’s eligibility for travel time
and expenses, but CBP took the position that the union’s
proposal was nonnegotiable because, in CBP’s view, the
proposal ran afoul of government travel regulations. The
Federal Labor Relations Authority (FLRA) agreed with CBP,
and the union now petitions for review. Because the FLRA’s
decision relies on a mathematical error and a misunderstanding
of the union’s proposal, we vacate and remand.

                                I.
     As directed by Congress, the General Services
Administration issued the Federal Travel Regulation (FTR), a
body of rules dictating by which planes, trains, and
automobiles federal employees may travel, as well as under
what conditions and to what extent those employees will be
compensated for the costs of their journeys. See 5 U.S.C.
§ 5707(a)(1); 41 C.F.R. §§ 300–1.1 et seq. Central to this case,
the FTR defines the area including and surrounding an
employee’s regular workplace—the employee’s “[o]fficial
station”—as a “mileage radius around a particular point, a
geographic boundary, or any other definite domain, provided
no part of the area is more than 50 miles from where the
employee regularly performs his or her duties.” 41 C.F.R.
§ 300–3.1. When traveling outside of their official stations,
federal employees may be eligible for overtime compensation,
see, e.g., 5 C.F.R. §§ 551.422(d), 550.112(j), and room-and-
board reimbursements, see, e.g., 41 C.F.R. § 301–11.1.
Additionally, and also central to this case, the FTR requires that
employees traveling for work use “the most expeditious means
practicable.” Id. § 301–70.100(b).

     CBP presently defines an official station in terms of fifty
as-the-crow-flies miles, that is, the Agency draws a circle with
                                3
a fifty mile radius around the employee’s regular workplace
and that area is the employee’s official station. But because
CBP employees are more likely to travel by car than by crow,
the National Treasury Employees Union—the exclusive
bargaining representative for CBP employees—sought during
collective bargaining to more accurately compensate
employees for the costs they actually incur. Specifically, the
Union proposed to define an employee’s “official station” as
“extend[ing] 50 road miles [in every direction] from the
employee’s official duty station.” Pet. for Review at 4, Joint
Appendix 4. (A “duty station” is the “location where an
employee normally reports for the workday.” National
Collective Bargaining Agreement Between U.S. Customs and
Border Protection and the National Treasury Employees Union
(NCBA) 64 (2017).) To illustrate, a crow flying from the
Metaline Falls, Washington CBP station to the Porthill, Idaho
station will travel 36 miles, but the lowly road driver will travel
55 miles—through a foreign country, no less—to get from one
station to the other. Under CBP’s current rule, employees
traveling the more-than fifty road miles from Metaline Falls to
Porthill receive no compensation for overtime and per diem
costs; under the Union’s proposal, they would be compensated.

     CBP took the position that the Union’s new way of
defining “official station” was nonnegotiable. Under federal
law, agencies “may not negotiate over proposed conditions of
employment that are ‘inconsistent with any Federal law or any
Government-wide rule or regulation,’” U.S. Department of Air
Force v. FLRA, 952 F.2d 446, 448 (D.C. Cir. 1991) (quoting 5
U.S.C. § 7117(a)(1)), and according to CBP, the Union’s
proposal conflicts with the FTR’s definition of “official
station.” CBP and the Union agreed to sever their dispute,
allowing the rest of the collective bargaining agreement to go
into effect, and to submit the issue to the FLRA. After hearing
the parties’ arguments, the FLRA sided with CBP. Analyzing
                               4
the Union’s road-mile proposal in light of the FTR’s definition
of “official station,” the FLRA concluded that the proposed
official station does not qualify as “a mileage radius around a
particular point [or] a geographic boundary.” National
Treasury Employees Union (“NTEU”), 70 F.L.R.A. 724, 725
(2018) (quoting 41 C.F.R. § 300–3.1). The sole question, then,
was whether the Union’s road-mile rule would create a
“definite domain.” Because “‘[d]efinite domain’ is not defined
within the FTR,” id. at 725 n.22, the FLRA began with the
dictionary: “Definite” means “clearly stated or decided; not
vague or doubtful,” id. (quoting New Oxford American
Dictionary (3d ed. 2010)); and “domain” means “[t]he territory
over which sovereignty is exercised,” id. (quoting Black’s Law
Dictionary (10th ed. 2014)). Relying on these definitions, the
FLRA ruled that the Union’s proposal ran afoul of the FTR: “It
is not a definite area, and could extend more than fifty miles
from where the employee regularly performs his or her duties
or vary with every employee and every trip.” Id. at 725–26.

     One FLRA member dissented. In response to the
majority’s concern that each trip would vary in road mileage,
the dissenter pointed out that the FTR requires employees to
travel “by the most expeditious means practicable,” thus
rendering “definite” the area in which an employee could travel
fifty road miles. Id. at 728 (DuBester, Member, dissenting)
(internal quotation marks omitted).

     The Union now petitions for review. See 5 U.S.C.
§ 7123(a) (“Any person aggrieved by any final order of the
[FLRA] . . . may . . . institute an action for judicial review of
the Authority’s order . . . in the United States Court of Appeals
for the District of Columbia.”).
                               5
                              II.
      If a reviewing court concludes that an FLRA decision is
“arbitrary, capricious, an abuse of discretion, or otherwise not
in accordance with law,” it must “hold [the decision] unlawful
and set [it] aside.” 5 U.S.C. § 706(2); see id. § 7123(c)
(incorporating section 706 standard for judicial review of
FLRA orders). Urging us to do just that, the Union argues that
its proposal qualifies as a “domain” because it defines an area
encompassing all points within fifty road miles of an
employee’s regular workplace and “definite” because each
boundary point—calculated using a “most efficient means”
standard—can be readily ascertained through widely available
mapping applications. Defending its decision, the FLRA
argues that the Union’s proposal does not constitute a
“domain” because it does not demarcate a geographic area, and
it is not “definite” because it leaves open too many variables,
such as which mapping app to use and how to adjust for bad
weather, traffic, or road closures.

     Although the FLRA repeatedly claims that its
interpretation of the regulation is “reasonabl[e],” Resp’t’s Br.
1, 2, 7, 10, it acknowledges, as it must, that we owe it no
deference because the Authority did not write the regulation,
and we “do not defer to the FLRA’s interpretation of
regulations promulgated by other agencies,” Air Force, 952
F.2d at 450; see Resp’t’s Br. 9–10. Of course, the General
Services Administration’s interpretation of “definite domain”
would be entitled to deference, but no one—not CBP, not the
Union, not even the FLRA—ever asked it for its views. See
Oral Arg. Rec. 6:46–8:04. Fortunately, we have no need to
define “definite domain” because, regardless of what the term
means, the FLRA’s decision rests on two glaring errors and is
thus arbitrary and capricious. See American Federation of
Government Employees, Local 2924 v. FLRA, 470 F.3d 375,
380 (D.C. Cir. 2006) (“To be upheld, the decision ‘must come
                                6
with [such] relevant evidence as a reasonable mind might
accept as adequate to support a conclusion.’” (alteration in
original) (internal quotation marks omitted) (quoting American
Federation of State, County & Municipal Employees Capital
Area Council 26 v. FLRA, 395 F.3d 443, 447 (D.C. Cir. 2005));
id. (“[I]f the result reached is ‘illogical on its own terms,’ the
Authority’s order is arbitrary and capricious.” (quoting IRS v.
FLRA, 963 F.2d 429, 439 (D.C. Cir. 1992)).

     Recall that the FLRA’s analysis appears in just one
sentence: “It is not a definite area, and could extend more than
fifty miles from where the employee regularly performs his or
her duties or vary with every employee and every trip.” NTEU,
70 F.L.R.A. at 725–26. Although this haphazardly comma’d
sentence is difficult to unpack, it appears to rest on two
propositions: that the Union’s proposal would create an official
station that, one, extends beyond a fifty-mile-radius circle and,
two, varies with each employee and every trip. Neither is
correct.

     The first proposition is mathematically false. Because the
shortest distance between two points is a straight line, see
James Pryde, Euclid’s Elements of Plane Geometry 18–19
(1860), an “official station” defined in road miles could never
“extend more than fifty miles from where the employee
regularly performs his or her duties,” NTEU, 70 F.L.R.A. at
725–26. The shortest path connecting an employee’s
workplace to the edge of a fifty-mile-radius circle is a straight
road, and that road would measure fifty miles whether
traversed by a fleet of cars or a murder of crows. Every other
long and winding road from the center of that circle to the edge
will exceed fifty road miles, meaning that it is impossible for
an area defined by every point an employee could travel within
fifty road miles to ever extend beyond a fifty-mile-radius circle.
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     The FLRA’s second proposition—that the Union’s
proposed “official station” will “vary with every employee and
every trip,” id. at 726—is also flawed, but for a different
reason. According to the FLRA, the official boundary will
constantly vary because “two trips from [one point to another]
could be greater or fewer than 50 miles depending on [the]
route taken by the driver,” Resp’t’s Br. 16. But the Authority
fails to account for the fact that the FTR requires federal
employees to travel “by the most expeditious means
practicable.” 41 C.F.R. § 301–70.100(b); see also NTEU, 70
F.L.R.A. at 728 (DuBester, Member, dissenting). Specifically,
employees “must travel to [their] destination[s] by the usually
traveled route[s] unless [their] agency authorizes or approves
[] different route[s] as officially necessary.” 41 C.F.R. § 301–
10.7. Moreover, in a provision titled “What is my liability if,
for personal convenience, I travel by an indirect route or
interrupt travel by a direct route?” the FTR clarifies that
employees’ “reimbursement[s] will be limited to the cost of
travel by a direct route . . . . [Employees] will be responsible
for any additional costs.” Id. § 301–10.8. Therefore, regardless
of how many extra miles wandering employees might drive,
their eligibility for time and expenses will be determined based
on the road miles of the most expeditious route.

    The FLRA insists that its sole job was to analyze the
Union’s proposal in light of “this one reg[ulation]” (section
300–3.1), Oral Arg. Rec. at 20:55–58, not in light of other FTR
provisions. But the collective bargaining agreement, in which
the Union seeks to include its road-mile metric, itself
incorporates a “most expeditious means” standard. The
agreement provides, “[n]o employee is entitled to
reimbursements that are not permitted pursuant to the Federal
Travel Regulation[]” and “the Employer will reimburse the
employee for travel and/or moving expenses in accordance
with applicable law, regulation (including the Federal Travel
                              8
Regulation[]) and the terms of this Agreement.” NCBA 66,
223. Additionally, the CBP’s own travel policies, contained in
its Travel Handbook—also incorporated by reference in the
collective bargaining agreement—deploy a “most expeditious
means” standard: “Employees must use the mode of
transportation that provides the most direct, most traveled
route.” U.S. Customs and Border Protection, HB 5300-13A,
Travel Handbook 2-7 (Nov. 2013). Echoing the FTR, the
Handbook provides that when an employee deviates from the
direct route “for personal reasons, or by unauthorized modes of
transportation,” that employee bears responsibility for the
additional costs because “[o]nly those travel expenses that are
necessary and/or incidental to official travel should be
authorized and approved.” Id. at 1-2, 2-7.

     Finally, the FLRA argues that “employees’ official
stations would be literally unknowable until their travel was
completed.” Resp’t’s Br. 15. But CBP’s Travel Handbook
expressly requires that employees “obtain electronic or written
approval to travel . . . before the start of a scheduled trip,”
Travel Handbook 1-1 (emphasis added), and it is presumably
during this pre-approval process that CBP, applying the “most
expeditious means” requirement, “will select the single,
specific route for employees to use.” Reply Br. 7; see also
NCBA at 68 (“Upon timely application, the Agency will take
all reasonable steps, consistent with current policies and
procedures, to provide travel advances to employees prior to
the date of departure on official travel.”).
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                              III.
     Although there are miles to go before the parties sleep, it
is here that we exit the highway. Because both of the FLRA’s
reasons for finding the proposal nonnegotiable were flatly
wrong, we grant the petition for review, vacate, and remand for
further proceedings consistent with this opinion.

                                                    So ordered.
