WILLIAMS, Circuit Judge.

Brothers Les and Jeffrey Lippert own a tile installation business that employs union workers. Some of their customers require or prefer that union workers be employed for tile installation projects, but others prefer nonunion labor because they can be cheaper. So in 2004 the brothers created a new tile installation company that employed non-union workers solely to serve this market. Pursuant to the governing collective bargaining agreement, the union filed a grievance with the joint arbitration committee ("JAC"), seeking union benefits for the non-union tile installers working for the new company. After the JAC granted this relief, the companies petitioned to vacate the award in federal district court, arguing that the new company should not have been bound by the arbitration award because it was not a party to the collective bargaining agreement. However, the district court granted the union's motion to enforce the award on summary judgment, finding that the nominally new company could be treated as one and the same with the old company for purposes of the agreement under the "single employer" doctrine. The companies appealed.

The companies first argue that the arbitration award is unenforceable because the National Labor Relations Board has never found that the non-union laborers are in the same bargaining unit as the union laborers. They maintain that such a finding is required to determine whether disputes concerning the non-union workers are subject to arbitration under the collective bargaining agreement. We do not resolve this issue because the companies waived this argument by failing to present it to the JAC. The companies next challenge the district court's finding that they are a "single employer," but we agree with the district court that the companies, which are centrally operated by the same entity, are one and the same for purposes of arbitrability under the contract. Finally, they assert that the JAC was tainted because the union representative who filed the grievance also sat on the JAC, but nothing in the contract forbids this practice. Therefore, we affirm.

I. BACKGROUND

The following facts are undisputed. Brothers Les and Jeff Lippert established Lippert Tile Company, Inc. ("Lippert Tile"), a floor tile installation company, in 2000. Lippert Tile services customers in the four-county Greater Milwaukee area. The Bricklayers and Allied Craftsmen, District Council of Wisconsin and its Local 5 (collectively, the "union") represent the tile installation workers of Lippert Tile. The governing collective bargaining agreement ("CBA") between the union and Lippert Tile provided for certain benefits and wages for the employees and prohibited Lippert Tile from "sublet[ting], assign[ing] or transfer[ring] any work covered by this Agreement to be performed at the site of a construction project to any person, firm or corporation except where the Employer signifies and agrees in writing to be bound by the full terms of this Agreement and complies with all of the terms and conditions of this Agreement." The CBA also provided for the creation of a joint arbitration committee, consisting of "three (3) Employers and three (3) Representatives of the Union for the purpose of deciding disputes, which may arise in connection with the application of this agreement." (In the case of a tie, the CBA provided for referral to the Wisconsin Employment Relations Commission for resolution.) The CBA added, "In the event an Employer or the Union does not comply with the Award of the arbitrator, the other party shall have the right to use all legal and economic recourse."

Lippert Tile's market for tile installation work includes general contractors subject to their own collective bargaining agreements, project owners having or wanting to use union-represented tile contractors, and government-regulated entities tending to use union labor due to prevailing wage regulations (the "union market"). Over the last 10 years, however, this market has been declining, and more customers in the region have sought non-union tile installers, generally because they are 25% to 45% cheaper (the "non-union market"). Because the Lippert brothers believed it was futile for Lippert Tile to try and compete in this growing non-union market, the brothers in 2004 created a new tile installation company, DeanAlan, that would only use non-union workers and compete only in the non-union tile installation market for the same four counties. (The creation of a non-union company for this purpose is known as "double-breasting.") They also created the Lippert Group, a corporate entity that would provide management services to both tile installation companies. Subsequently, Lippert Tile continued providing tile installation services to the union market, while DeanAlan provided tile installation services to the non-union market in the same area.

All three companies — Lippert Tile, DeanAlan, and the Lippert Group — lease office and warehouse space in the same building which is owned by the Lippert brothers. DeanAlan also rents trucks from, and orders its supplies through, Lippert Tile. The Lippert Group provides administrative services for the other two companies, maintaining business records, processing payroll, handling billing, and managing bank accounts. The Lippert Group also supplies both companies with office and warehouse staff, including salesmen and estimators, who decide which company will bid on a project and how much to bid. At the same time, the companies do not share space within the building and have separate lease arrangements (though with the same owners). They do not share equipment. They have different corporate officers, separate bank accounts, separate lines of credit, and separate insurance programs. And because the whole point of creating DeanAlan was to serve the non-union market with non-union labor, the companies naturally have separate employees and separate customers.

In 2010, the union director, Jeffrey Leckwee, discovered that DeanAlan had been created to perform non-union tile installation work in the same region, and filed a grievance against the three companies with the JAC. He alleged that this setup violated the CBA's assignment provision because it essentially assigned Lippert Tile's work to DeanAlan workers without giving DeanAlan workers the same union benefits. The companies argued as a threshold matter that the grievance was not arbitrable because DeanAlan and the Lippert Group were not parties to the CBA. The union responded that all three companies should essentially be considered a "single employer," i.e., that DeanAlan and the Lippert Group were the same entity as Lippert Tile, and that all three were therefore bound by the arbitrability provisions of the CBA. The companies also raised a host of procedural objections, including the fact that Leckwee himself sat on the six-member JAC, which allegedly biased the JAC against the companies. At no point, however, did the companies argue to the JAC that the dispute was not arbitrable because the non-union workers were not in the same bargaining unit as the union worker's covered by the CBA. Nor does any party suggest that they were not given ample opportunities to present arguments before the JAC.

In March 2011, the JAC upheld the grievance and adopted the union's requested decision and award. Without further explanation, the JAC found that "Lippert Tile, The Lippert Group and DeanAlan are a single employer and that the Agreement was violated by the failure of Lippert to apply the terms and conditions of the Agreement to DeanAlan." It did not say anything about whether the DeanAlan workers were in the same bargaining unit. It ordered that DeanAlan workers be made whole for work done since June 1, 2010, that the union be made whole for lost dues, and that union benefits be provided to DeanAlan workers from that point forward.

The companies together filed a petition with the federal district court to vacate the JAC award, and the union responded by asking the court to enforce it, in the form of a motion for summary judgment. The companies raised the same arguments they made before the JAC, except this time they argued for the first time that the dispute was not arbitrable by the JAC because the aggrieved DeanAlan workers were not part of the same bargaining unit as the union workers covered by the CBA. The district court granted the union's motion for summary judgment and ordered that the award be enforced. First, the court found that the only issue which it could decide de novo was the "single employer" issue, because that issue went to whether the dispute was properly subject to JAC arbitration under the CBA, and there was no "clear[] and unmistakabl[e]" agreement by the parties (e.g., nothing in the CBA suggesting) that only the JAC could make that threshold determination. On that issue, it agreed with the JAC that the companies were essentially a "single employer'" and so the dispute was arbitrable. Second, the court appeared to agree with the companies that the bargaining unit issue had to be resolved before the award could issue, but it did not view it as an arbitrability question. As a result, the court declined to decide it de novo, found that the JAC had implicitly decided that the DeanAlan workers were in the same bargaining unit as the union workers, and deferred to that decision because no decision from the National Labor Relations Board ("NLRB") ever suggested otherwise. Third, the court rejected the companies' argument that Leckwee's presence on the JAC invalidated the award, because all the CBA required was balanced employer-union representation and it was undisputed that the condition was met. Last, the court summarily rejected the companies' remaining procedural objections and arguments on the merits, according great deference to the JAC's resolution of those issues in the union's favor. The companies appealed.

II. ANALYSIS

Because this appeal challenges the district court's enforcement of a JAC award issued pursuant to a CBA, a brief review of our limited jurisdiction is in order. Section 301 of the Labor-Management Relations Act ("LMRA") provides for federal subject-matter jurisdiction over "[s]uits for violation of contracts between an employer and a labor organization" (such as collective bargaining agreements), "without respect to the amount in controversy or without regard to the citizenship of the parties...." 29 U.S.C. § 185(a). As the Supreme Court has explained, this provision provides federal courts jurisdiction to enforce "final and binding" arbitration awards issued pursuant to a CBA. Gen. Drivers v. Riss & Co., 372 U.S. 517, 519, 83 S.Ct. 789, 9 L.Ed.2d 918 (1963). However, given that Section 301 essentially limits the federal court's jurisdiction to applying the terms of a CBA, when a CBA provides for the submission of contractual disputes to an arbitrator, the court "is confined to ascertaining whether the party seeking arbitration is making a claim which on its face is governed by the contract." United Steelworkers v. Am. Mfg. Co., 363 U.S. 564, 568, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960). "[T]he judicial inquiry under s 301 must be strictly confined to the question whether the reluctant party did agree to arbitrate the grievance or did agree to give the arbitrator power to make the award he made." United Steelworkers v. Warrior & Gulf Nav. Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). In other words, "We are responsible only for the question of arbitrability." United Steel v. TriMas Corp., 531 F.3d 531, 535 (7th Cir. 2008). Consequently, "a court is not to rule on the potential merits of the underlying claims[,] ... even if it appears to the court to be frivolous." AT & T Techs., Inc. v. Commc'ns Workers of Am., 475 U.S. 643, 649-50, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986); see also TriMas Corp., 531 F.3d at 536 ("If the parties have in fact agreed to arbitrate their dispute, then they have bargained for the arbitrator's interpretation of their contract — not ours.").

A. Bargaining Unit Argument Waived Because Not Raised in Arbitration

The companies first argue that the dispute was not arbitrable under the CBA because no threshold finding had been made that the DeanAlan non-union workers were in the same bargaining unit as the Lippert Tile union workers. As they point out, other circuits have held that such a finding (in addition to the "single employer" finding, discussed separately infra) is a prerequisite for applying the CBA's arbitration provisions to non-contractual-party entities like DeanAlan and the Lippert Group. See So. Cal. Painters v. Rodin & Co., Inc., 558 F.3d 1028, 1034 (9th Cir.2009); Stardyne, Inc. v. NLRB, 41 F.3d 141, 152 n. 11 (3d Cir.1994); Amalgamated Lithographers v. Stearns & Beale, Inc., 812 F.2d 763, 769 (2d Cir. 1987); but cf. Moriarty v. Svec, 164 F.3d 323, 334 (7th Cir.1998) (rejecting this argument in ERISA context). The companies furthermore contend that only the NLRB may make such a bargaining-unit finding. See Local 334 v. Nor-Cal Plumbing, 48 F.3d 1465, 1470-71 (9th Cir.1994); but see Brown v. Sandimo Materials, 250 F.3d 120, 129 (2d Cir.2001); Trs. of Colo. Statewide Iron Workers v. A & P Steel, Inc., 812 F.2d 1518, 1526-27 (10th Cir.1987); Carpenters Local Union No. 1846 v. Pratt-Farnsworth, Inc., 690 F.2d 489, 514-17 (5th Cir.1982). The companies conclude that if the bargaining unit issue were appropriate for judicial determination, we should resolve it by concluding that the DeanAlan workers were not in the same bargaining unit as the union workers.

We agree with the union, however, that the companies waived all aspects of this bargaining unit argument, because they failed to raise it in any form before the JAC. "The failure to pose an available argument to the arbitrator waives that argument in collateral proceedings to enforce or vacate the arbitration award." Ganton Techs., Inc. v. UAW, 358 F.3d 459, 462 (7th Cir.2004). "Arbitration would not be an efficient and cost-effective method of resolving labor disputes if federal courts indulged late arguments that were not brought to the attention of the arbitrator below." Id.; see also Nat'l Wrecking Co. v. Teamsters Local 731, 990 F.2d 957, 960 (7th Cir.1993) ("Failure to present an issue before an arbitrator waives the issue in an enforcement proceeding."). The companies "cannot stand by during arbitration, withholding certain arguments, then, upon losing the arbitration, raise such arguments in federal court. We will not tolerate such sandbagging." Id.; see also United Food & Commercial Workers Local 100A v. John Hofmeister & Son, Inc., 950 F.2d 1340, 1344 (7th Cir.1991) ("If parties were allowed to withhold information during arbitration, and then use it to sandbag their opponents during enforcement proceedings, much of the efficiency and usefulness of arbitration would be lost."). There is also no suggestion that the companies had no opportunity to present such an argument, and indeed, they did not hesitate to present a host of other arbitrability and procedural arguments to the JAC.

This waiver rule applies equally to questions concerning arbitrability. See Environ. Barrier Co., LLC v. Slurry Sys., Inc., 540 F.3d 598, 607 (7th Cir.2008) ("[E]ven though the ordinary rule is that the question whether an agreement to arbitrate exists is one for the court, the right to a judicial determination of arbitrability is, like many rights, one that can be waived [in arbitration]." (citations omitted)). Of course, the companies insist that the bargaining unit issue can only be determined by the NLRB, not the JAC (or any other tribunal). But assuming this is true, the companies should have then asked the JAC to stay the proceedings pending an NLRB determination. If the stay were granted and the NLRB ruled in the companies' favor, the arbitration process would have ended without wasting time on other issues. At the very least, the companies could have reserved an objection to arbitrability on the bargaining unit issue, which might have caused the union to immediately go to the NLRB so that such a threshold issue could be efficiently resolved at the outset. See, e.g., id. at 606 ("There is not a hint in the record that SSI ever called this issue to the arbitrator's attention or sought to enjoin the arbitration on the ground that there was no agreement to arbitrate.... Anyone who wants to object to arbitrability is entitled to make her position known to the arbitrator and the other party; the other party may then, if it wishes, respond with a petition for an order to compel arbitration... and obtain a judicial determination on arbitrability."). For these reasons, we have repeatedly disapproved of the practice of remaining silent on an arbitrability issue during arbitration proceedings, only to play the arbitrability card in federal court after the party loses. See, e.g., Roughneck Concrete Drilling & Sawing Co. v. Plumbers' Pension Fund, 640 F.3d 761, 766-67 (7th Cir.2011) (criticizing this practice as a "heads I win, tails you lose" approach, and noting that a party "could have consented to have Judge Judy resolve the dispute, and would have been bound even though the collective bargaining agreement did not authorize her to resolve disputes"); Environ. Barrier Co., LLC, 540 F.3d at 606 ("Only after the arbitrator issued an award unfavorable to SSI and the case wound up in court did SSI raise an objection to the arbitrator's authority to decide the dispute.... This is not a tactic we can accept, for sound policy reasons. It is terribly wasteful of the arbitrator's time, the parties' time, and the court's time.... [K]eeping the arbitrability card close to the chest would allow a party like SSI to take a wait-and-see approach: if it had liked [the arbitrator's] decision, it would have remained silent, but since it did not, it is now complaining about arbitrability."); Slaney v. Int'l Amateur Athletic Fed'n, 244 F.3d 580, 591 (7th Cir. 2001) ("Slaney had the opportunity to show that she had never agreed to arbitrate the dispute when she was notified of the arbitration, but she let that opportunity pass. Slaney could not `sit back and allow the arbitration to go forward, and only after it was all done ... say: oh by the way, we never agreed to the arbitration clause. That is a tactic that the law of arbitration, with its commitment to speed, will not tolerate.'" (quoting Comprehensive Accounting Corp. v. Rudell, 760 F.2d 138, 140 (7th Cir.1985))); AGCO Corp. v. Anglin, 216 F.3d 589, 593 (7th Cir.2000) ("If a party willingly and without reservation allows an issue to be submitted to arbitration, he cannot await the outcome and then later argue that the arbitrator lacked authority to decide the matter."); Jones Dairy Farm v. Local No. P-1236, 760 F.2d 173, 175 (7th Cir.1985) ("[I]f a party voluntarily and unreservedly submits an issue to arbitration, he cannot later argue that the arbitrator had no authority to resolve it.").

Although the companies did at least bring the issue of arbitrability to the attention of the JAC on other grounds, unlike the parties in some of the cited cases who failed to raise the issue of arbitrability at all, we see no reason why the same efficiency considerations do not also apply when a party raises certain arbitrability issues before the arbitrator but not others. Cf. Ganton Techs., Inc., 358 F.3d at 462 (rejecting argument that "to preserve an argument for presentation in an enforcement proceeding, a party need only present the information that underlies the argument at the arbitration proceeding"). The JAC should have been given a meaningful opportunity to consider whether to hold off on an award pending an NLRB determination on the bargaining unit issue. So we disagree with the district court's suggestion that the JAC implicitly decided the issue; the JAC award made no mention of it. The companies did not give the JAC that opportunity, and we find the bargaining unit issue waived.

B. Dispute Arbitrable Because Companies Were "Single Employer"

Second, the companies challenge the district court's finding that the dispute was arbitrable because all three companies should be considered a "single employer," thereby binding DeanAlan and the Lippert Group to the CBA's arbitrability provisions even though they were not signatories to the CBA. Given that arbitrability is essentially a question of contract interpretation, we review the district court's determination of arbitrability de novo. Int'l Bhd. of Elec. Workers, Local 21 v. Ill. Bell Tel. Co., 491 F.3d 685, 687 (7th Cir.2007).

"The single employer doctrine holds that when two entities are sufficiently integrated, they will be treated as a single entity for certain purposes." Moriarty, 164 F.3d at 332. "To determine whether two nominally separate business entities are a single employer, one must examine four factors set out by the Supreme Court: (1) interrelation of operations, (2) common management, (3) centralized control of labor relations, and (4) common ownership." Trs. of Pension, Welfare, and Vacation Fringe Benefit Funds of IBEW Local 701 v. Favia Elec. Co., Inc., 995 F.2d 785, 788 (7th Cir.1993) (citing South Prairie Constr. Co. v. Local No. 627, 425 U.S. 800, 803, 96 S.Ct. 1842, 48 L.Ed.2d 382 (1976)). "No one of these factors is conclusive; instead, the decision-maker must weigh the totality of the circumstances." Id. "`Ultimately, single employer status ... is characterized by the absence of an arm's length relationship found among unintegrated companies.'" Lihli Fashions Corp., Inc. v. NLRB, 80 F.3d 743, 747 (2d Cir.1996) (citation omitted).

For essentially the same reasons set forth by the district court, we conclude that the three companies are a "single employer" for purposes of enforcing the arbitration provisions of the CBA. First, we agree with the companies that when analyzing the interrelation of operations, it is the "day-to-day operational matters" that are the most relevant. Yet it is for that very reason that this factor cuts against them. The same entity, the Lippert Group, maintains business records, processes payroll, handles billing, and manages bank accounts for both companies, and these shared, daily operations are critical to the smooth functioning of the project-by-project nature of both companies' work. More importantly, the Lippert Group personnel make the critical decision whether Lippert Tile or DeanAlan should make a bid on a particular project, and if so, what to bid, as if all three companies were part of the same organizational chart. The companies do not share the exact same space but are housed in the same warehouse, making shared supervision of both companies easier. The companies like to emphasize that they had different tile installers serving different markets, but they still served the same geographic area and performed the exact same labor. So on balance we find the operations to be extensively interrelated if not intertwined.

Second, though Lippert Tile and DeanAlan technically have different corporate officers, the "common management" factor looks at "actual or active control, as distinguished from potential control, over the other's day-to-day operations," Cimato Brothers, Inc., 352 NLRB 797, 799 (2008), and certainly not formal job titles. See, e.g., id. (disregarding fact that someone was "president" when he had no actual management responsibility). Because the same entity not only operates, but also controls, the bidding process and administrative tasks for both companies, the "common management" factor weighs in favor of a single employer finding. To the extent that any actual managerial functions are being performed separately, the companies do not point us to any examples. Third, the companies do not dispute that there was common ownership.

As for the last factor, we find that there was centralized control of labor relations because it was the Lippert brothers' decision in the first place to create a new company that would give room to a new, non-union labor system solely to serve the non-union market. See, e.g., Local 343, 48 F.3d at 1471. So while it is not entirely clear who was responsible for day-to-day labor relations decisions like setting wages (for the non-union workers), hiring, or firing, the overall parameters were set in place by the Lippert brothers when they decided to create separate union and non-union entities. The companies' only argument on this factor is that centralized control of labor relations is not present when one of the companies has no employees, citing Cimato Brothers, 352 NLRB at 799 ("Centralized control of labor relations is not present here because Cimato 1 had no statutory employees during the relevant time period."), and they point out that DeanAlan technically did not have employees, only subcontractors. But we do not see how Cimato Brothers helps them, because it goes on to say that this factor "is given less weight where, as in this case, one of the companies has no employees." Id. at 799 n. 9. So even if this factor favors the companies, it only does so slightly and does not overcome the other factors which favor the union.

In sum, we agree with the district court's conclusion that, "for all practical purposes, the Companies function as a single entity." While the distinction between the "union" and "nonunion" market is useful, the bottom line reason Lippert Group and DeanAlan were created was to increase the Lippert brothers' share of the tile installation market in the four-county Greater Milwaukee area by providing the same service at lower prices, just as any single company might attempt to capture a greater share of the market by reducing prices. Of course, we express no opinion whatsoever on whether this type of double-breasting practice was a violation of the CBA, because that was a merits determination by the JAC. And we certainly express no opinion as to whether this practice is good or bad. But solely for purposes of deciding whether the JAC had the power to decide whether their double-breasting practice was a violation of the CBA and issue a binding arbitration award, we find, under the "single employer" doctrine, that it did.

C. Leckwee's Presence on JAC Did Not Violate CBA

Last, the companies argue that the award should be vacated because Leckwee, the individual who filed the union grievance, sat on the same JAC that decided the grievance. They contend that in reviewing arbitration awards pursuant to the jurisdictional grant of Section 301 of the LMRA, federal courts are permitted to review awards for fundamental fairness. See, e.g., Carpenters 46 N. Cal. Counties Conf. Bd. v. Zcon Builders, 96 F.3d 410, 413 (9th Cir.1996). And they suggest that we should review labor arbitration awards for "evident partiality" just as we do in our review of arbitration awards under the Federal Arbitration Act ("FAA"). But we already explored at length, and rejected, this type of argument in Merryman Excavation, Inc. v. International Union of Operating Engineers, Local 150, 639 F.3d 286, 289-93 (7th Cir.2011).

Review of labor arbitration awards under Section 301 of the LMRA is different from the review of arbitration awards under the FAA, even if they resemble each other in some respects. See Merryman, 639 F.3d at 290 ("A failure to comply with a joint committee award is a breach of a federal labor contract subject to section 301 jurisdiction — not an FAA action."). Unlike in the FAA, see 9 U.S.C. § 10(a)(2) ("evident partiality" standard), "evident partiality" is not inherently built into the Section 301 review mechanism. See Merryman, 639 F.3d at 292-93. We, of course, agree with the companies that labor arbitration awards are subject to Section 301 review (a basic proposition to which their brief devotes several pages). The question is what that review includes, and Section 301 review simply does not include a free-floating procedural fairness standard absent a showing that some provision of the CBA was violated. See 29 U.S.C. § 185(a) (providing federal subject-matter jurisdiction over "[s]uits for violation of contracts between an employer and a labor organization").

And we do not find any such violation of the CBA. To the extent the CBA sought to deal with potential bias, all it required was that the panel consist of three employer representatives and three union representatives. So long as this equal representation requirement is met, nothing in the CBA prohibited the filer of a grievance from sitting on the JAC. See, e.g., Merryman, 639 F.3d at 292 ("Merryman agreed that disputes would be resolved in the first instance not by a neutral arbitrator but by a committee composed of an equal number of employer and union representatives. The agreement does not require the representatives on the joint committee to act like detached magistrates or neutral arbitrators. Rather, we rely on the balanced voting membership of the joint committee to provide fairness to the interested parties."). It is undisputed that the JAC consisted of three employer representatives and three union representatives (one of which was Leckwee). That resolves any argument concerning representation. See, e.g., id. at 292-93 (rejecting bias argument simply because the contract's equal representation requirement was met).

We acknowledge that it might seem unusual (at least to those outside the world of labor arbitration) to allow the filer of the grievance to sit on the panel that adjudicates it. If so, it is up to negotiating parties to make sure that a CBA prohibits it. Cf. Baravati v. Josephthal, Lyon & Ross, Inc., 28 F.3d 704, 709 (7th Cir.1994) ("Indeed, short of authorizing trial by battle or ordeal or, more doubtfully, by a panel of three monkeys, parties can stipulate to whatever procedures they want to govern the arbitration of their disputes; parties are as free to specify idiosyncratic terms of arbitration as they are to specify any other terms in their contract."). It is not for the courts to rewrite contracts.

III. CONCLUSION

For the above-stated reasons, we AFFIRM.